HMH Go Math

Redefine your true self with the Go Math Answer Key for Grade 5 curated by subject experts. Score higher grades in your exams and refer to Go Math Grade 5 Answer Key Chapter 9 Algebra: Patterns and Graphing to have strong command over fundamentals. Download the HMH Go Math 5th Grade Solution Key Chapter 9 free of cost and kick start your preparation immediately.

Go Math Grade 5 Answer Key Chapter 9 Algebra: Patterns and Graphing

You will get the necessary skillset needed to draw the line plots and graphs from 5th Grade Go Math Answer Key Ch 9. Access Detailed Solutions to all the problems and learn how to solve related problems when you encounter them during your exams. Seek Homework Help needed by accessing the Go Math Grade 5 Solution Key Chapter 9 Patterns and Graphing. Cross Check the Solutions from our Go Math Grade 5 Answer Key Algebra: Patterns and Graphing and understand the areas you are facing difficulty.

Lesson 1: Line Plot

• Share and Show – Page No. 371
• UNLOCK the Problem – Page No. 372

Lesson 2: Ordered Pairs

• Share and Show – Page No. 375
• Problem Solving – Page No. 376

Lesson 3: Investigate • Graph Data

• Share and Show – Page No. 379
• Problem Solving – Page No. 380

Lesson 4: Line Graphs

• Share and Show – Page No. 383
• Connect to science – Page No. 384

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 385
• Mid-Chapter Checkpoint – Page No. 386

Lesson 5: Numerical Patterns

• Share and Show – Page No. 389
• Problem Solving – Page No. 390

Lesson 6: Problem Solving • Find a Rule

• Share and Show – Page No. 393
• On Your Own – Page No. 394

Lesson 7: Graph and Analyze Relationships

• Share and Show – Page No. 397
• Problem Solving – Page No. 398

Chapter 9 Review/Test

• Chapter Review/Test – Page No. 399
• Chapter Review/Test – Page No. 400
• Chapter Review/Test – Page No. 401
• Chapter Review/Test – Page No. 402

Share and Show – Page No. 371

Use the data to complete the line plot. Then answer the questions.

Lilly needs to buy beads for a necklace. The beads are sold by mass. She sketches a design to determine what beads are needed and then writes down their sizes. The sizes are shown below.

\(\frac{2}{5} g, \frac{2}{5} g, \frac{4}{5} g, \frac{2}{5} g, \frac{1}{5} g, \frac{1}{5} g, \frac{3}{5} g, \frac{4}{5} g, \frac{1}{5} g, \frac{2}{5} g, \frac{3}{5} g, \frac{3}{5} g, \frac{2}{5} g\)
Think: There are ___ Xs above \(\frac{1}{5}\) on the line plot, so the combined mass of the beads is _____ fifths, or _____ gram.

Question 1.
What is the combined mass of the beads with a mass of 1/5 gram?
\(\frac{□}{□}\) grams

Answer: \(\frac{3}{5}\) grams

Explanation:
For first we will count the number of \(\frac{1}{5}\) grams for each amount. Draw an x for the number of times each amount is recorded to complete the line plot.
There are 3 xs above \(\frac{1}{5}\) on the line plot, so the combined mass of the beads is 3 fifths
3 × \(\frac{1}{5}\) = 3/5 gram.

Question 2.
What is the combined mass of all the beads with a mass of \(\frac{2}{5}\) gram?
_____ grams

Answer: 2

Explanation:
For first we will count the number of \(\frac{2}{5}\) grams for each amount. Draw an x for the number of times each amount is recorded to complete the line plot.
There are 5 xs above \(\frac{2}{5}\) on the line plot, so the combined mass of the beads is 5 two fifths.
5 × \(\frac{2}{5}\) = 2 grams

Question 3.
What is the combined mass of all the beads on the necklace?
_____ grams

Answer: 6

Explanation:
Total mass of all the beads on the necklace is \(\frac{3}{5}\) + 2 + \(\frac{8}{5}\) + \(\frac{9}{5}\) = \(\frac{30}{5}\) = 6
Therefore the combined mass of all the beads on the necklace is 6.

On Your Own

Use the data to complete the line plot. Then answer the questions.

A breakfast chef used different amounts of milk when making pancakes, depending on the number of pancakes ordered. The results are shown below.
\(\frac{1}{2} c, \frac{1}{4} c, \frac{1}{2} c, \frac{3}{4} c, \frac{1}{2} c, \frac{3}{4} c, \frac{1}{2} c, \frac{1}{4} c, \frac{1}{2} c, \frac{1}{2} c\)

Question 5.
How much milk combined is used in \(\frac{1}{4}\)-cup amounts?
\(\frac{□}{□}\) cup

Answer: \(\frac{1}{2}\) cup

Explanation:
For first we will count the number of \(\frac{1}{4}\) cups for each amount.
2 × \(\frac{1}{4}\) = \(\frac{1}{2}\)

Question 6.
How much milk combined is used in \(\frac{1}{2}\)-cup amounts?
______ cups

Answer: 3 cups

Explanation:
For first we will count the number of \(\frac{1}{2}\) cups for each amount.
There are 6 \(\frac{1}{2}\) cups
6 × \(\frac{1}{2}\) = 3 cups

Question 8.
How much milk is used in all the orders of pancakes?
_____ cups

Answer: 5 cups

Explanation:
\(\frac{1}{2} c\) + [/latex]\frac{1}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] +[/latex]\frac{1}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] + [/latex]\frac{1}{2} c[/latex]
= 3 + [/latex]\frac{1}{4} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{1}{4} c[/latex]
= 3 + 1 + 1 = 5cups
Therefore 5 cups of milk is used in all the orders of pancakes.

Question 9.
What is the average amount of milk used for an order of pancakes?
\(\frac{□}{□}\) cup of milk

Answer: \(\frac{1}{2}\) cup of milk

Explanation:
There are 6 \(\frac{1}{2}\) cups of milk.
The average amount of milk used for an order of pancakes is \(\frac{1}{2}\) cup.

Question 10.
Describe an amount you could add to the data that would make the average increase.
Type below:
_________

Answer: \(\frac{3}{4}\) cup
We can add \(\frac{3}{4}\) to the data to increase the average amount of milk.

UNLOCK the Problem – Page No. 372

Question 11.
For 10 straight days, Samantha measured the amount of food that her cat Dewey ate, recording the results, which are shown below. Graph the results on the line plot. What is the average amount of cat food that Dewey ate daily?

\(\frac{1}{2} c, \frac{3}{8} c, \frac{5}{8} c, \frac{1}{2} c, \frac{5}{8} c, \frac{1}{4} c, \frac{3}{4} c, \frac{1}{4} c, \frac{1}{2} c, \frac{5}{8} c\)
a. What do you need to know?
Type below:
_________

Answer: I need to know the average amount of cat food that Dewey ate daily.

Question 11.
b. How can you use a line plot to organize the information?

Type below:
_________

Answer:

We can draw the line plot by using the given information.

Question 11.
c. What steps could you use to find the average amount of food that Dewey ate daily?
Type below:
_________

Answer: \(\frac{1}{2}\) cup

Explanation:
Number of days = 10
1/4 + 1/4 + 3/8 + 1/2 + 1/2 + 1/2 + 5/8 + 5/8 + 5/8 + 3/4 = 1 + 1 + 1/4 + 3/8 + 1/2 + 15/8
2 + 18/8 + 3/4 = 2 + 3 = 5
The average amount of food is 5 ÷ 10 = 5/10 = \(\frac{1}{2}\) cup

Question 11.
d. Fill in the blanks for the totals of each amount measured.
\(\frac{1}{4}\) cup: __________
\(\frac{3}{8}\) cup: __________
\(\frac{1}{2}\) cup: __________
\(\frac{5}{8}\) cup: __________
\(\frac{3}{4}\) cup: __________
Type below:
_________

Answer:
There are 2 xs above \(\frac{1}{4}\) cup: 2
There is 1 x above \(\frac{3}{8}\) cup: 1
There are 3 xs above \(\frac{1}{2}\) cup: 3
There are 3 xs above \(\frac{5}{8}\) cup: 3
There is 1 x above \(\frac{3}{4}\) cup: 1

Question 11.
e. Find the total amount of cat food eaten over 10 days.
_____ + _____ + _____ + _____ + _____ = _____
So, the average amount of food Dewey ate daily was ______.
Type below:
_________

Answer:
Number of days = 10
1/4 + 1/4 + 3/8 + 1/2 + 1/2 + 1/2 + 5/8 + 5/8 + 5/8 + 3/4 = 1 + 1 + 1/4 + 3/8 + 1/2 + 15/8
2 + 18/8 + 3/4 = 2 + 3 = 5 cups

Question 12.
Test Prep How many days did Dewey eat the least amount of cat food?
Options:
a. 1 day
b. 2 day
c. 3 day
d. 4 day

Answer: 1 day
By seeing the above line plot we can say that Dewey eats the least amount of cat food on day 1.
Thus the correct answer is option A.

Share and Show – Page No. 375

Use Coordinate Grid A to write an ordered pair for the given point.

Question 1.
C( _____ , _____ )

Answer: 6, 3

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for C is (6, 3).

Question 2.
D( _____ , _____ )

Answer: 3, 0

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
Thus the ordered pair for D is (3, 0)

Question 3.
E( _____ , _____ )

Answer: 9, 9

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
Thus the ordered pair for E (9, 9)

Question 4.
F( _____ , _____ )

Answer: 10, 5

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
Thus the ordered pair for F is (10, 5)

Plot and label the points on Coordinate Grid A.

Question 5.
M (0, 9)
Type below:
_________

Answer:

Question 6.
H (8, 6)
Type below:
_________

Answer:

Question 7.
K (10, 4)
Type below:
_________

Answer:

Question 8.
T (4, 5)
Type below:
_________

Answer:

Question 9.
W (5, 10)
Type below:
_________

Answer:

Question 10.
R (1, 3)
Type below:
_________

Answer:

On Your Own

Use Coordinate Grid B to write an ordered pair for the given point.

Question 11.
G( _____ , _____ )

Answer: 6, 4

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for G is (6, 4)

Question 12.
H( _____ , _____ )

Answer: 4, 9

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for H is (4, 9)

Question 13.
I( _____ , _____ )

Answer: 0, 7

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for I is (0, 7)

Question 14.
J( _____ , _____ )

Answer: 9, 5

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for J is (9, 5)

Question 15.
K( _____ , _____ )

Answer: 3, 3

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for K is (3, 3)

Question 16.
L( _____ , _____ )

Answer: 5, 2

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for L is (5, 2)

Question 17.
M( _____ , _____ )

Answer: 1, 1

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for M is (1, 1)

Question 18.
N( _____ , _____ )

Answer: 2, 5

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for N is (2, 5)

Question 19.
O( _____ , _____ )

Answer: 7, 8

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for O is (7, 8)

Question 20.
P( _____ , _____ )

Answer: 10, 10

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for P is (10, 10)

Plot and label the points on Coordinate Grid B.

Question 21.
W (8, 2)

Answer:

Question 22.
E (0, 4)

Answer:

Question 23.
X (2, 9)

Answer:

Question 24.
B (3, 4)

Answer:

Question 25.
R (4, 0)

Answer:

Question 26.
F (7, 6)

Answer:

Question 27.
T (5, 7)

Answer:

Question 28.
A (7, 1)

Answer:

Question 29.
S (10, 8)

Answer:

Question 30.
Y (1, 6)

Answer:

Question 31.
Q (3, 8)

Answer:

Question 32.
V (3, 1)

Answer:

Problem Solving – Page No. 376

Nathan and his friends are planning a trip to New York City. Use the map for 33–38. Each unit represents 1 city block.

Question 33.
What ordered pair gives the location of Bryant Park?
( _____ , _____ )

Answer: 4, 8

Question 34.
What’s the Error? Nathan says that Madison Square Garden is located at (0, 3) on the map. Is his ordered pair correct? Explain.
Type below:
__________

Answer: He needs to put point 3 on Y-axis but he placed on X-Axis.

Question 35.
The Empire State Building is located 5 blocks right and 1 block up from (0, 0). Write the ordered pair for this location. Plot and label a point for the Empire State Building.
Type below:
__________

Answer: 5, 1

Question 36.
Paulo walks from point B to Bryant Park. Raul walks from point B to Madison Square Garden. If they only walk along the grid lines, who walks farther? Explain.
__________

Answer: Paulo
By seeing the above graph we can say that Paulo walks farther along the grid lines.

Question 37.
Explain how to find the distance between Bryant Park and a hot dog stand at the point (4, 2).
_____ city blocks

Answer: 6

Question 38.
Test Prep Use the map above. Suppose a pizzeria is located at point B. What ordered pair describes this point?
Options:
a. (4,2)
b. (3,4)
c. (2,4)
d. (4,4)

Answer: (2,4)

Share and Show – Page No. 379

Graph the data on the coordinate grid.

Question 1.
a. Write the ordered pairs for each point.
Type below:
__________

Answer: A(1, 30), B (2, 35), C (3, 38), D (4, 41), E (5, 44)

Question 1.
b. What does the ordered pair (3, 38) tell you about Ryan’s age and height?
Type below:
__________

Answer: The ordered pair tells that their age of Ryan is 3 and their height is 38 inches.

Question 1.
c. Why would points (6, 42) be nonsense?
Type below:
__________

Answer: The point (6, 42) be nonsense because the height will be increased. In the above-ordered pair the height is decreased. So, the statement is nonsense.

Question 2.
a. Write the ordered pairs for each point.
Type below:
__________

Answer: We can write the ordered pairs by using the above table Day is the x-axis and height is the y-axis. The coordinates are A (5,1), B (10,3), C (15, 8), D (20,12), E (25,16), F(30,19).

Question 2.
b. How would the ordered pairs be different if the heights of the plants were measured every 6 days for 30 days instead of every 5 days?

Answer:
If the heights of the plants were measured every 6 days for 30 days instead of every 5 days the coordinates will be A (6,1), B (12,3), C (18, 8), D (24,12), E (30,16)

Problem Solving – Page No. 380

What’s the Error?

Question 3.
Mary places a miniature car onto a track with launchers. The speed of the car is recorded every foot. Some of the data is shown in the table. Mary graphs the data on the coordinate grid below.

Look at Mary’s graphed data.
Find her error.


Graph the data and correct
the error.

• Describe the error Mary made.
Type below:
__________

Answer:

Graph the data and correct the error

Share and Show – Page No. 383

Use the table at the right for 1–3.

Question 1.
What scale and intervals would be appropriate to make a graph of the data?
Type below:
__________

Answer:
Scale is 1 cm = 10°F
Months will be on the x-axis.
The temperature will be on the y-axis.

Question 2.
Write the related pairs as ordered pairs.
Type below:
__________

Answer: The related pairs are A (Jan, 40), B (Feb, 44), C (Mar, 54), D (Apr, 62), E (May, 70)

Question 3.
Make a line graph of the data.
Type below:
__________

On Your Own

Use the table at the right for 5–7.

Question 5.
Write the related number pairs for the plant height as ordered pairs.
Type below:
__________

Answer: The related number pairs of the above table are A (1, 20), B(2, 25), C (3, 29), D (4, 32)

Question 6.
What scale and intervals would be appropriate to make a graph of the data?
Type below:
__________

Answer: The above table says that the X-Axis is Month and Y-Axis is Height in inches.
Scale is 1 cm = 5 inches.

Explanation:
The horizontal axis could represent months from 1 to 4. In this case, the scale interval is one month.
The vertical axis could represent height from 20 inches to 32 inches but we can show a break in the scale between 1 inch and 16 inches since there are no heights between 0 inches and 20 inches, the scale interval is 1 inch.

Question 7.
Make a line graph of the data.
Type below:
__________

Question 8.
Use the graph to find the difference in height between Month 1 and Month 2.
Type below:
__________

Answer: By observing the above graph we can say that the difference between months 1 and 2 is 5 inches.
25 – 20 = 5 inches
From the graph we can see that the plant grew the most between 1 and 2 months (about 5 inches), the least change is between 3 and 4 months (about 3 inches).

Question 9.
Use the graph to estimate the height at 1 \(\frac{1}{2}\) months.
_____ in.

Answer: The estimated height at 1 \(\frac{1}{2}\) months is 22.5 inches.
The average of month 1 and month 2 is (20 + 25) ÷ 2 = 45/2 = 22.5 inches.

Connect to science – Page No. 384

Evaporation changes water on Earth’s surface into water vapor. Water vapor condenses in the atmosphere and returns to the surface as precipitation. This process is called the water cycle. The ocean is an important part of this cycle. It influences the average temperature and precipitation of a place.

The overlay graph below uses two vertical scales to show monthly average precipitation and temperatures for Redding, California.

Use the graph for 10–13.

Question 10.
About how much precipitation falls in Redding, California, in February?
_____ inches

Answer: From the graph, we can see that the precipitation in February is 4.2 inches.

Question 11.
What is the average temperature for Redding, California, in February?
_____ °F

Answer: From the graph, we can see that the temperature in February is 50°F.

Question 12.
Explain how the overlay graph helps you relate precipitation and temperature for each month.
Type below:
__________

Answer: The average temperature for each month is plotted on the graph with the blue line and the red bar graph represents the precipitation. As the temperature increases the precipitation decreases.

Question 13.
Describe how the average temperature changes in the first 5 months of the year.
Type below:
__________

Answer: From the graph, we can see that the temperature in the first 5 months of the year but the amount of precipitation is decreasing. It’s logical because when the temperature is increasing the amount of precipitation is decreasing.

Question 14.
Test Prep Which day had an increase of 3 feet of snow from the previous day?

Options:
a. Day 2
b. Day 3
c. Day 5
d. Day 6

Answer: Day 5

Explanation:
By seeing the above graph we can say that the snow level has increased 3 feet from day 4 to Day 5.
Thus the correct answer is option C.

Mid-Chapter Checkpoint – Vocabulary – Page No. 385

Choose the best term from the box.

Question 1.
The ______ is the horizontal number line on the coordinate grid.
__________

Answer: X-Axis
The X-Axis is the horizontal number line on the coordinate grid.

Question 2.
A ______ is a graph that uses line segments to show how data changes over time.
__________

Answer: Line graph
A Line graph is a graph that uses line segments to show how data changes over time.

Concepts and Skills

Use the line plot at the right for 3–5.

Question 3.
How many kittens weigh at least \(\frac{3}{8}\) of a pound?
______ kittens

Answer: 9

Explanation:
The line plot shows that there are 4 xs above \(\frac{3}{8}\), 3 xs above \(\frac{1}{2}\) and 2 xs on \(\frac{5}{8}\).
To find the kittens weigh at least \(\frac{3}{8}\) we need to add all above \(\frac{3}{8}\)
= 4 + 3 + 2 = 9

Use the coordinate grid at the right for 6–13.

Write an ordered pair for the given point.

Question 6.
A( ______ , ______ )

Answer: 1, 6
The ordered pair for A is (1,6)

Question 7.
B( ______ , ______ )

Answer: 2, 2
The ordered pair for B is (2, 2)

Question 8.
C( ______ , ______ )

Answer: 4, 4
The ordered pair for C is (4, 4)

Question 9.
D( ______ , ______ )

Answer: 0, 3
The ordered pair for D is (0, 3)

Plot and label the point on the coordinate grid.

Question 10.
E(6, 2)
Type below:
__________

Answer:

Question 11.
F(5, 0)
Type below:
__________

Answer:

Question 12.
G(3, 4)
Type below:
__________

Answer:

Question 13.
H(3, 1)
Type below:
__________

Answer:

Mid-Chapter Checkpoint – Page No. 386

Question 14.
Jane drew a point that was 1 unit to the right of the y-axis and 7 units above the x-axis. What is the ordered pair for this location?
( ______ , ______ )

Answer: (1, 7)
The ordered pair for the location is (1, 7).

Question 15.
The graph below shows the amount of snowfall in a 6-hour period.

Between which hours did the least amount of snowfall?
between hour ______ and hour ______

Answer: From the graph, we can see that the least amount of snowfall between 2 hours and 4 hours, 0 inches.

Question 16.
Joy recorded the distances she walked each day for five days. How far did she walk in 5 days?

______ \(\frac{□}{□}\) miles

Answer: 2 \(\frac{1}{6}\) miles

Explanation:
There are 3 xs above \(\frac{1}{3}\) = 3 × \(\frac{1}{3}\) = 1
There are 1 x above \(\frac{1}{2}\) = 1 × \(\frac{1}{2}\) = \(\frac{1}{2}\)
There is 1 x above \(\frac{2}{3}\) = 1 × \(\frac{2}{3}\) = \(\frac{2}{3}\)
1 + \(\frac{2}{3}\) + \(\frac{1}{2}\) = (6 + 3 + 4)/6 = 13/6
The mixed fraction of 13/6 is 2 \(\frac{1}{6}\) miles
Thus she walked 2 \(\frac{1}{6}\) miles in 5 days.

Share and Show – Page No. 389

Use the given rules to complete each sequence. Then, complete the rule that describes how nickels are related to dimes.

Question 1.

Type below:
__________

Answer: The number of Dimes is 2 times the number of Nickels.
We need to add 5 to Nickels = 5 + 5 + 5 + 5 + 5 = 25
We need to add 10 to Dimes = 10 + 10 + 10 + 10 + 10 = 50

Complete the rule that describes how one sequence is related to the other. Use the rule to find the unknown term.

Question 2.
Multiply the number of books by ______ to find the amount spent.

______
Explain:
__________

Answer: The amount spent is 4 times the number of books so we multiply the number of books by 4 to find the amount spent.
Multiply 4 to the amount spent = 24 × 4 = 96

Question 3.
Divide the weight of the bag by _____ to find the number of marbles.

______
Explain:
__________

Answer: The weight of Bag is 3 times the number of marbles So, we divide the weight of Bag by 3 to find the number of marbles.
Divide 360 by 3
360/3 = 120

On Your Own

Complete the rule that describes how one sequence is related to the other. Use the rule to find the unknown term.

Question 4.
Multiply the number of eggs by _______ to find the number of muffins.

Type below:
__________

Answer: The muffins is 6 times the number of eggs so we multiply the number of eggs by 6 to find the muffins.
The unknown term in the table we will find when multiply 18 by 6.
18 × 6 = 108
The unknown term is 108.

Question 5.
Divide the number of meters by _______ to find the number of laps.

Type below:
__________

Answer: The number of meters is 400 times the number of laps so we divide the number of meters by 400 to find the number of laps.
The unknown term in the table we will find when divide 6400 by 400.
6400 ÷ 400 = 16
The unknown term is 16.

Question 6.
Suppose the number of eggs used in Exercise 4 is changed to 3 eggs for each batch of 12 muffins, and 48 eggs are used. How many batches and how many muffins will be made?
______ batches
______ muffins

Answer: 16 batches 192 muffins will be made.

Explanation:
If we change to 3 eggs for each batch of 12 muffins and 48 eggs are used we will have 16 batches.
16 × 3 = 48
The muffins are 4 times the number of eggs so we multiply the number of eggs by 4 to fins the number of muffins.
If the number of batches is 16 and there are 48 eggs to find the number of muffins we will multiply the number of eggs 48 with 4:
48 × 4 = 192
192 muffins will be made.

Problem Solving – Page No. 390

Question 9.
In the cafeteria, tables are arranged in groups of 4, with each table seating 8 students. How many students can sit at 10 groups of tables? Write the rule you used to find the number of students.
______ students

Answer: 320 students

Explanation:
Tables are arranged in groups of 4, with each table seating 8 students, so in one group sit
4 × 8 = 32 students
To find how many students can sit at 10 groups of tables, we will find when multiplying 32 students with 10.
32 × 10 = 320
Finally, 320 students can sit at 10 groups of tables. The rule which we used to find the number of students is to multiply by 32 which is marked is a solution.

Question 10.
Test Prep What is the unknown number in Sequence 2 in the chart? What rule could you write that relates Sequence 1 to Sequence 2?

Options:
a. 70; Multiply by 2.
b. 100; Add 25.
c. 105; Multiply by 3.
d. 150; Add 150.

Answer: 105; Multiply by 3.

Explanation:
The unknown number in Sequence number 7 we will get when multiply 35 with 3 because the rule that releases the number of miles to the number of runners is multiplying by 3.
The unknown number is: 35 × 3 = 105
Thus the correct answer is option C.

Share and Show – Page No. 393

Question 1.
Max builds rail fences. For one style of fence, each section uses 3 vertical fence posts and 6 horizontal rails. How many posts and rails does he need for a fence that will be 9 sections long?



First, think about what the problem is asking and what you know. As each section of fence is added, how does the number of posts and the number of rails change?

Next, make a table and look for a pattern. Use what you know about 1, 2, and 3 sections. Write a rule for the number of posts and rails needed for 9 sections
of fence.

Possible rule for posts: _____________
Possible rule for rails: ______________
Finally, use the rule to solve the problem.
Type below:
__________

Answer:
Possible rule for posts: 27
Possible rule for rails: 54

Explanation:
The number of posts is 3 times the number of sections. So, we multiply the number of posts by 3.
With using the rule the unknown number is 9 × 3 = 27
Thus the possible rule for posts is 27.
Now multiply the number of rails by 2.
With using the rule the unknown number is 27 × 2 = 54
Thus the possible rule for rails is 54.

Question 2.
What if another style of rail fencing has 6 rails between each pair of posts? How many rails are needed for 9 sections of this fence?

Possible rule for rails: ____________________
______ rails

Answer: 108 rails

Explanation:
The number of posts is 3 times the number of sections. So, we multiply the number of posts by 3.
Using the rule the unknown number is 9 × 3 = 27
Thus the possible rule for posts is 27.
Now multiply the number of rails by 4.
Using the rule the unknown number is 27 × 4 = 108
Thus the possible rule for rails is 108.

Question 3.
Leslie is buying a coat on layaway for $135. She will pay $15 each week until the coat is paid for. How much will she have left to pay after 8 weeks?

$ ______

Answer: $15

Explanation:
Leslie is buying a coat on layaway for $135. She will pay $15 each week until the coat is paid for.
Multiply the number of weeks by 15.
15 × 8 = $120
Now subtract $120 from $135
= $135 – $120 = $15

On Your Own – Page No. 394

Question 4.
Jane works as a limousine driver. She earns $50 for every 2 hours that she works. How much does Jane earn in one week if she works 40 hours per week? Write a rule and complete the table.
Possible rule: _____________

$ ______

Answer: 1000

Explanation:
The possible rule for Hour Worked: We can see that the difference between terms is 2.
So, the rule which describes this is Add 2.
The possible rule for Jane’s Pay: We can see that the difference between terms is 50.
So, the rule which describes this is Add 50.
Jane’s Pay is 25 times the hours worked so, we will multiply the hours worked by 25 to find Jane’s Pay.
The unknown number Jane’s Pay we will find when multiplying 40 with 25:
40 × 25 = 1000
She earns 1000 dollars.

Question 5.
Rosa joins a paperback book club. Members pay $8 to buy 2 tokens, and can trade 2 tokens for 4 paperback books. Rosa buys 30 tokens and trades them for 60 paperback books. How much money does she spend? Write a rule and complete the table.
Possible rule: _______________

$ ______

Answer: 120

Explanation:
Possible rule for Tokens: We can see that the difference between terms is 8.
So, the rule which describes this is Add 8.
Possible rule for Games: We can see that the difference between terms is 4.
So, the rule which describes this is Add 4.
Tokens are 2 times the games so, we will divide the tokens by 2 to find how many games can she3 play.
The unknown number of games we will find when dividing 120 by 2:
120 ÷ 2 = 60
She can play 60 games for 120 tokens.

Question 7.
Test Prep Which expression could describe the next figure in the pattern, Figure 4?

Options:
a. 2 × 5
b. 2 + 4 + 4
c. 2 + 4 + 4 + 4
d. 16

Answer: 2 + 4 + 4 + 4

Explanation:
We can see that the difference between two consecutive figures is 4 squares.
So, the rule which describes this is Add 4.
Thus figure 4 has 14 squares.
Thus the correct answer is option C.

Share and Show – Page No. 397

Graph and label the related number pairs as ordered pairs.
Then complete and use the rule to find the unknown term.

Question 1.
Multiply the number of tablespoons by ___ to find its weight in ounces.


Type below:
_________

Answer: Multiply the number of tablespoons by 2 to find its weight in ounces.
5 × 2 = 10

Question 2.
Multiply the number of hours by ____ to find the distance in miles.


Type below:
_________

Answer: Multiply the number of hours by 3 to find the distance in miles.
4 × 3 = 12 miles

On Your Own

Graph and label the related number pairs as ordered pairs.
Then complete and use the rule to find the unknown term.

Question 3.
Multiply the number of inches by ____ to find the distance in miles.


Type below:
_________

Answer: Multiply the number of inches by 5 to find the distance in miles.
10 × 5 = 50

Question 4.
Multiply the number of centiliters by ____ to find the equivalent number of milliliters.

Answer:
Multiply the number of centiliters by 10 to find the equivalent number of milliliters.
5 × 10 = 50 milliliters

Problem Solving – Page No. 398

Sense or Nonsense?

Question 5.
Elsa solved the following problem.

Lou and George are making chili for the Annual Firefighter’s Ball. Lou uses 2 teaspoons of hot sauce for every 2 cups of chili that he makes, and George uses 3 teaspoons of the same hot sauce for every cup of chili in his recipe. Who has the hotter chili, George or Lou?

Write the related number pairs as ordered pairs and then graph them. Use the graph to compare who has the hotter chili, George or Lou.

Lou’s chili: (2, 2), (4, 4), (6, 6), (8, 8)
George’s chili: (1, 3), (2, 6), (3, 9), (4, 12)

Elsa said that George’s chili was hotter than Lou’s because the graph showed that the amount of hot sauce in George’s chili was always 3 times as great as the amount of hot sauce in Lou’s chili.

Does Elsa’s answer make sense, or is it nonsense?
Explain.

Answer: Elsa’s Answer makes sense.

Explanation:
Elsa’s answer makes sense because the amount of hot sauce in George’s chili was always 3 times as great as the amount of hot sauce in Lou’s chili. To prove this we will take two points from the graph which has an equal amount of cups of chili and compares the amount of hot sauce in George’s chili with the amount of hot sauce in Lou’s chili.
If we take 4 cups of George’s chili and Lou’s chili the amount of hot sauce in George’s chili is 12 teaspoons and the amount of hot sauce in Lou’s chili is 4 teaspoons.
12 is 3 times greater than 4 so Elsa’s answer makes sense.

Chapter Review/Test – Vocabulary – Page No. 399

Choose the best term from the box.

Question 1.
The __________ is the point where the x-axis and y-axis meet. Its __________ is 0, and its __________ is 0.
The ________ is the point where the x-axis and y-axis meet.
Its ________ is 0,
and its ________ is 0.

Answer:
The Origin is the point where the x-axis and y-axis meet.
Its x-coordinate is 0,
and its y-coordinate is 0.

Question 2.
A __________ uses line segments to show how data changes over time.

Answer: A line graph uses line segments to show how data changes over time.

Check Concepts

Use the table for 3–4.

Question 3.
Write related number pairs of data as ordered pairs.
Type below:
__________

Answer:
The ordered pair for week 1 is (1, 2)
The ordered pair for week 2 is (2, 6)
The ordered pair for week 3 is (3, 14)
The ordered pair for week 4 is (4, 16)

Question 4.
Make a line graph of the data.

Type below:
__________

Answer:

The ordered pair for week 1 is (1, 2)
The ordered pair for week 2 is (2, 6)
The ordered pair for week 3 is (3, 14)
The ordered pair for week 4 is (4, 16)

Complete the rule that describes how one sequence is related to the other. Use the rule to find the unknown term.

Question 5.
Multiply the number of eggs by ________ to find the number of cupcakes.

_______

Answer:
Multiply the number of eggs by 6 to find the number of cupcakes.
The unknown number in batches 6 we will get when multiply 18 with 6 because the rule that releases the number of eggs to the number of cupcakes is multiplying by 6.
The number of eggs is multiple of 3 and the number of cupcakes is multiple of 6.

Chapter Review/Test – Page No. 400

Fill in the bubble completely to show your answer.

Question 6.
The letters on the coordinate grid represent the locations of the first four holes on a golf course.

Which ordered pair describes the location of the hole labeled T?
Options:
a. (0, 7)
b. (1, 7)
c. (7, 0)
d. (7, 1)

Answer: (0, 7)
By seeing the above graph we can find the location of the hole label T i.e., (0, 7)

Use the line plot at the right for 7–8.

Question 7.
What is the average of the data in the line plot?
Options:
a. \(\frac{1}{2}\) pound
b. 1 pound
c. 6 pounds
d. 6 \(\frac{3}{4}\) pounds

Answer: 6 pounds

Explanation:
There are 3 xs above \(\frac{1}{2}\) pound = 3 × \(\frac{1}{2}\) = 3/2
There are 4 xs above \(\frac{2}{3}\) pound = 4 × \(\frac{2}{3}\) = 8/3
There is 1 x above \(\frac{5}{6}\) pound = 5/6
There are 2 xs above \(\frac{1}{6}\) = 2/6
There are 2 xs above \(\frac{1}{3}\) = 2/3
3/2 + 8/3 + 5/6 + 2/6 + 2/3 = 6 pounds
Thus the correct answer is option C.

Question 8.
How many bags of rice weigh at least \(\frac{1}{2}\) pound?
Options:
a. 2
b. 3
c. 5
d. 8

Answer: 8

Explanation:
By seeing the above line plot we can find the number of bags of rice weigh at least \(\frac{1}{2}\) pound
There are 3 xs above \(\frac{1}{2}\) pound = 3 × \(\frac{1}{2}\) = 3/2
There are 4 xs above \(\frac{2}{3}\) pound = 4 × \(\frac{2}{3}\) = 8/3
There is 1 x above \(\frac{5}{6}\) pound = 5/6
Total number of bags of rice weigh at least \(\frac{1}{2}\) pound = 3 + 4 + 1 = 8
Thus the correct answer is option D.

Chapter Review/Test – Page No. 401

Fill in the bubble completely to show your answer.

Use the table for 9–10.

Question 9.
Compare Tori’s and Martin’s savings. Which of the following statements is true?
Options:
a. Tori saves 4 times as much per week as Martin.
b. Tori will always have exactly $15 more in savings than Martin has.
c. Tori will save 15 times as much as Martin will.
d. On week 5, Martin will have $30 and Tori will have $90.

Answer: Tori saves 4 times as much per week as Martin.

Explanation:
By seeing the above table we can say that Tori saves 4 times as much per week as Martin.
Thus the correct answer is option A.

Question 10.
What rule could you use to find Tori’s savings after 10 weeks?
Options:
a. Add 10 from one week to the next.
b. Multiply the week by 2.
c. Multiply Martin’s savings by 4.
d. Divide Martin’s savings by 4.

Answer: Multiply Martin’s savings by 4.

Explanation:
We can find the savings of Tori by multiplying the savings of Martins by 4.
Thus the suitable statement is Multiply Martin’s savings by 4.
Therefore the correct answer is option C.

Question 11.
In an ordered pair, the x-coordinate represents the number of hexagons and the y-coordinate represents the total number of sides. If the x-coordinate is 7, what is the y-coordinate?
Options:
a. 6
b. 7
c. 13
d. 42

Answer: 6

Explanation:
Given that x-coordinate represents the number of hexagons.
Thus x-coordinate is 6.
And also given that the y-coordinate represents the number of sides.
The figure hexagon contains 6 sides.
So, the y-coordinate is 6.
Thus the ordered pair is (7, 6)
Therefore the correct answer is option A.

Question 12.
Point A is 2 units to the right and 4 units up from the origin. What ordered pair describes point A?
Options:
a. (2, 0)
b. (2, 4)
c. (4, 2)
d. (0, 4)

Answer: (2, 4)

Explanation:
Point A is 2 units to the right and 4 units up from the origin.
2 units will be located on the x-axis and 4 units will be on the y-axis.
Thus the ordered pair for point A is (2, 4)
Therefore the correct answer is option B.

Chapter Review/Test – Page No. 402

Constructed Response

Question 13.
Mr. Stevens drives 110 miles in 2 hours, 165 miles in 3 hours, and 220 miles in 4 hours. How many miles will he drive in 5 hours?
Explain how the number of hours he drives is related to the number of miles he drives.
_____ miles

Answer: 275 miles

Explanation:
Given that, Mr. Stevens drives 110 miles in 2 hours, 165 miles in 3 hours, and 220 miles in 4 hours.
We have to divide the number of miles by number of hours
That means, 110/2, 165/3, 220/4
the distance gone in 5 hours can be found with this equation
110/2 x ?/5
multiply 110 by 5 then divide the product by 2
110 × 5= 550
550/2 =275
Thus the answer is Mr. Stevens goes 275 miles in 5 hr.

Performance Task

Question 14.
Tim opens the freezer door and measures the temperature of the air inside. He continues to measure the temperature every 2 minutes, as the door stays open, and records the data in the table.

A). On the grid below, make a line graph showing the data in the table.

Type below:
__________

Question 14.
B). Use the graph to estimate the temperature at 7 minutes.
Estimate: _____ °F

Answer: By seeing the above graph we can say that the estimated temperature at 7 minutes is 15°F.

Question 14.
C). Write a question that can be answered by making a prediction. Then answer your question and explain how you made your prediction.
Type below:
__________

Question: Estimate the temperature at 5 minutes by using the graph.
Answer: By seeing the above table we can say that the estimated temperature at 5 minutes is 13°F

Conclusion

Fall in love with Maths by utilizing the Go Math 5th Standard 5 Answer Key. Make use of the Go Math Grade 5 Answer Key Chapter 9 Algebra: Patterns and Graphing as a reference for all your queries. Keep in touch with our site to avail updates on Class Specific Go Math Answer Key at your fingertips.

Get Chapter 10 Area of Parallelograms Go Math Grade 6 Answer Key from this page. Here you can know the formulas of the area of a parallelogram. In order to solve the problems first, you have to know what is parallelogram and how to calculate the area of a parallelogram. Download HMH Go Math Grade 6 Solution Key Area of Parallelograms pdf here.

Go Math Grade 6 Answer Key Chapter 10 Area of Parallelograms

Check out the topics covered in Chapter 10 Area of Parallelograms before you start practicing the problems. Area of Parallelograms includes topics like the area of triangles, Area of Trapezoids, Area of Regular Polygons, Composite Figures, etc. Practice the problems a number of times and enhance your math skills. After that solve the questions given in the mid-chapter checkpoint and review test. We have also provided the solutions of mid-chapter and review test here.

Lesson 1: Algebra • Area of Parallelograms

• Share and Show – Page No. 535
• Problem Solving + Applications – Page No. 536
• Area of Parallelograms – Page No. 537
• Lesson Check – Page No. 538

Lesson 2: Investigate • Explore Area of Triangles

• Share and Show – Page No. 541
• Sense or Nonsense? – Page No. 542
• Explore Area of Triangles – Page No. 543
• Lesson Check – Page No. 544

Lesson 3: Algebra • Area of Triangles

• Share and Show – Page No. 547
• Unlock the Problem – Page No. 548
• Area of Triangles – Page No. 549
• Lesson Check – Page No. 550

Lesson 4: Investigate • Explore Area of Trapezoids

• Share and Show – Page No. 553
• What’s the Error? – Page No. 554
• Explore Area of Trapezoids – Page No. 555
• Lesson Check – Page No. 556

Lesson 5: Algebra • Area of Trapezoids

• Share and Show – Page No. 559
• Problem Solving + Applications – Page No. 560
• Area of Trapezoids – Page No. 561
• Lesson Check – Page No. 562

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 563
• Mid-Chapter Checkpoint – Page No. 564

Lesson 6: Area of Regular Polygons

• Share and Show – Page No. 567
• Page No. 568
• Area of Regular Polygons – Page No. 569
• Lesson Check – Page No. 570

Lesson 7: Composite Figures

• Share and Show – Page No. 573
• Unlock the Problem – Page No. 574
• Composite Figures – Page No. 575
• Lesson Check – Page No. 576

Lesson 8: Problem Solving • Changing Dimensions

• Share and Show – Page No. 579
• On Your Own – Page No. 580
• Problem Solving Changing Dimensions – Page No. 581
• Lesson Check – Page No. 582

Lesson 9: Figures on the Coordinate Plane

• Share and Show – Page No. 585
• Problem Solving + Applications – Page No. 586
• Figures on the Coordinate Plane – Page No. 587
• Lesson Check – Page No. 588

Chapter 10 Review/Test

• Chapter 10 Review/Test – Page No. 589
• Chapter 10 Review/Test – Page No. 590
• Chapter 10 Review/Test – Page No. 591
• Chapter 10 Review/Test – Page No. 592
• Chapter 10 Review/Test – Page No. 593
• Chapter 10 Review/Test – Page No. 594

Share and Show – Page No. 535

Find the area of the parallelogram or square.

Question 1.

_______ m²

Answer: 9.96

Explanation:
Given that
Base = 8.3 m
Height = 1.2 m
We know that the area of the parallelogram is base × height
A = bh
A = 8.3 m × 1.2 m
A = 9.96 square meters
Thus the area of the parallelogram for the above figure is 9.96 m²

Question 2.

_______ ft²

Answer: 90

Explanation:
Given,
Base = 15 ft
Height = 6 ft
Area = ?
We know that,
Area of the parallelogram = bh
A = 15 ft × 6 ft
A = 90 square feet
Thus the area of the parallelogram for the above figure is 90 ft²

Question 3.

_______ mm²

Answer: 6.25

Explanation:
The above figure is a square
The side of the square is a × a
A = 2.5 mm × 2.5 mm
A = 6.25 square mm
Thus the area of the square is 6.25 mm²

Question 4.

\(\frac{□}{□}\) ft²

Answer: 1/2

Explanation:
Given
Base = 3/4 ft
Height = 2/3 ft
Area of the parallelogram is base × height
A = bh
A = 3/4 × 2/3
A = 1/2
Thus the area of the above parallelogram is 1/2 ft²

Find the unknown measurement for the parallelogram.

Question 5.
Area = 11 yd²

_______ yd

Answer: 2

Explanation:
Given,
A = 11 yd²
B = 5 1/2 yd
We know that
A = bh
11 = 5 1/2 × h
11 = 11/2 × h
22 = 11 × h
H = 2 yd
Thus the height of the above figure is 2 yards.

Question 6.
Area = 32 yd²

_______ yd

Answer: 8 yd

Explanation:
Given
Area = 32 yd²
Base = 4 yd
Height = ?
We know that
A = b × h
32 = 4 yd × h
H = 32/4
H = 8 yd
Therefore the height of the above figure is 8 yards.

On Your Own

Find the area of the parallelogram.

Question 7.

_______ m²

Answer: 58.24

Explanation:
Given
Base = 9.1 m
Height = 6.4 m
A = b × h
A = 9.1 m × 6.4 m
A = 58.24 square meters
Thus the area of the parallelogram for the above figure is 58.24 m²

Question 8.

_______ ft²

Answer: 168

Explanation:
Given
Base = 21 ft
Height = 8ft
We know that the area of the parallelogram is  base × height
A = 21 ft × 8ft
A = 168 square feet
Therefore the area of the above figure is 168 ft²

Find the unknown measurement for the figure.

Question 9.
square
A = ?
s = 15 ft
A = _______ ft

Answer: 225

Explanation:
Given,
S = 15 ft
The area of the square is s × s
A = 15 ft × 15 ft
A = 225 ft²
Thus the area of the square is 225 square feet.

Question 10.
parallelogram
A = 32 m²
b = ?
h = 8 m
b = _______ m

Answer: 4

Explanation:
Given
A = 32 m²
H = 8m
B = ?
To find the base we have to use the area of parallelogram formula
A = bh
32 m² = b × 8 m
B = 32/8
B = 4 m
Thus the base is 4 meters

Question 11.
parallelogram
A = 51 \(\frac{1}{4}\) in.²
b = 8 \(\frac{1}{5}\) in.
h = ?
________ \(\frac{□}{□}\) in.

Answer: 6 \(\frac{1}{4}\) in.

Explanation:
Given,
A = 51 \(\frac{1}{4}\) in.²
b = 8 \(\frac{1}{5}\) in.
H = ?
We know that the area of the parallelogram is  base × height
A = bh
51 \(\frac{1}{4}\) = h × 8 \(\frac{1}{5}\) in.
h = 51 \(\frac{1}{4}\) ÷ 8 \(\frac{1}{5}\) in.
h = 205/4 ÷ 41/5
h = 1025/164
h = 6 \(\frac{1}{4}\) in.
Thus the height of the parallelogram is 6 \(\frac{1}{4}\) in.

Question 12.
parallelogram
A = 121 mm²
b = 11 mm
h = ?
________ mm

Answer: 11 mm

Explanation:
Given
A = 121 mm²
B = 11 mm
H = ?
We know that
A = b × h
121 mm² = 11 mm × h
H = 121/11
H = 11 mm
Thus the height is 11 mm.

Problem Solving + Applications – Page No. 536

Question 14.
Jane’s backyard is shaped like a parallelogram. The base of the parallelogram is 90 feet, and the height is 25 feet. What is the area of Jane’s backyard?

________ ft²

Answer: 2250

Explanation:
Jane’s backyard is shaped like a parallelogram.
The base of the parallelogram is 90 feet, and the height is 25 feet.
A = bh
A = 90 ft × 25 ft
A = 2250 square feet
Therefore the area of the parallelogram for the above figure is 2250 ft²

Question 15.
Jack made a parallelogram by putting together two congruent triangles and a square, like the figures shown at the right. The triangles have the same height as the square. What is the area of Jack’s parallelogram?

________ cm²

Answer: 104

Explanation:
Jack made a parallelogram by putting together two congruent triangles and a square, like the figures shown at the right.
The triangles have the same height as the square.
Base = 8 cm + 5 cm = 13 cm
Height = 8 cm
Area = bh
A = 13 cm × 5 cm
A = 104 square cm
Thus the area of the parallelogram is 104 cm²

Question 17.
Verify the Reasoning of Others Li Ping says that a square with 3-inch sides has a greater area than a parallelogram that is not a square but has sides that have the same length. Does Li Ping’s statement make sense? Explain.

Type below:
_______________

Answer: 9

Explanation:
Base = 3 in
Height = 3 in
A = bh
A = 3 in × 3 in
A = 9 square inches
Therefore the area of the above figure is 9 in²

Question 18.
Find the area of the parallelogram.

________ in.²

Answer: 60

Explanation:
Base = 12 in
H = 5 in
A = bh
A = 12 in × 5 in
A = 60 square inches
A = 60 in²

Area of Parallelograms – Page No. 537

Find the area of the figure.

Question 1.

________ ft²

Answer: 126

Explanation:
The base of the figure is 18 ft
Height = 7 ft
The area of the parallelogram is bh
A = 18 ft × 7 ft
A = 126 square feet
Thus the area of the parallelogram is 126 ft²

Question 2.

________ cm²

Answer: 35

Explanation:
Base = 7 cm
Height = 5 cm
A = bh
A = 7 cm × 5 cm
A = 35 square cm
A = 35 cm²

Find the unknown measurement for the figure.

Question 3.
parallelogram
A = 9.18 m²
b = 2.7 m
h = ?
h = ________ m

Answer: 3.4

Explanation:
A = 9.18 m²
b = 2.7 m
h = ?
A = bh
9.18 m² = 2.7 m × h
h = 9.18/2.7
A = 3.4 m

Question 4.
parallelogram
A = ?
b = 4 \(\frac{3}{10}\) m
h = 2 \(\frac{1}{10}\) m
A = ________ \(\frac{□}{□}\) m²

Explanation:
b = 4 \(\frac{3}{10}\) m
h = 2 \(\frac{1}{10}\) m
A = ?
A = bh
A = 4 \(\frac{3}{10}\) m × 2 \(\frac{1}{10}\) m
A = \(\frac{43}{10}\) m × \(\frac{21}{10}\) m
A = \(\frac{903}{100}\) m²
A = 9 \(\frac{3}{100}\) m²

Question 5.
square
A = ?
s = 35 cm
A = ________ cm²

Answer: 1225

Explanation:
s = 35 cm
A = s × s
A = 35 cm × 35 cm
A = 1225 cm²
Area of the parallelogram is 1225 cm²

Question 6.
parallelogram
A = 6.3 mm²
b = ?
h = 0.9 mm
b = ________ mm

Answer: 7

Explanation:
A = 6.3 mm²
b = ?
h = 0.9 mm
A = bh
6.3 mm² = b × 0.9 mm
b = 6.3/0.9
b = 7 mm
Thus the base of the parallelogram is 7 mm.

Problem Solving

Question 9.
Copy the two triangles and the square in Exercise 15 on page 536. Show how you found the area of each piece. Draw the parallelogram formed when the three figures are put together. Calculate its area using the formula for the area of a parallelogram.
Type below:
_______________

Answer:

First, we need to add the base of the triangle and square
So, base = 8 cm + 5 cm
base = 13 cm
The height of the triangle and square are the same.
So, h = 8 cm
Area of the parallelogram is base × height
A = bh
A = 13 cm × 5 cm
A = 104 square cm
Thus the area of the parallelogram is 104 cm²

Lesson Check – Page No. 538

Question 2.
Square County is a square-shaped county divided into 16 equal-sized square districts. If the side length of each district is 4 miles, what is the area of Square County?
________ square miles

Answer: 256 square miles

Explanation:
Square County is a square-shaped county divided into 16 equal-sized square districts.
If the side length of each district is 4 miles
4 × 4 = 16
A = 16 × 16 = 256 square miles

Spiral Review

Question 3.
Which of the following values of y make the inequality y < ^–4 true?
y = ^–4     y = ^–6      y = 0    y = ^–8    y = 2
Type below:
_______________

Answer: y = -6

Question 4.
On a winter’s day, 9°F is the highest temperature recorded. Write an inequality that represents the temperature t in degrees Fahrenheit at any time on this day.
Type below:
_______________

Answer: t ≤ 9

Explanation:
On a winter’s day, 9°F is the highest temperature recorded.
t will be less than or equal to 9.
The inequality is t ≤ 9

Question 5.
In 2 seconds, an elevator travels 40 feet. In 3 seconds, the elevator travels 60 feet. In 4 seconds, the elevator travels 80 feet. Write an equation that gives the relationship between the number of seconds x and the distance y the elevator travels.
Type below:
_______________

Answer: y = 20x

Explanation:
x represents the number of seconds
y represents the distance the elevator travels.
The elevator travels 20 feet per second.
Thus the equation is y = 20x

Question 6.
The linear equation y = 4x represents the number of bracelets y that Jolene can make in x hours. Which ordered pair lies on the graph of the equation?
Type below:
_______________

Answer: (4, 16)

Explanation:
y = 4x
If x = 4
Then y = 4(4)
y = 16
Thus the ordered pairs are (4, 16)

Share and Show – Page No. 541

Question 1.
Trace the parallelogram, and cut it into two congruent triangles. Find the areas of the parallelogram and one triangle, using square units.

Type below:
_______________

Answer:
Base = 9 units
Height = 4 units
Area of the parallelogram = base × height
A = 9 × 4
A = 36 sq. units
Area of the triangle = ab/2
A = (9 × 4)/2
A = 18 sq. units
Area of another triangle = ab/2
A = (9 × 4)/2
A = 18 sq. units

Find the area of each triangle.

Question 2.

_______ in.²

Answer: 40

Explanation:
The area of the right triangle is bh/2
A = (8 × 10)/2
A = 80/2
A = 40 in.²
Thus the area of the triangle for the above figure is 40 in.²

Question 3.

_______ ft²

Answer: 180

Explanation:
The area of the right triangle is bh/2
A = (18 × 20)/2
A = 360/2
A = 180 ft²

Question 4.

_______ yd²

Answer: 22

Explanation:
The area of the right triangle is bh/2
A = (4 × 11)/2
A = 44/2
A = 22
A = 22 yd²
Thus the area of the triangle is 22 yd²

Question 5.

_______ mm²

Answer: 495

Explanation:
The area of the right triangle is bh/2
A = (30 × 33)/2
A = 990/2
A = 495 mm²
Thus the area of the triangle is 495 mm²

Question 6.

_______ in.²

Answer: 190

Explanation:
The area of the right triangle is bh/2
A = (19 × 20)/2
A = 380/2
A = 190 in.²
Thus the area of the triangle is 190 in.²

Question 7.

_______ cm²

Answer: 96

Explanation:
The area of the right triangle is bh/2
A = (16 × 12)/2
A = 192/2
A = 96 Sq. cm
Thus the area of the triangle is 96 Sq. cm

Problem Solving + Applications

Question 8.
Communicate Describe how you can use two triangles of the same shape and size to form a parallelogram.
Type below:
_______________

Answer: Put them together like a puzzle. if the sides are parallel then it would be a parallelogram.

Sense or Nonsense? – Page No. 542

Question 10.
Cyndi and Tyson drew the models below. Each said his or her drawing represents a triangle with an area of 600 square inches. Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.
Tyson’s Model:

Cyndi’s Model:

Type below:
_______________

Answer: Tyson’s Model makes sense.
The base of the figure is 30 in.
The height of the figure is 40 in
Area of the triangle = bh/2
A = (30 × 40)/2
A = 1200/2 = 600 sq. in
Cyndi’s Model doesn’t make sense because there is no base for the triangle.

Question 11.
A flag is separated into two different colors. Find the area of the white region. Show your work.

_______ ft.²

Answer: 7.5 ft.²

Explanation:
A flag is separated into two different colors.
B = 5 ft
H = 3 ft
Area of the triangle = bh/2
A = (3 × 5)/2
A = 15/2
A = 7.5 sq. ft

Explore Area of Triangles – Page No. 543

Find the area of each triangle.

Question 1.

_______ ft²

Answer: 30

Explanation:
Given,
Base = 6 ft
Height = 10 ft
Area of the triangle = bh/2
A = (6 ft × 10 ft)/2
A = 60 sq. ft/2
A = 30 ft²
Thus the area of the triangle for the above figure is 0 ft²

Question 2.

_______ cm²

Answer: 925

Explanation:
Given,
Base = 50 cm
Height = 37 cm
Area of the triangle = bh/2
A = (50 × 37)/2
A = 1850/2
A = 925 sq. cm
Therefore the area of the above figure is 925 cm²

Question 3.

_______ mm²

Answer: 400

Explanation:
Given,
Base = 40 mm
Height = 20 mm
Area of the triangle = bh/2
A = (40 × 20)/2
A = 800/2
A = 400 mm²
Therefore the area of the above figure is 400 mm²

Question 4.

_______ in.²

Answer: 180

Explanation:
Given,
Base = 12 in.
Height = 30 in.
Area of the triangle = bh/2
A = (12 × 30)/2
A = 360/2
A = 180 in.²
Therefore the area of the above figure is 180 in.²

Question 5.

_______ cm²

Answer: 225

Explanation:
Given,
Base = 15 cm
Height = 30 cm
Area of the triangle = bh/2
A = (15 × 30)/2
A = 450/2
A = 225 cm²
Therefore the area of the above figure is 225 cm²

Question 6.

_______ cm²

Answer: 450

Explanation:
Given,
Base = 20 cm
Height = 45 cm
Area of the triangle = bh/2
A = (20 × 45)/2
A = 900/2
A = 450 cm²
Therefore the area of the above figure is 450 cm²

Problem Solving

Question 9.
Draw 3 triangles on grid paper. Draw appropriate parallelograms to support the formula for the area of the triangle. Tape your drawings to this page.
Type below:
_______________

Lesson Check – Page No. 544

Question 1.
What is the area of a triangle with a height of 14 feet and a base of 10 feet?
_______ ft²

Answer: 70

Explanation:
Given,
Base = 10 feet
Height = 14 feet
Area of the triangle = bh/2
A = (14 × 10)/2
A = 140/2
A = 70 ft²
Therefore the area of the triangle is 70 ft²

Spiral Review

Question 3.
Jack bought 3 protein bars for a total of $4.26. Which equation could be used to find the cost c in dollars of each protein bar?
Type below:
_______________

Answer: 3c = 4.26

Explanation:
Jack bought 3 protein bars for a total of $4.26.
c represents the cost of each protein bar
3c = 4.26

Question 4.
Coach Herrera is buying tennis balls for his team. He can solve the equation 4c = 92 to find how many cans c of balls he needs. How many cans does he need?
_______ cans

Answer: 23

Explanation:
Coach Herrera is buying tennis balls for his team.
4c = 92
c = 92/4
c = 23
Therefore he need 23 cans.

Question 5.
Sketch the graph of y ≤ ^–7 on a number line.
Type below:
_______________

Answer:

Question 6.
A square photograph has a perimeter of 20 inches. What is the area of the photograph?
_______ in.²

Answer: 25

Explanation:
A square photograph has a perimeter of 20 inches.
p = 4s
20 = 4s
s = 20/4
s = 5 in.
Area of the square is s × s
A = 5 × 5 = 25
Thus the area of square photograph = 25 in.²

Share and Show – Page No. 547

Question 1.
Find the area of the triangle.

A = _______ cm²

Answer: 56

Explanation:
B = 14 cm
H = 8 cm
Area of the triangle = bh/2
A = (14 × 8)/2
A = 14 × 4
A = 56 sq. cm
Thus the area of the above figure is 56 cm²

Question 2.
The area of the triangle is 132 in.². Find the height of the triangle

h = _______ in.

Answer: 12

Explanation:
B = 22 in.
H = ?
A = 132 in.²
Area of the triangle = bh/2
132 sq. in  = 22 in × h
h = 132 sq. in/22 in
h = 12 in
Thus the height of the above figure is 12 in.

Find the area of the triangle.

Question 3.

A = _______ mm²

Answer: 540

Explanation:
B = 27 mm
H = 40 mm
Area of the triangle = bh/2
A = (27 × 40)/2
A = 27 × 20 = 540
A = 540 mm²
Therefore the area of the above figure is 540 mm²

Question 4.

A = _______ mm²

Answer: 11

Explanation:
B = 5.5 mm
H = 4 mm
Area of the triangle = bh/2
A = (5.5 mm × 4 mm)/2
A = 5.5 mm × 2 mm
A = 11 mm²
Therefore the area of the above figure is 11 mm²

On Your Own

Find the unknown measurement for the figure.

Question 5.

h = _______ in.

Answer: 21

Explanation:
B = 5 in
H =?
A = 52.5 sq. in
Area of the triangle = bh/2
52.5 sq. in = (5 × h)/2
52.5 sq. in × 2 = 5h
h = 21 in
Thus the height of the above figure is 21 in

Question 6.

h = _______ cm

Answer: 4.3

Explanation:
B = 80 mm = 8 cm
H = ?
A = 17.2 sq. cm
Area of the triangle = bh/2
17.2 sq. cm = (8 cm × h)/2
17.2 × 2 = 8 × h
h = 4.3 cm
Thus the height of the above figure is 4.3 cm

Unlock the Problem – Page No. 548

Question 8.
Alani is building a set of 4 shelves. Each shelf will have 2 supports in the shape of right isosceles triangles. Each shelf is 14 inches deep. How many square inches of wood will she need to make all of the supports?

a. What are the base and height of each triangle?
Base: ___________ in.
Height: ___________ in.

Answer:
Base: 14 in
Height: 14 in

Explanation:
Given that,
Each shelf is 14 inches deep.
Height = 14 inches
By seeing the above figure we can say that the base of the shelves is 14 inches
Base = 14 inches

Question 8.
b. What formula can you use to find the area of a triangle?
Type below:
_______________

Answer: The formula to find the Area of the triangle = bh/2

Question 8.
c. Explain how you can find the area of one triangular support.
Type below:
_______________

Answer:
We can find the area of one triangle support by substituting the base and height in the formula.
A = (14 × 14)/2
A = 98 sq. in

Question 8.
d. How many triangular supports are needed to build 4 shelves?
_______ supports

Answer: 8
By seeing the above figure we can say that 8 triangular supports are needed to build 4 shelves.

Question 8.
e. How many square inches of wood will Alani need to make all the supports?
_______ in.²

Answer: 784

Explanation:
The depth of each shelf made by Alamo is 14 inches.
So the base of the right isosceles triangular supporter is 14 inches.
So one equal side is 14 cm. Now by using the Pythagoras theorem we can calculate the other side of the supporter = = 19.8 inches.
The area of the right isosceles triangle is given by × base ×height. Here the base and height are equal to 14 inches.
Therefore the area of each right isosceles triangular supporter is
A = (14 × 14)/2
A = 98 sq. in
Each shelf would require two such supporters and there are 4 such shelves. Thus the total number of supporters required is 8.
Square inches of wood necessary for 8 right isosceles triangular supporters = 98 × 8 = 784 square inches.

Question 10.
The area of a triangle is 30 ft².
For numbers, 10a–10d, select Yes or No to tell if the dimensions given could be the height and base of the triangle.
10a. h = 3, b = 10
10b. h = 3, b = 20
10c. h = 5, b = 12
10d. h = 5, b = 24
10a. ___________
10b. ___________
10c. ___________
10d. ___________

Answer:
10a. No
10b. yes
10c. Yes
10d. No

Explanation:
The area of a triangle is 30 ft².
10a. h = 3, b = 10
Area of the triangle = bh/2
A = (3 × 10)/2
A = 15 ft².
Thus the answer is no.
10b. h = 3, b = 20
Area of the triangle = bh/2
A = (3 × 20)/2
A = 30 ft².
Thus the answer is yes.
10c. h = 5, b = 12
Area of the triangle = bh/2
A = (5 × 12)/2
A = 30 ft².
Thus the answer is yes.
10d. h = 5, b = 24
Area of the triangle = bh/2
A = (5 × 24)/2
A = 60 ft².
Thus the answer is no.

Area of Triangles – Page No. 549

Find the area.

Question 1.

_______ in.²

Answer: 45

Explanation:
Given,
Base = 15 in.
Height = 6 in.
Area of the triangle = bh/2
A = (15 × 6)/2
A = 90/2
A = 45 in.²

Question 2.

_______ m²

Answer: 0.36

Explanation:
Given,
Base = 1.2 m
Height = 0.6 m
Area of the triangle = bh/2
A = (1.2 × 0.6)/2
A = 0.72/2
A = 0.36 m²

Question 3.

_______ ft²

Answer: 6

Explanation:
Given,
Base = 4 1/2 ft
Height = 2 2/3 ft
Area of the triangle = bh/2
A = (4 1/2 × 2 2/3)/2
A = 12/2
A = 6 ft²

Find the unknown measurement for the triangle.

Question 4.
A = 0.225 mi²
b = 0.6 mi
h = ?
h = _______ mi

Answer: 0.75

Explanation:
Given,
A = 0.225 mi²
b = 0.6 mi
h = ?
Area of the triangle = bh/2
0.225 = (0.6 × h)/2
0.450 = 0.6 × h
h = 0.450/0.6
h = 0.75 mi

Question 5.
A = 4.86 yd²
b = ?
h = 1.8 yd
b = _______ yd

Answer: 5.4 yd

Explanation:
Given,
A = 4.86 yd²
b = ?
h = 1.8 yd
Area of the triangle = bh/2
4.86 yd² = (b × 1.8 yd)/2
4.86 × 2 = b × 1.8
9.72 = b × 1.8
b = 9.72/1.8
b = 5.4 yd

Question 6.
A = 63 m²
b = ?
h = 12 m
b = _______ m

Answer: 10.5

Explanation:
Given,
A = 63 m²
b = ?
h = 12 m
Area of the triangle = bh/2
63 = (b × 12)/2
63 = b × 6
b = 63/6
b = 10.5 m

Question 7.
A = 2.5 km²
b = 5 km
h = ?
h = _______ km

Answer: 1

Explanation:
Given,
A = 2.5 km²
b = 5 km
h = ?
Area of the triangle = bh/2
2.5 = (5 km × h)/2
2.5 km² = 2.5 km × h
h = 2.5/2.5
h = 1 km

Problem Solving

Question 9.
Alicia is making a triangular sign for the school play. The area of the sign is 558 in.². The base of the triangle is 36 in. What is the height of the triangle?
_______ in.

Answer: 31

Explanation:
Given,
Alicia is making a triangular sign for the school play.
The area of the sign is 558 in.²
The base of the triangle is 36 in.
Area of the triangle = bh/2
558 = (36 × h)/2
558 = 18 × h
h = 558/18
h = 31 inches

Question 10.
Describe how you would find how much grass seed is needed to cover a triangular plot of land.
Type below:
_______________

Answer:

You will need to find the area
A=height multiplied by the base divided by 2
Area of the triangle = bh/2

Lesson Check – Page No. 550

Spiral Review

Question 3.
Tina bought a t-shirt and sandals. The total cost was $41.50. The t-shirt cost $8.95. The equation 8.95 + c = 41.50 can be used to find the cost c in dollars of the sandals. How much did the sandals cost?
$ _______

Answer: $32.55

Explanation:
Tina bought a t-shirt and sandals.
The total cost was $41.50.
The t-shirt cost $8.95.
8.95 + c = 41.50
c = 41.50 – 8.95
c = $32.55

Question 4.
There are 37 paper clips in a box. Carmen places more paper clips in the box. Write an equation to show the total number of paper clips p in the box after Carmen places n more paper clips in the box.
Type below:
_______________

Answer: 37 + n = p

Explanation:
There are 37 paper clips in a box. Carmen places more paper clips in the box.
n represents number of paper clips in the box
The equation is 37 + n = p

Question 5.
Name another ordered pair that is on the graph of the equation represented by the table.

Type below:
_______________

Answer: The ordered pairs are (1, 6), (2, 12), (3, 18), (4, 16)

Question 6.
Find the area of the triangle that divides the parallelogram in half.

_______ cm²

Answer: 58.5

Explanation:
Given,
b = 13 cm
h = 9 cm
Area of the triangle = bh/2
A = (13 × 9)/2
A = 117/2
A = 58.5 cm²

Share and Show – Page No. 553

Question 1.
Trace and cut out two copies of the trapezoid. Arrange the trapezoids to form a parallelogram. Find the areas of the parallelogram and one trapezoid using square units

Type below:
_______________

Answer:
Figure 1:
Base 1 = 3 units
Base 2= 7 units
Height = 4 units
Area of the trapezium = (b1 + b2)h/2
A = (3 + 7)4/2
A = 10 × 2
A = 20 sq. units
Figure 2:
Base 1 = 7 units
Base 2= 3 units
Height = 4 units
Area of the trapezium = (b1 + b2)h/2
A = (7 + 3)4/2
A = 10 × 2
A = 20 sq. units

Find the area of the trapezoid.

Question 2.

_______ cm²

Answer: 40

Explanation:
Base 1 = 6 cm
Base 2 = 10 cm
Height = 5 cm
We know that the Area of the trapezium is the sum of bases into height divided by 2.
Area of the trapezium = (b1 + b2)h/2
A = (6 cm + 10 cm)5 /2
A = (16 × 5)/2
A = 40 sq. cm

Question 3.

_______ in.²

Answer: 48

Explanation:
b1 = 3 in
b2 = 9 in.
h = 8 in.
We know that the Area of the trapezium is the sum of bases into height divided by 2.
Area of the trapezium = (b1 + b2)h/2
A = (3 + 9)8/2
A = 12 × 4
A = 48 sq. in

Question 4.

_______ ft²

Answer: 64

Explanation:
b1 = 11 ft
b2 = 5 ft
h = 8 ft
We know that the Area of the trapezium is the sum of bases into height divided by 2.
Area of the trapezium = (b1 + b2)h/2
A = (11 + 5)8/2
A = 16 × 4
A = 64 sq. ft

Question 5.

_______ cm²

Answer: 266

Explanation:
b1 = 16 cm
b2 = 22 cm
h = 14 cm
We know that the Area of the trapezium is the sum of bases into height divided by 2.
Area of the trapezium = (b1 + b2)h/2
A = (16 + 22)14/2
A = 38 × 7
A = 266 sq. cm

Question 6.

_______ mm²

Answer: 71.5

Explanation:
b1 = 8 mm
b2 = 14 mm
h = 6.5 mm
We know that the Area of the trapezium is the sum of bases into height divided by 2.
Area of the trapezium = (b1 + b2)h/2
A = (8 + 14)6.5/2
A = 11 × 6.5
A = 71.5 sq. mm

Question 7.

_______ in.²

Answer: 31.5

Explanation:
b1 = 3 1/2 in.
b2 = 8 1/2 in.
h = 5 1/4 in.
We know that the Area of the trapezium is the sum of bases into height divided by 2.
Area of the trapezium = (b1 + b2)h/2
b = 3 1/2 + 8 1/2
b = 12
A = 5 1/4 × 12/2
A = 5 1/4 × 6
A = 31.5 sq. in

Problem Solving + Applications

Question 8.
Describe a Method Explain one way to find the height of a trapezoid if you know the area of the trapezoid and the length of both bases.
Type below:
_______________

Answer:
1) Add the length of both bases: [Total Length = Length 1 + Length 2]
2) Divide the length that you found by 2. [Average Length = Total Length ÷ 2]
3) Divide the Area by the length found [Height = Area ÷ average length]

What’s the Error? – Page No. 554

Question 10.
Except for a small region near its southeast corner, the state of Nevada is shaped like a trapezoid. The map at the right shows the approximate dimensions of the trapezoid. Sabrina used the map to estimate the area of Nevada.
Look at how Sabrina solved the problem. Find her error.
Two copies of the trapezoid can be put together to form a rectangle.
length of rectangle: 200 + 480 = 680 mi
width of rectangle: 300 mi
A = lw
A = 680 × 300
A = 204,000
The area of Nevada is about 204,000 square miles.
Describe the error. Find the area of the trapezoid to estimate the area of Nevada.
Type below:
_______________

Answer:
The area of Nevada is she didn’t divide by 2.
Area of the trapezium = (b1 + b2)h/2
A = (200 + 480)300/2
A = 680 × 150
A = 102000 sq. miles

Question 11.
A photo was cut in half at an angle. What is the area of one of the cut pieces?

_______ in.²

Answer: 30

Explanation:
b1= 3 in
b2 = 7 in
h = 6 in.
Area of the trapezium = (b1 + b2)h/2
A = (3 + 7)6/2
A = 10 × 3
A = 30 sq. in
Thus the area of the trapezium is 30 in.²

Explore Area of Trapezoids – Page No. 555

Question 1.
Trace and cut out two copies of the trapezoid. Arrange the trapezoids to form a parallelogram. Find the areas of the parallelogram and the trapezoids using square units.

Type below:
_______________

Answer:
Figure 1:
b1 = 2 units
b2 = 6 units
h = 3 units
Area of the trapezium = (b1 + b2)h/2
A = (2 + 6)3/2
A = (8)(3)/2
A = 24/2 = 12
A = 12 sq. units
Figure 2:
b1 = 6 units
b2 = 2 units
h = 3 units
Area of the trapezium = (b1 + b2)h/2
A = (6 + 2)3/2
A = (8)(3)/2
A = 24/2 = 12
The area of figure 2 is 12 sq. units

Find the area of the trapezoid.

Question 2.

_______ in.²

Answer: 38.5

Explanation:
Given,
b1 = 9 in
b2 = 2 in
h = 7 in
Area of the trapezium = (b1 + b2)h/2
A = (9 + 2)7/2
A = (11 × 7)/2
A = 77/2 = 38.5 in.²

Question 3.

_______ yd²

Answer: 3600

Explanation:
Given,
b1 = 24 yd
b2 = 48 yd
h = 100 yd
Area of the trapezium = (b1 + b2)h/2
A = (24 + 48)100/2
A = 72 × 50
A = 3600 yd²

Question 4.

_______ ft²

Answer: 64

Explanation:
Given,
b1 = 4.5 ft
b2 = 11.5 ft
h = 8 ft
Area of the trapezium = (b1 + b2)h/2
A = (4.5 + 11.5)8/2
A = 16 × 4
A = 64 sq. ft

Problem Solving

Question 5.
A cake is made out of two identical trapezoids. Each trapezoid has a height of 11 inches and bases of 9 inches and 14 inches. What is the area of one of the trapezoid pieces?
_______ in.²

Answer: 126.5

Explanation:
Given,
A cake is made out of two identical trapezoids.
Each trapezoid has a height of 11 inches and bases of 9 inches and 14 inches.
Area of the trapezium = (b1 + b2)h/2
A = (9 + 14)11/2
A = 23 × 11/2
A = 126.5 in.²

Question 7.
Find the area of a trapezoid that has bases that are 15 inches and 20 inches and a height of 9 inches.
_______ in.²

Answer: 157.5

Explanation:
b1 = 15 inches
b2 = 20 inches
h = 9 inches
Area of the trapezium = (b1 + b2)h/2
A = (15 + 20)9/2
A = (35 × 9)/2
A = 157.5 sq. in

Lesson Check – Page No. 556

Question 8.

_______ yd²

Answer: 84

Explanation:
b1 = 9 yd
b2 = 15 yd
h = 7 yd
Area of the trapezium = (b1 + b2)h/2
A = (9 + 15)7/2
A = 24 × 3.5
A = 84 sq. yd

Question 2.
Maggie colors a figure in the shape of a trapezoid. The trapezoid is 6 inches tall. The bases are 4.5 inches and 8 inches. What is the area of the figure that Maggie colored?
_______ in.²

Answer: 37.5

Explanation:
Maggie colors a figure in the shape of a trapezoid.
The trapezoid is 6 inches tall.
The bases are 4.5 inches and 8 inches.
b1 = 4.5 in
b2 = 8 in
h = 6 in
Area of the trapezium = (b1 + b2)h/2
A = (4.5 in + 8 in)6/2
A = 12.5 in × 3
A = 37.5 sq. in

Spiral Review

Question 4.
Ginger makes pies and sells them for $14 each. Write an equation that represents the situation, if y represents the money that Ginger earns and x represents the number of pies sold.
Type below:
_______________

Answer: y = 14x

Explanation:
Ginger makes pies and sells them for $14 each.
y represents the money that Ginger earns
x represents the number of pies sold
The equation is y = 14x

Question 5.
What is the equation for the graph shown below?

Type below:
_______________

Answer: y = 2x
By seeing the graph we can say that y = 2x

Question 6.
Cesar made a rectangular banner that is 4 feet by 3 feet. He wants to make a triangular banner with the same area as the other. The triangular banner will have a base of 4 feet. What should its height be?
_______ feet

Answer: 6

Explanation:
6 Because 4×3=12 and (4× 6)/2=12

Share and Show – Page No. 559

Question 1.
Find the area of the trapezoid.

A = _______ cm²

Answer: 18

Explanation:
Given,
b1 = 6 cm
b2 = 3 cm
h = 4 cm
We know that,
Area of the trapezium = (b1 + b2)h/2
A = (6 cm + 3 cm)4 cm/2
A = 9 cm × 2 cm
A = 18 sq. cm
Therefore the area of the trapezoid is 18 cm²

Question 2.
The area of the trapezoid is 45 ft². Find the height of the trapezoid.

h = _______ ft

Answer: 5

Explanation:
b1 = 10 ft
b2 = 8 ft
The area of the trapezoid is 45 ft²
We know that,
Area of the trapezium = (b1 + b2)h/2
45 ft² = (10 ft + 8 ft)h/2
90 = 18 × h
h = 90/18
h = 5 ft
Thus the height of the above figure is 5 ft.

Question 3.
Find the area of the trapezoid.

_______ mm²

Answer: 540

Explanation:
b1 = 17 mm
b2 = 43 mm
h = 18 mm
We know that,
Area of the trapezium = (b1 + b2)h/2
A = (17 + 43)18/2
A = 60 mm × 9 mm
A = 540 sq. mm
Thus the area of the trapezoid is 540 mm²

On Your Own

Find the area of the trapezoid.

Question 4.

A = _______ in.²

Answer: 266

Explanation:
Given,
b1 = 17 in
b2 = 21 in
h = 14 in
We know that,
Area of the trapezium = (b1 + b2)h/2
A = (17 in + 21 in)14/2
A = 38 in × 7 in
A = 266 sq. in
Therefore Area of the trapezium is 266 in.²

Question 5.

A = _______ m²

Answer: 25.2 m²

Explanation:
Given,
b1 = 9.2 m
b2 = 2.8 m
h = 4.2 m
We know that,
Area of the trapezium = (b1 + b2)h/2
A = (9.2 + 2.8)4.2/2
A = 12 × 2.1
A = 25.2 sq. m
Therefore the area of the trapezium is 25.2 m²

Find the height of the trapezoid.

Question 6.

h = _______ in.

Answer: 25

Explanation:
Given,
b1 = 27.5 in
b2 = 12.5 in
h = ?
A = 500 sq. in
We know that,
Area of the trapezium = (b1 + b2)h/2
500 sq. in = (27.5 in + 12.5 in)h/2
500 sq. in = 40 × h/2
500 sq. in = 20h
h = 500/20
h = 25 inches
Thus the height of the above figure is 25 inches.

Question 7.

h = _______ cm

Answer: 15

Explanation:
A = 99 sq. cm
b1 = 3.2 cm
b2 = 10 cm
h = ?
We know that,
Area of the trapezium = (b1 + b2)h/2
99 sq. cm = (3.2 cm+ 10 cm)h/2
99 sq. cm = (13.2 cm)h/2
99 sq. cm = 6.6 × h
h = 99 sq. cm/6.6 cm
h = 15 cm

Problem Solving + Applications – Page No. 560

Use the diagram for 8–9.

Question 8.
A baseball home plate can be divided into two trapezoids with the dimensions shown in the drawing. Find the area of home plate.
_______ in.²

Answer: 21.75

Explanation:
The bases of the trapezoid area are 8.5 in and 17 in and the height is 8.5 in.
We know that,
Area of the trapezium = (b1 + b2)h/2
A = 1/2 (8.5 + 17)8.5
A = (25.5)(8.5)/2
A = 1/2 × 216.75
The area of the home plate is double the area of a trapezoid.
So, the area of the home plate is 216.75 sq. in.

Question 9.
Suppose you cut the home plate along the dotted line and rearranged the pieces to form a rectangle. What would the dimensions and the area of the rectangle be?
Type below:
_______________

Answer:
The dimensions of the rectangle would be 25.5 in by 8.5 in.
The area would be 216.75 sq. in.

Question 10.
A pattern used for tile floors is shown. A side of the inner square measures 10 cm, and a side of the outer square measures 30 cm. What is the area of one of the yellow trapezoid tiles?

_______ cm²

Answer: 200 sq. cm

Explanation:
A side of the inner square measures 10 cm, and a side of the outer square measures 30 cm.
The bases of the trapezoid are 10 cm and 30 cm and the height of the trapezoid is 10 cm.
We know that,
Area of the trapezium = (b1 + b2)h/2
A = (10 + 30)10/2
A = 40 cm × 5 cm
A = 200 sq. cm
So, the area of one of the yellow trapezoid tiles is 200 sq. cm

Question 12.
Which expression can be used to find the area of the trapezoid? Mark all that apply.

Options:
a. \(\frac{1}{2}\) × (4 + 1.5) × 3.5
b. \(\frac{1}{2}\) × (1.5 + 3.5) × 4
c. \(\frac{1}{2}\) × (4 + 3.5) × 1.5
d. \(\frac{1}{2}\) × (5) × 4

Answer: \(\frac{1}{2}\) × (1.5 + 3.5) × 4

Explanation:
b1 = 3.5 ft
b2 = 1.5 ft
h = 4 ft
We know that,
Area of the trapezium = (b1 + b2)h/2
A = (3.5 ft + 1.5 ft)4ft/2
A = \(\frac{1}{2}\) × (1.5 + 3.5) × 4
Thus the correct answer is option B.

Area of Trapezoids – Page No. 561

Find the area of the trapezoid.

Question 1.

_______ cm²

Answer: 252 cm²

Explanation:
Given that,
long base b1 = 17 cm
short base b2 = 11 cm
h = 18 cm
We know that,
The Area of the trapezium = (b1 + b2)h/2
A = (17 cm + 11 cm)18 cm/2
A = 28 cm × 9 cm
A = 252 cm²
Thus the area of the trapezium for the above figure is 252 cm²

Question 2.

_______ ft²

Answer: 30 ft²

Explanation:
Given,
b1 = 6.5 ft
b2 = 5.5 ft
h = 5 ft
We know that,
The Area of the trapezium = (b1 + b2)h/2
A = (6.5 + 5.5)5/2
A = 12 ft × 2.5 ft
A = 30 sq. ft
Therefore the area of the trapezium is 30 ft²

Question 3.

_______ cm²

Answer: 0.08 cm²

Explanation:
Given,
b1 = 0.6 cm
b2 = 0.2 cm
h = 0.2 cm
We know that,
The Area of the trapezium = (b1 + b2)h/2
A = (0.6 cm + 0.2 cm)0.2 cm/2
A = 0.8 cm × 0.1 cm
A = 0.08 sq. cm
Thus the area of the trapezium is 0.08 sq. cm

Question 4.

_______ in.²

Answer: 37.5 in.²

Explanation:
Given,
b1 = 5 in
b2 = 2 1/2
h = 10 in
We know that,
The Area of the trapezium = (b1 + b2)h/2
A = (5 in + 2 1/2 in)10/2
A = 7 1/2 × 5
A = 37.5 sq. in
Thus the area of the trapezium is 37.5 in.²

Problem Solving

Question 5.
Sonia makes a wooden frame around a square picture. The frame is made of 4 congruent trapezoids. The shorter base is 9 in., the longer base is 12 in., and the height is 1.5 in. What is the area of the picture frame?
_______ in.²

Answer: 63

Explanation:
Given,
Sonia makes a wooden frame around a square picture.
The frame is made of 4 congruent trapezoids.
The shorter base is 9 in., the longer base is 12 in., and the height is 1.5 in.
We know that,
The Area of the trapezium = (b1 + b2)h/2
A = (9 in + 12 in)1.5/2
A = 21 in × 1.5 in/2
A = 63 sq. in
Thus the area of the trapezium is 63 in.²

Question 6.
Bryan cuts a piece of cardboard in the shape of a trapezoid. The area of the cutout is 43.5 square centimeters. If the bases are 6 centimeters and 8.5 centimeters long, what is the height of the trapezoid?
_______ cm

Answer: 6 cm

Explanation:
Given,
Bryan cuts a piece of cardboard in the shape of a trapezoid.
The area of the cutout is 43.5 square centimeters.
If the bases are 6 centimeters and 8.5 centimeters long.
We know that,
The Area of the trapezium = (b1 + b2)h/2
43.5 sq. cm = (6 + 8.5)h/2
43.5 × 2 = 14.5 × h
h = 6 cm
Therefore the height of the trapezoid is 6 cm.

Lesson Check – Page No. 562

Question 1.
Dominic is building a bench with a seat in the shape of a trapezoid. One base is 5 feet. The other base is 4 feet. The perpendicular distance between the bases is 2.5 feet. What is the area of the seat?
_______ ft²

Answer: 11.25 sq. ft

Explanation:
Given,
Dominic is building a bench with a seat in the shape of a trapezoid.
One base is 5 feet. The other base is 4 feet.
The perpendicular distance between the bases is 2.5 feet.
We know that,
The Area of the trapezium = (b1 + b2)h/2
A = (5 ft + 4 ft)2.5/2
A = 4.5 ft × 2.5 ft
A = 11.25 sq. ft
Thus the area of the seat is 11.25 sq. ft

Question 2.
Molly is making a sign in the shape of a trapezoid. One base is 18 inches and the other is 30 inches. How high must she make the sign so its area is 504 square inches?
_______ in.

Answer: 21 in.

Explanation:
Given,
Molly is making a sign in the shape of a trapezoid.
One base is 18 inches and the other is 30 inches.
A = 504 sq. in
We know that,
The Area of the trapezium = (b1 + b2)h/2
504 sq. in = (18 + 30)h/2
504 sq. in = 24 × h
h = 504 sq. in÷ 24 in
h = 21 inches
Thus the height of the trapezoid is 21 inches.

Spiral Review

Question 3.
Write these numbers in order from least to greatest.
3 \(\frac{3}{10}\)     3.1       3 \(\frac{1}{4}\)
Type below:
_______________

Explanation:
First, convert the fraction into a decimal.
3 \(\frac{3}{10}\) = 3.3
3 \(\frac{1}{4}\) = 3.25
Now write the numbers from least to greatest.
3.1 3.25 3.3

Question 4.
Write these lengths in order from least to greatest.
2 yards       5.5 feet        70 inches
Type below:
_______________

Answer: 5.5 feet, 70 inches, 2 yards

Explanation:
First, convert from inches to feet.
1 feet = 12 inches
70 inches = 5.8 ft
1 yard = 3 feet
2 yards = 2 × 3 ft
2 yards = 6 feet
Now write the numbers from least to greatest.
5.5 ft 5.8 ft 6 ft

Question 6.
Brian frosted a cake top shaped like a parallelogram with a base of 13 inches and a height of 9 inches. Nancy frosted a triangular cake top with a base of 15 inches and a height of 12 inches. Which cake’s top had the greater area? How much greater was it?
Type below:
_______________

Explanation:
Parallelogram Formula = Base × Height
A=bh
A=13 × 9=117 in
Triangle Formula=
A=1/2bh
A=1/2 × 15 × 12 = 90 in
Brian’s cake top has a greater area, and by 27 inches.

Mid-Chapter Checkpoint – Vocabulary – Page No. 563

Choose the best term from the box to complete the sentence.

Question 1.
A _____ is a quadrilateral that always has two pairs of parallel sides.
Type below:
_______________

Answer: A parallelogram is a quadrilateral that always has two pairs of parallel sides.

Question 2.
The measure of the number of unit squares needed to cover a surface without any gaps or overlaps is called the _____.
Type below:
_______________

Answer: The measure of the number of unit squares needed to cover a surface without any gaps or overlaps is called the Area.

Question 3.
Figures with the same size and shape are _____.
Type below:
_______________

Answer: Figures with the same size and shape are Congruent.

Concepts and Skills

Find the area.

Question 4.

_______ cm²

Answer: 19.38

Explanation:
b = 5.7 cm
h = 3.4 cm
Area of parallelogram = bh
A = 5.7 cm × 3.4 cm
A = 19.38 cm²
Thus the area of the parallelogram is 19.38 cm²

Question 5.

_______ \(\frac{□}{□}\) in.²

Answer: 42 \(\frac{1}{4}\) in.²

Explanation:
b = 6 \(\frac{1}{2}\)
h = 6 \(\frac{1}{2}\)
Area of parallelogram = bh
A = 6 \(\frac{1}{2}\) × 6 \(\frac{1}{2}\)
A = 42 \(\frac{1}{4}\) in.²
Thus the area of the parallelogram is 42 \(\frac{1}{4}\) in.²

Question 6.

_______ mm²

Answer: 57.4

Explanation:
b = 14 mm
h = 8.2 mm
A = bh/2
A = (14 mm × 8.2 mm)/2
A = 57.4 mm²

Question 7.

Answer: 139.5

Explanation:
b1 = 13 cm
b2= 18 cm
h = 9 cm
Area of the trapezium = (b1 + b2)h/2
A = (13 + 18)9/2
A = 31 × 4.5
A = 139.5 sq. cm

Page No. 564

Question 10.
The height of a parallelogram is 3 times the base. The base measures 4.5 cm. What is the area of the parallelogram?
_______ cm²

Answer: 60.75

Explanation:
The height of a parallelogram is 3 times the base. The base measures 4.5 cm.
A = bh
h = 3 × 4.5
h = 13.5 cm
b = 4.5 cm
A = 13.5 cm × 4.5 cm
A = 60.75 cm²

Question 11.
A triangular window pane has a base of 30 inches and a height of 24 inches. What is the area of the window pane?
_______ in.²

Answer: 360

Explanation:
A triangular window pane has a base of 30 inches and a height of 24 inches.
b = 30 in
h = 24 in
A = bh/2
A = (30 × 24)/2
A = 30 × 12
A = 360 in.²

Question 12.
The courtyard behind Jennie’s house is shaped like a trapezoid. The bases measure 8 meters and 11 meters. The height of the trapezoid is 12 meters. What is the area of the courtyard?
_______ m²

Answer: 114

Explanation:
Given,
The courtyard behind Jennie’s house is shaped like a trapezoid.
The bases measure 8 meters and 11 meters.
The height of the trapezoid is 12 meters.
Area of the trapezium = (b1 + b2)h/2
A = (8 + 11)12/2
A = 19 × 6
A = 114 m²

Question 13.
Rugs sell for $8 per square foot. Beth bought a 9-foot-long rectangular rug for $432. How wide was the rug?
_______ feet

Answer: 6 feet

Explanation:
If you know the rugs sell for 8$ per square foot and the total spend was $432.
You divide 432 by 8 to find the total number of square feet of the rug.
To find the total square foot you find the area.
So the area of a rectangle is L × W. So 54 = 9 × width.
So just divide 54 by 9 and you get the width of the rug.
The width is 6 feet.
Now you check. A nine by 6 rug square foot is 54. and then times by 8 and you get 432 total.

Share and Show – Page No. 567

Find the area of the regular polygon.

Question 1.

_______ cm²

Answer: 120

Explanation:
b = 5 cm
h = 6 cm
Number of congruent figures inside the figure: 8
Area of each triangle = bh/2
A = (5 cm)(6 cm)/2
A = 15 sq. cm
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular octagon = 8 × 15 sq. cm
A = 120 sq. cm
Therefore the area of the regular octagon for the above figure = 120 sq. cm

Question 2.

_______ m²

Answer: 60

Explanation:
Given,
b = 6 m
h = 4 m
Number of congruent figures inside the figure: 5
Area of each triangle = bh/2
A = (6 m)(4 m)/2
A = 12 sq. m
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular pentagon = 5 × 12 sq. m
A = 60 sq. m
Therefore the area of the above figure is 60 sq. m.

Question 3.

_______ mm²

Answer: 480

Explanation:
Given,
b = 8 mm
h = 12 mm
Number of congruent figures inside the figure: 10
Area of each triangle = bh/2
A = (12 mm)(8 mm)/2
A = 48 sq. mm
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 10 × 48 sq. mm
A = 480 sq. mm
Therefore, the area of the regular polygon is 480 sq. mm

On Your Own

Find the area of the regular polygon.

Question 4.

_______ cm²

Answer: 168

Explanation:
Given,
b = 8 cm
h = 7 cm
Number of congruent figures inside the figure: 6
Area of each triangle = bh/2
A = (8 cm)(7 cm)/2
A = 28 sq. cm
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular hexagon = 6 × 28 sq. cm
A = 168 sq. cm
Thus the area of the above figure is 168 sq. cm

Question 5.

_______ in.²

Answer: 6020

Explanation:
Given,
b = 28 in
h = 43 in
Number of congruent figures inside the figure: 10
Area of each triangle = bh/2
A = (28 in)(43 in)/2
A = 602 sq. in
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 10 × Area of each triangle
A = 10 × 602 sq. in
A = 6020 sq. in
Therefore the area of the regular polygon is 6020 sq. in

Question 6.
Explain A regular pentagon is divided into congruent triangles by drawing a line segment from each vertex to the center. Each triangle has an area of 24 cm². Explain how to find the area of the pentagon
Type below:
_______________

Answer: 120

Explanation:
Given,
Each triangle has an area of 24 cm².
Pentagon has 5 sides. The number of congruent figures is 5.
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular pentagon = 5 × 24 sq. cm
A = 120 sq. cm
Therefore the area of the pentagon is 120 sq. cm

Page No. 568

Question 7.
Name the polygon and find its area. Show your work.

_______ in.²

Answer: 76.8 sq. in

Explanation:
b = 4 in
h = 4.8 in
Number of configured figures of the regular polygon: 8
Area of the triangle = bh/2
A = (4)(4.8)/2
A = 9.6 sq. in.
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 8 × area of the triangle
A = 8 × 9.6 sq. in.
A = 76.8 sq. in
Thus the area of the regular polygon is 76.8 sq. in.

Regular polygons are common in nature

One of the bestknown examples of regular polygons in nature is the small hexagonal cells in honeycombs constructed by honeybees. The cells are where bee larvae grow. Honeybees store honey and pollen in the hexagonal cells. Scientists can measure the health of a bee population by the size of the cells.

Question 8.
Cells in a honeycomb vary in width. To find the average width of a cell, scientists measure the combined width of 10 cells, and then divide by 10.
The figure shows a typical 10-cell line of worker bee cells. What is the width of each cell?

_______ cm

Answer: 0.52 cm

Explanation:
Since the combined width of 10 cells is 5.2 cm, the width of each cell is 5.2 ÷ 10 = 0.52 cm.

Question 9.
The diagram shows one honeycomb cell. Use your answer to Exercise 8 to find h, the height of the triangle. Then find the area of the hexagonal cell.

Type below:
_______________

Answer: 0.234 sq. cm

Explanation:
The length of the h, the height of the triangle, is half of the width of each cell.
Since the width of each cell is 0.52 cm
h = 0.52 ÷ 2 = 0.26 cm
Area of the triangle = bh/2
A = (0.3)(0.26)/2
A = 0.078/2
A = 0.039
The area of the hexagon is:
6 × 0.039 = 0.234 sq. cm.

Area of Regular Polygons – Page No. 569

Find the area of the regular polygon.

Question 1.

_______ mm²

Answer: 168

Explanation:
Given,
b = 8 mm
h = 7 mm
Number of congruent figures inside the figure: 6
Area of each triangle = bh/2
A = (8)(7)/2
A = 28 sq. mm
Now to find the area of regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 6 × 28 sq. mm
A = 168 sq. mm
Therefore the area of the regular polygon for the above figure is 168 sq. mm

Question 2.

_______ yd²

Answer: 139.5

Explanation:
Given,
b = 9 yd
h = 6.2 yd
Number of congruent figures inside the figure: 5
Area of each triangle = bh/2
A = (9 yd) (6.2 yd)/2
A = 9 yd × 3.1 yd
A = 27.9 sq. yd
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 5 × 27.9 sq. yd
A = 139.5 sq. yd
Thus the area of the regular polygon for the above figure is 139.5 sq. yd.

Question 3.

_______ in.²

Answer: 52.8

Explanation:
Given,
b = 3.3 in
h = 4 in
Number of congruent figures inside the figure: 8
Area of each triangle = bh/2
A = (3.3 in)(4 in)/2
A = 6.6 sq. in
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 8 × 6.6 sq. in
A = 52.8 sq. in
The area of the regular polygon is 52.8 sq. in

Problem Solving

Question 4.
Stu is making a stained glass window in the shape of a regular pentagon. The pentagon can be divided into congruent triangles, each with a base of 8.7 inches and a height of 6 inches. What is the area of the window?
_______ in.²

Answer: 130.5

Explanation:
Stu is making a stained glass window in the shape of a regular pentagon.
The pentagon can be divided into congruent triangles, each with a base of 8.7 inches and a height of 6 inches.
Number of congruent figures inside the figure: 5
Area of each triangle = bh/2
A = (8.7 in)(6 in)/2
A = 8.7 in × 3 in
A = 26.1 sq. in.
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 5 × 26.1 sq. in
A = 130.5 sq. in
Thus the area of the window is 130.5 sq. in

Question 6.
A square has sides that measure 6 inches. Explain how to use the method in this lesson to find the area of the square.
Type below:
_______________

Answer: 36 sq. in

Explanation:
A square has sides that measure 6 inches.
s = 6 in
We know that,
Area of the square = s × s
A = 6 in × 6 in
A = 36 sq. in
Thus the area of the square is 36 sq. in

Lesson Check – Page No. 570

Question 1.
What is the area of the regular hexagon?

________ \(\frac{□}{□}\) m²

Answer: 30 \(\frac{3}{5}\) m²

Explanation:
Given,
b = 3 \(\frac{2}{5}\) m
h = 3 m
Area of each triangle = bh/2
A = 3 \(\frac{2}{5}\) m × 3/2 m
A = 5.1 sq. m
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of the regular hexagon = 6 × 5.1 = 30.6
= 30 \(\frac{6}{10}\) m²
= 30 \(\frac{3}{5}\) m²
Therefore the area of the regular hexagon is 30 \(\frac{3}{5}\) m²

Question 2.
A regular 7-sided figure is divided into 7 congruent triangles, each with a base of 12 inches and a height of 12.5 inches. What is the area of the 7-sided figure?
________ in.²

Answer: 525 sq. in

Explanation:
A regular 7-sided figure is divided into 7 congruent triangles, each with a base of 12 inches and a height of 12.5 inches.
Area of each triangle = bh/2
A = (12 in)(12.5 in)/2
A = 12.5 in × 6 in
A = 75 sq. inches
Thus the area of each triangle = 75 sq. in
Now to find the area of the regular polygon we have to multiply the area of each triangle and number of congruent figures.
Area of regular polygon = 7 × 75 sq. in
A = 525 sq. in
Thus the area of the 7-sided figure is 525 sq. in

Spiral Review

Question 3.
Which inequalities have b = 4 as one of its solutions?
2 + b ≥ 2      3b ≤ 14
8 − b ≤ 15     b − 3 ≥ 5
Type below:
_______________

Answer: b − 3 ≥ 5

Explanation:
Substitute b = 4 in the inequality
i. 2 + b ≥ 2
2 + 4 ≥ 2
6 ≥ 2
ii. 3b ≤ 14
3(4) ≤ 14
12 ≤ 14
iii. 8 − b ≤ 15
8 – 4 ≤ 15
4 ≤ 15
iv. b − 3 ≥ 5
4 – 3 ≥ 5
1 ≥ 5
1 is not greater than or equal to 5.

Question 5.
What is the area of triangle ABC?

________ ft²

Answer: 30 ft²

Explanation:
b = 6 ft
h = 10 ft
We know that,
Area of each triangle = bh/2
A = (6 ft)(10 ft)/2
A = 60 sq. ft/2
A = 30 sq. ft
Therefore the area of triangle ABC is 30 sq. ft

Question 6.
Marcia cut a trapezoid out of a large piece of felt. The trapezoid has a height of 9 cm and bases of 6 cm and 11 cm. What is the area of Marcia’s felt trapezoid?
________ cm²

Answer: 76.5 cm²

Explanation:
Marcia cut a trapezoid out of a large piece of felt.
The trapezoid has a height of 9 cm and bases of 6 cm and 11 cm.
Area of the trapezium = (b1 + b2)h/2
A = (6 + 11)9/2
A = 17 cm × 4.5 cm
A = 76.5 sq. cm
Therefore the area of Marcia’s felt trapezoid is 76.5 cm²

Share and Show – Page No. 573

Question 1.
Find the area of the figure.

________ ft²

Answer: 126 sq. ft

Explanation:
Figure 1:
l = 10 ft
w = 5 ft
A = lw
A = 10 ft × 5 ft
A = 50 sq. ft
Figure 2:
l = 10 ft
w = 5 ft
A = lw
A = 10 ft × 5 ft
A = 50 sq. ft
Figure 3:
b = 5 ft + 5 ft + 3 ft
b = 13 ft
h = 4 ft
Area of triangle = bh/2
A = 13 ft × 4 ft/2
A = 13 ft × 2 ft
A = 26 sq. ft
Add the areas of all the figures = 50 sq. ft + 50 sq. ft + 26 sq. ft
Thus the Area of the composite figure is 126 sq. ft.

Find the area of the figure.

Question 2.

________ mm²

Answer: 128.2 sq. mm

Explanation:
Figure 1:
b1 = 11 mm
b2 = 11 mm
h = 8.2 mm
Area of the trapezoid = (b1 + b2)h/2
A = (11 mm + 11 mm)8.2 mm/2
A = 22 mm × 4.1 mm
A = 90.2 sq. mm
Figure 2:
b1 = 11mm
b2 = 8mm
h = 4mm
Area of the trapezoid = (b1 + b2)h/2
A = (11mm + 8mm)4mm/2
A = 19mm × 2mm
A = 38 sq. mm
Add the areas of both figures = 90.2 sq. mm + 38 sq. mm
Thus the area of the figure is 128.2 sq. mm

Question 3.

________ m²

Answer: 144 sq. m

Explanation:
Figure 1:
l = 12 m
w = 7 m
Area of Rectangle = lw
A = 12m × 7m
A = 84 sq. m
Figure 2:
Area of right triangle = ab/2
a = 5m
b = 12m
A = (5m)(12m)/2
A = 30 sq. m
Figure 3:
Area of right triangle = ab/2
a = 5m
b = 12m
A = (5m)(12m)/2
A = 30 sq. m
Area of all figures = 84 sq. m + 30 sq. m + 30 sq. m = 144 sq. m.
Therefore the area of the figure is 144 sq. m

On Your Own

Question 4.
Find the area of the figure.

________ in.²

Answer: 184 sq. in

Explanation:
Figure 1:
b = 8 in
h = 6 in
Area of right triangle = ab/2
A = 8 in × 6 in/2
A = 24 sq. in
Figure 2:
Area of Rectangle = lw
A = 16 in × 6 in
A = 96 sq. in
Figure 3:
Area of right triangle = ab/2
b = 8 in
h = 8 in
A = 8 in × 8 in/2
A = 32 sq. in
Figure 4:
Area of right triangle = ab/2
b = 8 in
h = 8 in
A = 8 in × 8 in/2
A = 32 sq. in
Area of all figures = 24 sq. in + 96 sq. in + 32 sq. in + 32 sq. in = 184 sq. in
Thus the area of the figure = 184 sq. in.

Question 5.
Attend to Precision Find the area of the shaded region.

________ m²

Answer: 96.05 sq. m

Explanation:
Figure 1:
Area of Rectangle = lw
A = 12.75 m × 8.8 m
A = 112.2 sq. m
Figure 2:
Area of Rectangle = lw
l = 4.25 m
w = 3.3 m
A = 4.25 m × 3.3 m
A = 16.15 sq. m
Area of all the figures = 112.2 sq. m + 16.15 sq. m = 90.05 sq. m
Therefore the area of the figure = 90.05 sq. m

Unlock the Problem – Page No. 574

Question 6.
Marco made the banner shown at the right. What is the area of the yellow shape?

a. Explain how you could find the area of the yellow shape if you knew the areas of the green and red shapes and the area of the entire banner.
Type below:
_______________

Answer: I can find the area of the yellow shape by subtracting the areas of the green and red shapes from the area of the entire banner.

Question 6.
b. What is the area of the entire banner? Could you explain how you found it?
The area of the banner is ________ in.²

Answer: 1440 sq. in

Explanation:
The banner is a rectangle with a width of 48 inches and a length of 30 inches.
A = lw
A = 48 in × 30 in
A = 1440 sq. in
Therefore, the area of the banner is 1440 sq. in.

Question 6.
c. What is the area of the red shape? What is the area of each green shape?
The area of the red shape is ________ in.²
The area of each green shape is ________ in.²

Answer:
The area of the red shape is 360 in.²
The area of each green shape is 360 in.²

Explanation:
The red shape is a triangle with a base of 30 inches and a height of 24 inches.
A = bh/2
A = (30)(24)/2
A = 360 sq. in.
The area of the red triangle is 360 sq. in.
Each green shape is a triangle with a base of 15 inches and a height of 48 inches.
A = bh/2
A = 1/2 × 15 × 48
A = 720/2
A = 360 sq. in
Therefore the area of each green triangle is 360 sq. in.

Question 6.
d. What equation can you write to find A, the area of the yellow shape?
Type below:
_______________

Answer: A = 1440 – (360 + 360 + 360)

Question 6.
e. What is the area of the yellow shape?
The area of the yellow shape is ________ in.²

Answer: 360 sq. in

Explanation:
A = bh/2
A = 1/2 × 15 × 48
A = 720/2
A = 360 sq. in
Therefore the area of the yellow shape is 360 sq. in

Question 8.
Sabrina wants to replace the carpet in a few rooms of her house. Select the expression she can use to find the total area of the floor that will be covered. Mark all that apply.

Options:
a. 8 × 22 + 130 + \(\frac{1}{2}\) × 10 × 9
b. 18 × 22 − \(\frac{1}{2}\) × 10 × 9
c. 18 × 13 + \(\frac{1}{2}\) × 10 × 9
d. \(\frac{1}{2}\) × (18 + 8) × 22

Answer: 8 × 22 + 130 + \(\frac{1}{2}\) × 10 × 9

Explanation:
Figure 1:
l = 13 ft
w = 10 ft
Area of the rectangle = lw
A = 13 ft × 10 ft = 130
Figure 2:
b = 9 ft
h = 10 ft
Area of the triangle = bh/2
A = (9)(10)/2
A = 45 sq. ft
Figure 3:
Area of the rectangle = lw
l = 22 ft
w = 8 ft
The area of the composite figure is 8 × 22 + 130 + \(\frac{1}{2}\) × 10 × 9
Thus the correct answer is option A.

Composite Figures – Page No. 575

Find the area of the figure

Question 1.

________ cm²

Answer: 37 cm²

Explanation:
Area of square = s × s
A = 3 × 3 = 9 sq. cm
Area of Triangle = bh/2
A = 2 × 8/2 = 8 sq. cm
Area of the trapezoid = (b1 + b2)h/2
A = (5 + 3)5/2
A = 4 × 5 = 20 sq. in
Area of composite figure = 9 sq. cm + 8 sq. cm + 20 sq. in
A = 37 cm²

Question 2.

________ ft²

Answer:

Explanation:
Figure 1:
b = 9 ft
h = 6 ft
Area of Triangle = bh/2
A = (9ft)(6ft)/2
A = 27 sq. ft
Figure 2:
l = 12 ft
w = 9 ft
Area of the rectangle = lw
A = (12ft)(9ft)/2
A = 12 ft × 9 ft
A = 108 sq. ft
Figure 3:
Area of Triangle = bh/2
b = 9 ft
h = 10 ft
A = (10ft)(9ft)/2
A = 45 sq. ft
Area of the composite figure = 27 sq. ft + 108 sq. ft + 45 sq. ft = 180 sq. ft

Question 3.

________ yd²

Answer: 128 yd²

Explanation:
Figure 1:
b1 = 7 yd
b2 = 14 yd
h = 8 yd
Area of the trapezoid = (b1 + b2)h/2
A = (7yd + 14yd)8yd/2
A = 21 yd × 4 yd
A = 84 sq. yd
Figure 2:
b = 11 yd
h = 4 yd
Area of the parallelogram = bh
A = 11yd × 4yd = 44 sq. yd
Area of the composite figure = 84 sq. yd + 44 sq. yd = 128 sq. yd

Problem Solving

Question 4.
Janelle is making a poster. She cuts a triangle out of poster board. What is the area of the poster board that she has left?

________ in.²

Answer: 155 sq. in

Explanation:
The poster is a parallelogram, and it’s area is:
A = bh
A = 20 x 10
A = 200 sq. in
The area of the triangle that Janelle cut out of the poster board is:
A = 1/2bh
A = 1/2 x 10 x 9
A = 90/2
A = 45 sq. in
The area of the poster board that she has left is 200 sq. in – 45 sq. in = 155 sq. in

Question 5.
Michael wants to place grass on the sides of his lap pool. Find the area of the shaded regions that he wants to cover with grass.

________ yd²

Answer: 204 yd²

Explanation:
The area of the shaded region can be found by finding the total area and subtracting the area of the lap pool.
Total area = Area of the trapezium = 1/2 × (Sum of parallel sides) × distance between them
Sum of parallel sides = 25 yd + (3 + 12) = 40 yd
Distance between them = 12 yd
Total area = 1/2 × 40 × 12 = 240 yd²
Find the area of the lap pool.
Area = length × width = 12 × 3 = 36 yd²
Find the area of the shaded region
Area to be covered with grass = 240 – 36 = 204 yd²

Question 6.
Describe one or more situations in which you need to subtract to find the area of a composite figure.
Type below:
_______________

Answer:

Figure 1:
Area of Rectangle = lw
A = 12.75 m × 8.8 m
A = 112.2 sq. m
Figure 2:
Area of Rectangle = lw
l = 4.25 m
w = 3.3 m
A = 4.25 m × 3.3 m
A = 16.15 sq. m
Area of all the figures = 112.2 sq. m + 16.15 sq. m = 90.05 sq. m
Therefore the area of the figure = 90.05 sq. m

Lesson Check – Page No. 576

Question 1.
What is the area of the composite figure?

________ m²

Answer: 227 m²

Explanation:
Figure 1:
b = 7 m
h = 7 m
Area of the triangle = bh/2
A = (7m)(7m)/2
A = 24.5 sq. m
Figure 2:
b1 = 7m
b2 = 10m
h = 9m
Area of the trapezoid = (b1 + b2)h/2
A = (7m + 10m)9m/2
A = 17m × 4.5 m
A = 76.5 sq. m
Area of the rectangle = lw
A = 18m × 7m
A = 126 sq. m
Area of the figures = 24.5 sq. m + 76.5 sq. m + 126 sq. m = 227 sq. m
Thus the area of the figure is 227 sq. m

Question 2.
What is the area of the shaded region?

________ in.²

Answer: 251.5 in.²

Explanation:
Figure 1:
l = 21 in
w = 15 in
Area of triangle = bh/2
A = 21 in × 15 in/2
A = 157.5 sq. in
Figure 2:
b1 = 12 in
b2 = 15 in
h = 11 in
Area of the trapezoid = (b1 + b2)h/2
A = (12 in + 15 in)11 in/2
A = 27 in × 5.5 in
A = 148.5 sq. in
Figure 3:
b = 13 in
h = 14.4 in
Area of trinagle = bh/2
A = 13 × 14.4in/2
A = 13in × 7.2 in
A = 94 sq. in
The area of the shaded region is 94 sq. in + 157.5 sq. in = 251.5 in.²

Spiral Review

Question 3.
In Maritza’s family, everyone’s height is greater than 60 inches. Write an inequality that represents the height h, in inches, of any member of Maritza’s family.
Type below:
_______________

Answer: h > 60

Explanation:
Given, Maritza’s family, everyone’s height is greater than 60 inches.
The inequality is h > 60

Question 4.
The linear equation y = 2x represents the cost y for x pounds of apples. Which ordered pair lies on the graph of the equation?
Type below:
_______________

Answer: (2, 4)

Explanation:
y = 2x
put x = 2
y = 2(2)
y = 4
The ordered pair is (2,4)

Question 6.
A regular hexagon has sides measuring 7 inches. If the hexagon is divided into 6 congruent triangles, each has a height of about 6 inches. What is the approximate area of the hexagon?
________ in.²

Answer: 126 in.²

Explanation:
b = 7 in
h = 6 in
Number of congruent figures: 6
Area of the triangle = bh/2
A = (7in)(6in)/2
A = 21 sq. in
Area of regular hexagon = 6 × area of each triangle
A = 6 × 21 sq. in
A = 126 sq. in
Thus the approximate area of the hexagon is 126 sq. in.

Share and Show – Page No. 579

Question 1.
The dimensions of a 2-cm by 6-cm rectangle are multiplied by 5. How is the area of the rectangle affected?
Type below:
_______________

Answer: 25

Explanation:
The dimensions of a 2-cm by 6-cm rectangle are multiplied by 5.
Original Area:
Area of rectangle = lw
A = 2cm × 6cm = 12 sq. cm
New dimensions:
l = 6 × 5 = 30 cm
w = 2 × 5 = 10 cm
The new area is:
A = 10 cm × 30 cm = 300 sq. cm
New Area/ Original Area = 300/12 = 25
So, the new area is 25 times the original area.

Question 3.
Evan bought two square rugs. The larger one measured 12 ft square. The smaller one had an area equal to \(\frac{1}{4}\) the area of the larger one. What fraction of the side lengths of the larger rug were the side lengths of the smaller one?
Type below:
_______________

Answer:
Since the area of the smaller rug is \(\frac{1}{4}\) times the area of the larger rug, the side lengths of the smaller rug are \(\frac{1}{2}\) of the side lengths of the larger one.

Question 4.
On Silver Island, a palm tree, a giant rock, and a buried treasure form a triangle with a base of 100 yd and a height of 50 yd. On a map of the island, the three landmarks form a triangle with a base of 2 ft and a height of 1 ft. How many times the area of the triangle on the map is the area of the actual triangle?

Type below:
_______________

Answer: 45,000

Explanation:
Area of triangle= (1/2) (base x height)
1 yard = 3 foot
Base of the actual triangle= 100 yards= 300ft
Height of the actual triangle= 50 yards= 150ft.
Area of the actual triangle= (1/2) (300 x 150) = 45000 square ft
The base of the triangle on the map = 2ft
Height of the triangle on the map= 1ft
Area of the triangle on the map= (1/2) (2 x 1) = 1 square ft.
The actual area is 45000 time the area of the map

On Your Own – Page No. 580

Question 5.
A square game board is divided into smaller squares, each with sides one-ninth the length of the sides of the board. Into how many squares is the game board divided?
________ small squares

Answer: 81 small squares

Explanation:
Each side of the game board is divided into 9 lengths.
The game board is divided into 9 × 9 = 81 small squares.
Thus, the board is divided into 81 small squares.

Question 6.
Flynn County is a rectangle measuring 9 mi by 12 mi. Gibson County is a rectangle with an area 6 times the area of Flynn County and a width of 16 mi. What is the length of Gibson County?
________ mi

Answer: 40.5 mi.

Explanation:
Flynn County is a rectangle measuring 9 mi by 12 mi.
Gibson County is a rectangle with an area 6 times the area of Flynn County and a width of 16 mi.
The area of Flynn Country is
A = 9 × 12 = 108 sq. mi
The area of Gibson Country is
A = 6 × 108 = 648 sq. mi
A = lw
648 = 16 × l
l = 648/16
l = 40.5 mi
Therefore the length of Gibson Country is 40.5 miles.

Question 7.
Use Diagrams Carmen left her house and drove 10 mi north, 15 mi east, 13 mi south, 11 mi west, and 3 mi north. How far was she from home?
________ miles

Answer:
15 mi – 11 mi = 4 miles
Thus Carmen is 4 miles from home.

Question 8.
Bernie drove from his house to his cousin’s house in 6 hours at an average rate of 52 mi per hr. He drove home at an average rate of 60 mi per hr. How long did it take him to drive home?
________ hours

Answer: 5.2 hours

Explanation:
Given,
Bernie drove from his house to his cousin’s house in 6 hours at an average rate of 52 mi per hr. He drove home at an average rate of 60 mi per hr.
The distance from Bernie’s house to his cousin’s house is
52 mi/hr × 6hr = 52 × 6mi = 312 miles
On the way back, he drove for
312mi ÷ 60mi/hr = 5.2 hours
Therefore it takes 5.2 hours for Bernie to drive home.

Problem Solving Changing Dimensions – Page No. 581

Read each problem and solve.

Question 1.
The dimensions of a 5-in. by 3-in. rectangle are multiplied by 6. How is the area affected?
Type below:
_______________

Answer: 36

Explanation:
Original area: A = 5 × 3 = 15 sq. in
new dimensions:
l = 6 × 5 = 30 in
w = 6 × 3 = 18 in
New Area = l × w
A = 30 in × 18 in
A = 540 sq. in
Thus new area = 540 sq. in
new area/original area = 540/15 = 36
Thus the area was multiplied by 36.

Question 3.
The dimensions of a 3-ft by 6-ft rectangle are multiplied by \(\frac{1}{3}\). How is the area affected?
Type below:
_______________

Answer: 1/9

Explanation:
Original area: A = 3 ft × 6 ft = 18 sq. ft
new dimensions:
l = 3 ft × \(\frac{1}{3}\) = 1 ft
w = 6 ft × \(\frac{1}{3}\) = 2 ft
New area: A = 1 ft × 2 ft = 2 sq. ft
new area/original area = 2/18 = 1/9
The area was multiplied by 1/9.

Question 4.
The dimensions of a triangle with base 10 in. and height 4.8 in. are multiplied by 4. How is the area affected?
Type below:
_______________

Answer: 16

Explanation:
original area: A = 10 in × 4.8 in = 48 sq. in
new dimensions:
l = 10 in × 4 = 40 in
w = 4.8 in × 4 = 19.2 in
new area = l × w
A = 40 in × 19.2 in
A = 768 sq. in
new area/original area = 768/48
Thus the area was multiplied by 16.

Question 5.
The dimensions of a 1-yd by 9-yd rectangle are multiplied by 5. How is the area affected?
Type below:
_______________

Answer: 25

Explanation:
original area: A = 1 yd × 9 yd = 9 sq. yd
new dimensions:
l = 1 yd × 5 = 5 yd
w = 9 yd × 5 = 45 yd
new area = 5 yd × 45 yd = 225 sq. yd
new area/original area = 225 sq. yd/9 sq. yd
Thus the area was multiplied by 25.

Question 7.
The dimensions of a triangle are multiplied by \(\frac{1}{4}\). The area of the smaller triangle can be found by multiplying the area of the original triangle by what number?
Type below:
_______________

Answer: 1/16

Explanation:
We can find the area of the original triangle by multiplying with \(\frac{1}{4}\)
\(\frac{1}{4}\) × \(\frac{1}{4}\) = \(\frac{1}{16}\)
Thus the area was multiplied by \(\frac{1}{16}\)

Question 8.
Write and solve a word problem that involves changing the dimensions of a figure and finding its area.
Type below:
_______________

Answer:
The dimensions of a triangle with a base 1.5 m and height 6 m are multiplied by 2. How is the area affected?
Original area:
Area of triangle = bh/2
A = (1.5m)(6m)/2
A = 4.5 sq. m
new dimensions:
b = 1.5m × 2 = 3 m
h = 6 m × 2 = 12 m
Area of triangle = bh/2
A = (12m × 3m)/2
A = 6m × 3m
A = 18 sq. m
new area/original area = 18 sq. m/4.5 sq. m
The area was multiplied by 4.

Lesson Check – Page No. 582

Question 1.
The dimensions of Rectangle A are 6 times the dimensions of Rectangle B. How do the areas of the rectangles compare?
Type below:
_______________

Answer: Area of Rectangle A = 36 × Area of Rectangle B

Explanation:
The area of Rectangle A will always be 36 times the area of Rectangle B.
If Rectangle B has length 1 and width 2, Rectangle A will have length 6 and width 12. By multiplying, Rectangle A will have an area of 72 and B 2. Divide the two numbers and you will have 36.

Question 2.
A model of a triangular piece of jewelry has an area that is \(\frac{1}{4}\) the area of the jewelry. How do the dimensions of the triangles compare?
Type below:
_______________

Answer: Model dimensions = 1/2 jewelry dimensions

Explanation:
The dimensions of the model area
1/4 ÷ 2 = 1/2 times the dimensions of the piece of jewelry.

Spiral Review

Question 4.
Graph y > 3 on a number line.
Type below:
_______________

Answer:

Question 5.
The parallelogram below is made from two congruent trapezoids. What is the area of the shaded trapezoid?

________ mm²

Answer: 1312.5 sq. mm

Explanation:
Given,
b1 = 25mm
b2 = 50mm
h = 35mm
Area of the trapezoid = (b1 + b2)h/2
A = (25mm + 50mm)35mm/2
A = 75mm × 35mm/2
A = 1312.5 sq. mm
Thus the area of the shaded region is 1312.5 sq. mm

Question 6.
A rectangle has a length of 24 inches and a width of 36 inches. A square with side length 5 inches is cut from the middle and removed. What is the area of the figure that remains?
________ in.²

Answer: 839 sq. in

Explanation:
Area of rectangle = lw
A = 24 in × 36 in
A = 864 sq. in
Area of square = s × s
s = 5 in
A = 5 in × 5 in
A = 25 sq. in
Area of the figure that remains = 864 sq. in – 25 sq. in
A = 839 sq. in

Share and Show – Page No. 585

Question 1.
The vertices of triangle ABC are A(−1, 3), B(−4, −2), and C(2, −2). Graph the triangle and find the length of side \(\overline { BC } \).
________ units

Answer: 6 units

Give the coordinates of the unknown vertex of rectangle JKLM, and graph.

Question 2.

Type below:
_______________

Answer:

Question 3.

Type below:
_______________

Answer:

On Your Own

Question 4.
Give the coordinates of the unknown vertex of rectangle PQRS, and graph.

Type below:
_______________

Answer:

Question 5.
The vertices of pentagon PQRST are P(9, 7), Q(9, 3), R(3, 3), S(3, 7), and T(6, 9). Graph the pentagon and find the length of side \(\overline { PQ } \).
________ units

Answer: 4 units

Problem Solving + Applications – Page No. 586

The map shows the location of some city landmarks. Use the map for 6–7.

Question 6.
A city planner wants to locate a park where two new roads meet. One of the new roads will go to the mall and be parallel to Lincoln Street which is shown in red. The other new road will go to City Hall and be parallel to Elm Street which is also shown in red. Give the coordinates for the location of the park.
Type below:
_______________

Answer:

By seeing we can say that the coordinates for the location of the park is (1,1)

Question 7.
Each unit of the coordinate plane represents 2 miles. How far will the park be from City Hall?
________ miles

Answer: 8 units

Explanation:
The distance from City Hall to Park is 4 units.
Each unit = 2 miles
So, 2 miles × 4 = 8 miles
The distance from City Hall to Park is 8 miles.

Question 8.
\(\overline { PQ } \) is one side of right triangle PQR. In the triangle, ∠P is the right angle, and the length of side \(\overline { PR } \) is 3 units. Give all the possible coordinates for vertex R.

Type below:
_______________

Answer:

The coordinates of S are (-2,-2)
The coordinates of R are (3,-2)

Question 9.
Use Math Vocabulary Quadrilateral WXYZ has vertices with coordinates W(−4, 0), X(−2, 3), Y(2, 3), and Z(2, 0). Classify the quadrilateral using the most exact name possible and explain your answer.
Type below:
_______________

Answer: Trapezoid

By seeing the above graph we can say that a suitable quadrilateral is a trapezoid.

Question 10.
Kareem is drawing parallelogram ABCD on the coordinate plane. Find and label the coordinates of the fourth vertex, D, of the parallelogram. Draw the parallelogram. What is the length of side CD? How do you know?

Type below:
_______________

Answer:

Figures on the Coordinate Plane – Page No. 587

Question 1.
The vertices of triangle DEF are D(−2, 3), E(3, −2), and F(−2, −2). Graph the triangle, and find the length of side \(\overline { DF } \).
________ units

Answer: 5 units

Explanation:
Vertical distance of D from 0: |3| = 3 units
Vertical Distance of F from 0: |-2| = 2 units
The points are in different quadrants, so add to find the distance from D to F: 3 + 2 = 5

Graph the figure and find the length of side \(\overline { BC } \).

Question 2.
A(1, 4), B(1, −2), C(−3, −2), D(−3, 3)
________ units

Answer: 4 units

Question 3.
A(−1, 4), B(5, 4), C(5, 1), D(−1, 1)
________ units

Answer: 3 units

Problem Solving

Question 4.
On a map, a city block is a square with three of its vertices at (−4, 1), (1, 1), and (1, −4). What are the coordinates of the remaining vertex?
Type below:
_______________

Answer: (-4, -4)

Question 5.
A carpenter is making a shelf in the shape of a parallelogram. She begins by drawing parallelogram RSTU on a coordinate plane with vertices R(1, 0), S(−3, 0), and T(−2, 3). What are the coordinates of vertex U?
Type below:
_______________

Answer: (2, 3)

Question 6.
Explain how you would find the fourth vertex of a rectangle with vertices at (2, 6), (−1, 4), and (−1, 6).
Type below:
_______________

Answer:

Explanation:
Midpoint of AC = (2 + (-1))/2 = 1/2; (6 + 6)/2 = 6
Midpoint of AC = (1/2, 6)
Midpoint of BD = (-1 + a)/2 = (-1 + a)/2; (b + 4)/2
(-1 + a)/2 = 1/2
-1 + a = 1
a = 2
(b + 4)/2 = 6
b + 4 = 12
b = 12 – 4
b = 8
So, the fouth vertex D is (2, 8)

Lesson Check – Page No. 588

Question 1.
The coordinates of points M, N, and P are M(–2, 3), N(4, 3), and P(5, –1). What coordinates for point Q make MNPQ a parallelogram?
Type below:
_______________

Answer: Q (-1, -1)

Question 2.
Dirk draws quadrilateral RSTU with vertices R(–1, 2), S(4, 2), T(5, –1), and U( 2, –1). Which is the best way to classify the quadrilateral?
Type below:
_______________

Answer:
The bases and height are not equal.
So, the best way to classify the quadrilateral is Trapezoid.

Spiral Review

Question 3.
Marcus needs to cut a 5-yard length of yarn into equal pieces for his art project. Write an equation that models the length l in yards of each piece of yarn if Marcus cuts it into p pieces.
Type below:
_______________

Answer:
Given,
Marcus needs to cut a 5-yard length of yarn into equal pieces for his art project.
To find the length we have to divide 5 by p.
Thus the equation is l = 5 ÷ p

Question 5.
A trapezoid is 6 \(\frac{1}{2}\) feet tall. Its bases are 9.2 feet and 8 feet long. What is the area of the trapezoid?
________ ft²

Answer: 55.9

Explanation:
Given that,
A trapezoid is 6 \(\frac{1}{2}\) feet tall. Its bases are 9.2 feet and 8 feet long.
We know that
Area of trapezoid = (b1 + b2)h/2
A = (9.2 + 8)6.5/2
A = (17.2 × 6.5)/2
A = 55.9 ft²

Question 6.
The dimensions of the rectangle below will be multiplied by 3. How will the area be affected?

Type below:
_______________

Answer:
3 × 3 = 9
the area will be multiplied by 9.

Chapter 10 Review/Test – Page No. 589

Question 1.
Find the area of the parallelogram.

________ in.²

Answer: 67.5

Explanation:
b = 9 in
h = 7.5 in
Area of the parallelogram is bh
A = 9 in × 7.5 in
A = 67.5 sq. in
Thus the area of the parallelogram is 67.5 in.²

Question 2.
A wall tile is two different colors. What is the area of the white part of the tile? Explain how you found your answer.

________ in.²

Answer: 11 in.²

Explanation:
b = 5.5 in
h = 4 in
We know that
The area of the triangle is bh/2
A = (5.5 in × 4 in)/2
A = 22/2 sq. in
A = 11 sq. in
Thus the area of one triangle is 11 in.²

Question 3.
The area of a triangle is 36 ft². For numbers 3a–3d, select Yes or No to tell if the dimensions could be the height and base of the triangle.
3a. h = 3 ft, b = 12 ft
3b. h = 3 ft, b = 24 ft
3c. h = 4 ft, b = 18 ft
3d. h = 4 ft, b = 9 ft
3a. ____________
3b. ____________
3c. ____________
3d. ____________

Answer:
3a. No
3b. Yes
3c. Yes
3d. No

Explanation:
The area of a triangle is 36 ft².
3a. h = 3 ft, b = 12 ft
The area of the triangle is bh/2
A = (12 × 3)/2
A = 6 × 3 = 18
A = 18 sq. ft
Thus the answer is no.
3b. h = 3 ft, b = 24 ft
The area of the triangle is bh/2
A = (3 × 24)/2
A = 3 × 12
A = 36 sq. ft
Thus the answer is yes.
3c. h = 4 ft, b = 18 ft
The area of the triangle is bh/2
A = (4 × 18)/2
A = 4 × 9
A = 36 sq. ft
Thus the answer is yes.
3d. h = 4 ft, b = 9 ft
The area of the triangle is bh/2
A = (4 × 9)/2
A = 2 ft × 9 ft
A = 18 sq. ft
Thus the answer is no.

Question 4.
Mario traced this trapezoid. Then he cut it out and arranged the trapezoids to form a rectangle. What is the area of the rectangle?

________ in.²

Answer: 112

Explanation:
b1 = 10 in
b2 = 4 in
h = 8 in
We know that
Area of trapezoid = (b1 + b2)h/2
A = (10 in + 4 in)8 in/2
A = 14 in × 4 in
A = 56 sq. in
Thus the area of the trapezoid for the above figure is 56 sq. in

Chapter 10 Review/Test Page No. 590

Question 5.
The area of the triangle is 24 ft². Use the numbers to label the height and base of the triangle.

Type below:
_______________

Answer: 6, 8

Explanation:

Area of the triangle = bh/2
A = (6 ft × 8 ft)/2
A = 6 ft × 4 ft
A = 24 ft²

Question 6.
A rectangle has an area of 50 cm². The dimensions of the rectangle are multiplied to form a new rectangle with an area of 200 cm². By what number were the dimensions multiplied?
Type below:
_______________

Answer: 2

Explanation:
Let A₁ = the original area a
and A₂ = the new area
and n = the number by which the dimensions were multiplied
A₁ = lw
A₂ = nl × nw = n²lw
A₂/A₁ = (n²lw)/(lw) = 200/50
n² = 4
n = 2

Question 7.
Sami put two trapezoids with the same dimensions together to make a parallelogram.

The formula for the area of a trapezoid is \(\frac{1}{2}\)(b₁ + b₂)h. Explain why the bases of a trapezoid need to be added in the formula.
Type below:
_______________

Answer:
A trapezoid is a 4-sided figure with one pair of parallel sides. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height
sum by the height of the trapezoid, and then divide the result by 2.

Question 8.
A rectangular plastic bookmark has a triangle cut out of it. Use the diagram of the bookmark to complete the table.


Type below:
_______________

Answer: 10 – 0.5 = 9.5

Chapter 10 Review/Test Page No. 591

Question 10.
A pillow is in the shape of a regular pentagon. The front of the pillow is made from 5 pieces of fabric that are congruent triangles. Each triangle has an area of 22 in.². What is the area of the front of the pillow?
________ in.²

Answer: 110 in.²

Explanation:
Given,
Each triangle has an area of 22 in.²
The front of the pillow is made from 5 pieces of fabric that are congruent triangles.
Area of front pillow = 5 × 22 in.² = 110 in.²

Question 11.
Which expressions can be used to find the area of the trapezoid? Mark all that apply.

Options:
a. \(\frac{1}{2}\) × (5 + 2) × 4.5
b. \(\frac{1}{2}\) × (2 + 4.5) × 5
c. \(\frac{1}{2}\) × (5 + 4.5) × 2
d. \(\frac{1}{2}\) × (6.5) × 5

Answer: \(\frac{1}{2}\) × (2 + 4.5) × 5

Explanation:
b1 = 4.5 in
b2 = 2
h = 5 in
We know that,
Area of trapezoid = (b1 + b2)h/2
A = \(\frac{1}{2}\) × (2 + 4.5) × 5
Thus the correct answer is option B.

Question 12.
Name the polygon and find its area. Show your work.

Type below:
_______________

Answer: 31 sq. in.

Explanation:
b = 5 in
h = 6.2 in
The area of the triangle is bh/2
A = (5 × 6.2)/2
A = 31/2
A = 15.5 sq. in
There are 2 triangles.
To find the area of the regular polygon we have to multiply the area of the triangle and number of triangles.
A = 15.5 × 2 = 31

Chapter 10 Review/Test Page No. 592

Question 13.
A carpenter needs to replace some flooring in a house.

Select the expression that can be used to find the total area of the flooring to be replaced. Mark all that apply.
Options:
a. 19 × 14
b. 168 + 12 × 14 + 60
c. 19 × 24 − \(\frac{1}{2}\) × 10 × 12
d. 7 × 24 + 12 × 14 + \(\frac{1}{2}\) × 10 × 12

Answer: B, C, D

Explanation:

Here we have to use the Area of the parallelogram, Area of the rectangle, and area of triangle formulas.
Thus the suitable answers are 168 + 12 × 14 + 60, 19 × 24 − \(\frac{1}{2}\) × 10 × 12 and 7 × 24 + 12 × 14 + \(\frac{1}{2}\) × 10 × 12.

Question 14.
Ava wants to draw a parallelogram on the coordinate plane. She plots these 3 points.

Part A
Find and label the coordinates of the fourth vertex, K, of the parallelogram. Draw the parallelogram
Type below:
_______________

Answer: K (2, 1)

Question 14.
Part B
What is the length of side JK? How do you know?
Type below:
_______________

Answer:
By using the above graph we can find the length of JK.
The length of the JK is 2 units.

Chapter 10 Review/Test Page No. 593

Question 15.
Joan wants to reduce the area of her posters by one-third. Draw lines to match the original dimensions in the left column with the correct new area in the right column. Not all dimensions will have a match.

Type below:
_______________

Answer:

Question 16.
Alex wants to enlarge a 4-ft by 6-ft vegetable garden by multiplying the dimensions of the garden by 2.
Part A
Find each area.
Area of original garden : ________ ft²
Area of enlarged garden : ________ ft²

Answer:
B = 4 ft
w = 6 ft
Area of original garden = 4 ft × 6 ft
A = 24 sq. ft
Now multiply 2 to base and width
b = 4 × 2 = 8 ft
w = 6 × 2 = 12 ft
Area of original garden = bw
A = 8 ft × 12 ft
A = 96 sq. ft

Question 16.
Suppose the point (3, 2) is changed to (3, 1) on this rectangle. What other point must change so the figure remains a rectangle? What is the area of the new rectangle?

Type below:
_______________

Answer:
Point: (-2, 2) would change to (-2, 1)
Rectangle:
B = 5 units
W = 4 units
Area of the rectangle = b × w
A = 5 × 4 = 20
A = 20 sq. units

Chapter 10 Review/Test Page No. 594

Question 18.
Look at the figure below. The area of the parallelogram and the areas of the two congruent triangles formed by a diagonal are related. If you know the area of the parallelogram, how can you find the area of one of the triangles?

Type below:
_______________

Answer:
Each of the diagonals of a parallelogram divides it into two congruent triangles, as we saw when we proved properties like that the opposite sides are equal to each other or that the two pairs of opposite angles are congruent. Since those two triangles are congruent, their areas are equal.
We also saw that the diagonals of the parallelogram bisect each other, and so create two additional pairs of congruent triangles.
When comparing the ratio of areas of triangles, we often look for an equal base or an equal height.

Question 20.
Eliana is drawing a figure on the coordinate grid. For numbers 20a–20d, select True or False for each statement.
20a. The point (−1, 1) would be the fourth vertex of a square.
20b. The point (1, 1) would be the fourth vertex of a trapezoid.
20c. The point (2, -1) would be the fourth vertex of a trapezoid.
20d. The point (−1, -1) would be the fourth vertex of a square.
20a. ____________
20b. ____________
20c. ____________
20d. ____________

Answer:
20a. False
20b. False
20c. True
20d. True

Conclusion:

With the help of the above-provided links you can complete the homework within time without any mistakes. Test your knowledge by solving the problems mentioned in our website. Stay with us to get the solution keys of all Go Math Grade 6 Chapters from 1 to 13.

Go Math Grade 2 Answer Key Chapter 5 2-Digit Subtraction answer key is useful for students who are preparing for their examinations and can download this pdf for free of cost. In this chapter, each and every question was explained in detail which helps students to understand easily. Go Math Grade 2 Answer Key Chapter 5 2-Digit Subtraction explains different types of questions on 2 Digit Subtraction.

Go Math Grade 2 Answer Key Chapter 5 2-Digit Subtraction

In this chapter, we can see different topics on Break Apart Ones to Subtract, Break Apart Numbers to Subtract, Model Regrouping for Subtraction, Model and Record 2-Digit Subtraction, 2-Digit Subtraction, etc. Those topics were being set up by the mathematical professionals as indicated by the most recent release. Look down this page to get the answers to all the inquiries. Click on the links to look at the subjects shrouded in this chapter 2-Digit Subtraction.

Chapter: 9-  2-Digit Subtraction

2-Digit Subtraction Show What You Know
2-Digit Subtraction Vocabulary Builder
2-Digit Subtraction Game: Subtraction Search
2-Digit Subtraction Vocabulary Game

Lesson 1: Algebra • Break Apart Ones to Subtract

Lesson 5.1 Algebra • Break Apart Ones to Subtract
Algebra • Break Apart Ones to Subtract Homework & Practice 5.1

Lesson 2: Algebra • Break Apart Numbers to Subtract

Lesson 5.2 Algebra • Break Apart Numbers to Subtract
Algebra • Break Apart Numbers to Subtract Homework & practice 5.2

Lesson 3: Model Regrouping for Subtraction

Lesson 5.3 Model Regrouping for Subtraction
Model Regrouping for Subtraction Homework & Practice 5.3

Lesson 4: Model and Record 2-Digit Subtraction

Lesson 5.4 Model and Record 2-Digit Subtraction
Model and Record 2-Digit Subtraction Homework & Practice 5.4

Lesson 5: 2-Digit Subtraction

Lesson 5.5 2-Digit Subtraction
2-Digit Subtraction Homework & practice 5.5

Lesson 6: Practice 2-Digit Subtraction

Lesson 5.6 Practice 2-Digit Subtraction
Practice 2-Digit Subtraction Homework & Practice 5.6

Mid-Chapter Checkpoint

2-Digit Subtraction Mid-Chapter Checkpoint

Lesson 7: Rewrite 2-Digit Subtraction

Lesson 5.7 Rewrite 2-Digit Subtraction
Rewrite 2-Digit Subtraction Homework & Practice 5.7

Lesson 8: Add to Find Differences

Lesson 5.8 Add to Find Differences
Add to Find Differences Homework & practice 5.8

Lesson 9: Problem Solving • Subtraction

Lesson 5.9 Problem Solving • Subtraction
Problem Solving • Subtraction Homework & Practice 5.9

Lesson 10: Algebra • Write Equations to Represent Subtraction

Lesson 5.10 Algebra • Write Equations to Represent Subtraction
Algebra • Write Equations to Represent Subtraction Homework & Practice 5.10

Lesson 11: Solve Multistep problems

Lesson 5.11 Solve Multistep Problems
Solve Multistep Problems Homework & Practice 5.11

Chapter 5 Review/Test

2-Digit Subtraction Chapter 5 Review Test

Curious about Math

There are hundreds of different kinds of dragonflies. If 52 dragonflies are in a garden and 10 fly away, how many dragonflies are left? How many are left if 10 more fly away?

Answer:
The total number of files left is 32 files.

Explanation:
As there are hundreds of different kinds of dragonflies and if 52 dragonflies are in a garden and 10 flies away, so the number of files left is 52 – 10= 42 files and again there are 10 more flies away. So there will be 42 – 10= 32 files left.

2-Digit Subtraction Show What You Know

Subtraction Patterns
Subtract 2. Complete each subtraction sentence.

Question 1.

Question 2.
6 – __ = ___

Answer:
On subtracting 6 – 2 we will get the result as 4.

Explanation:
By subtracting 2 with 6 we will get the result as 6 – 2= 4.

Question 3.
5 – __ = __

Answer:
On subtracting 5 – 2 we will get the result as 3.

Explanation:
By subtracting 2 with 5 we will get the result as 5 – 2= 3.

Question 4.
4 – ___ = __

Answer:
On subtracting 4 – 2 we will get the result as 2.

Explanation:
By subtracting 2 with 4 we will get the result as 4 – 2= 2.

Question 5.
3 – __ = __

Answer:
On subtracting 3 – 2 we will get the result as 1.

Explanation:
By subtracting 2 with 3 we will get the result as 3 – 2= 1.

Question 6.
2 – _ = __

Answer:
On subtracting 2 – 2 we will get the result as 0.

Explanation:
By subtracting 2 with 2 we will get the result as 2 – 2= 0.

Subtraction Facts
Write the difference.

Question 7.

Answer:
On subtracting 8 – 5 we will get the result as 3.

Explanation:
By subtracting 5 with 8 we will get the result as 8 – 5= 3.

Question 8.

Answer:
On subtracting 14 – 6 we will get the result as 8.

Explanation:
By subtracting 6 with 14 we will get the result as 14 – 6= 8.

Question 9.

Answer:
On subtracting 9 – 6 we will get the result as 3.

Explanation:
By subtracting 6 with 9 we will get the result as 9 – 6= 3.

Question 10.

Answer:
On subtracting 16 – 7 we will get the result as 9.

Explanation:
By subtracting 7 with 16 we will get the result as 16 – 7= 9.

Question 11.

Answer:
On subtracting 12 – 6 we will get the result as 6.

Explanation:
By subtracting 6 with 12 we will get the result as 12 – 6= 6.

Question 12.

Answer:
On subtracting 10 – 8 we will get the result as 2.

Explanation:
By subtracting 8 with 10 we will get the result as 10 – 8= 2.

Tens and Ones
Write how many tens and ones are in each model.

Question 13.
54

__ tens __ ones

Answer:
The number of tens is 5 and the number of ones is 4.

Explanation:
In the above image, we can see 10 blocks with 5 rows. Which are 10 × 5= 50 blocks, so there are 5 tens and we can see 4 blocks which are 4 ones. So the total number of blocks is 50 + 4= 54 blocks.

Question 14.
45

__ tens __ ones

Answer:
The number of tens is 4 and the number of ones is 5.

Explanation:
In the above image, we can see 10 blocks with 4 rows. Which are 10 × 4= 40 blocks, so there are 4 tens and we can see 5 blocks which are 5 ones. So the total number of blocks is 40 + 5= 45 blocks.

2-Digit Subtraction Vocabulary Builder

Visualize It
Fill in the boxes of the graphic organizer.

Understand Vocabulary
Draw a line to complete the sentence.

Answer:
1. A digit can be 0,1,2,3,4,5,6,7,8, or 9.
2. You can regroup to trade 10 ones for 1 ten.
3. 20 ones are the same as 2 tens.

Explanation:

1.  A digit is a single symbol that is used to make numerals, so the digits can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 are the ten digits which we will use every day.
2. Here, regrouping is defined as the process of making and then carrying out the operation like addition with two-digit numbers or larger than the two-digit numbers. And we use regrouping in addition when the sum of two digits in the place value column is greater than nine. And Regrouping in subtraction is a method of interchanging one ten into ten ones. This regrouping of subtraction is used to work out the different subtraction problems. We can regroup to trade 10 ones for 1 ten. And we can regroup to trade 10 ones for 1 ten.
3. 20 ones are the same as 2 tens. As two tens mean 2 × 10= 20 and 20 × 1= 20, so 20 ones are the same as 2 tens.

2-Digit Subtraction Game: Subtraction Search

Materials Search
• 3 sets of number cards 4 – 9 • 18
Play with a partner.
1. Shuffle all the cards. Place them face down in one stack.
2. Take one card. Find a square with a subtraction problem with this number as the difference. Your partner checks your answer.
3. If you are correct, place a on that square. If there is no match, skip your turn.
4. Take turns. The first player to have on all the squares wins.

2-Digit Subtraction Vocabulary Game

Going Places with GOMATH! Words

Bingo

For 3 to 6 players

Materials

• 1 set of word cards
• 1 Bingo board for each player
• game markers

How to Play

1. The caller chooses a word card and reads the word. Then the caller puts the word card in a second pile.
2. Players put a marker on the word each time they find it on their Bingo boards.
3. Repeat steps 1 and 2 until a player marks 5 boxes in a line going down, across, or on a slant and calls “Bingo.”
4. Check the answers. Have the player who said “Bingo” read the words aloud while the caller checks the word cards in the second pile.

The Write Way

Reflect
Choose one idea. Write about it in the space below.

• Explain how drawing quick pictures helps you add 2-digit numbers.
• Tell about all the different ways you can add 2-digit numbers.
• Write about a time that you helped explain something to a classmate. What was your classmate having trouble with? How did you help him or her?

Lesson 5.1 Algebra • Break Apart Ones to Subtract

Essential Question
How does breaking apart a number make subtracting easier?

Listen and Draw

Write two addends for each sum.

Answer:
The two addends for the first image are 3 and 4.
The two addends for the second image are 4 and 5.
The two addends for the third image are 2 and 3.
The two addends for the fourth image are 3 and 3.
The two addends for the fifth image are 2 and 2.
The two addends for the sixth image are 4 and 4.

Explanation:

As addend can be defined as the numbers are added together to get the sum. Here the given sum is 7, so to get the sum 7 we will take the two addends as 3 + 4 so we can get the sum as 7. The given sum is 9, so to get the sum 9 we will take the two addends 4 + 5 so we can get the sum as 9. The given sum is 5, so to get the sum 5 we will take the two addends 2 + 3 so we can get the sum as 5. The given sum is 6, so to get the sum 6 we will take the two addends 3 + 3 so we can get the sum as 6. the given sum is 4, so to get the sum 4 we will take the two addends 2 + 2 so we can get the sum as 4. The given sum is 8, so to get the sum 8 we will take the two addends
4 + 4 so we can get the sum as 8.

Math Talk
MATHEMATICAL PRACTICES

Describe how you chose addends for each sum.

Answer:
The addends are chosen by the given sum. As addend can be defined as the numbers are added to together to get the sum. So we have chosen the two addends by the given sum.

Model and Draw

Break apart ones. Subtract in two steps.

So, 63 − 7 = ___.

Answer:
The subtraction of 63 – 7 is 56.

Explanation:
Here, we have started at 63 and subtracted 3, to subtract 3 on the number line jump makes a jump from 63 to 60 and the size of the jump is 3 and we will get 60. Then we have to subtract 4, so we will start from 60 on the number line jump makes a jump from 60 to 56 and the size of the jump is 4 and we will get 56. So the subtraction of 63 – 7 is 56.

Share and Show MATH BOARD

Break apart ones to subtract. Write the difference.

Question 1.

Answer:
The subtraction of 55 – 8 is 47.

Explanation:
Here, we have started at 55 and subtracted 5, to subtract 5 on the number line jump makes a jump from 55 to 50 and the size of the jump is 5 and we will get 50. Then we have to subtract 3, so we will start from 50 on the number line jump makes a jump from 50 to 47 and the size of the jump is 3 and we will get 47. So the subtraction of 55 – 8 is 47.

Question 2.

Answer:
The subtraction of 42 – 5 is 37.

Explanation:
Here, we have started at 42 and subtracted 2, to subtract 2 on the number line jump makes a jump from 42 to 40 and the size of the jump is 2 and we will get 40. Then we have to subtract 3, so we will start from 40 on the number line jump makes a jump from 40 to 37 and the size of the jump is 3 and we will get 37. So the subtraction of 42 – 5 is 37.

Question 3.
41 – 9 = __

Answer:
The subtraction of 41 – 9 is 32.

Explanation:
Here, we have started at 41 and subtracted 4, to subtract 4 on the number line jump makes a jump from 41 to 37 and the size of the jump is 4 and we will get 37. Then we have to subtract 5, so we will start from 37 on the number line jump makes a jump from 37 to 32 and the size of the jump is 5 and we will get 32. So the subtraction of 41 – 9 is 32.

Question 4.
53 – 6 = __

Answer:
The subtraction of 53 – 6 is 47.

Explanation:
Here, we have started at 53 and subtracted 3, to subtract 3 on the number line jump makes a jump from 53 to 50 and the size of the jump is 3 and we will get 50. Then we have to subtract 3, so we will start from 50 on the number line jump makes a jump from 50 to 47 and the size of the jump is 3 and we will get 47. So the subtraction of 53 – 6 is 47.

Question 5.
44 – 7 = __

Answer:
The subtraction of 44 – 7 is 37.

Explanation:
Here, we have started at 44 and subtracted 3, to subtract 3 on the number line jump makes a jump from 44 to 41 and the size of the jump is 3 and we will get 41. Then we have to subtract 4, so we will start from 41 on the number line jump makes a jump from 41 to 37 and the size of the jump is 4 and we will get 37. So the subtraction of 44 – 7 is 37.

Question 6.
52 – 8 = __

Answer:
The subtraction of 52 – 8 is 44.

Explanation:
Here, we have started at 52 and subtracted 4, to subtract 4 on the number line jump makes a jump from 52 to 48 and the size of the jump is 4 and we will get 48. Then we have to subtract 4, so we will start from 48 on the number line jump makes a jump from 48 to 44 and the size of the jump is 4 and we will get 44. So the subtraction of 52 – 8 is 44.

On Your Own

Break apart ones to subtract. Write the difference.

Question 7.

Answer:
The subtraction of 75 – 7 is 68.

Explanation:
Here, we have started at 75 and subtracted 3, to subtract 3 on the number line jump makes a jump from 75 to 72 and the size of the jump is 3 and we will get 72. Then we have to subtract 4, so we will start from 72 on the number line jump makes a jump from 72 to 68 and the size of the jump is 4 and we will get 68. So the subtraction of 75 – 7 is 68.

Question 8.

Answer:
The subtraction of 86 – 8 is 78.

Explanation:
Here, we have started at 86 and subtracted 4, to subtract 4 on the number line jump makes a jump from 86 to 82 and the size of the jump is 4 and we will get 82. Then we have to subtract 4, so we will start from 82 on the number line jump makes a jump from 82 to 78 and the size of the jump is 4 and we will get 78. So the subtraction of 86 – 8 is 78.

Question 9.
82 – 5 = __

Answer:
The subtraction of 82 – 5 is 77.

Explanation:
Here, we have started at 82 and subtracted 3, to subtract 3 on the number line jump makes a jump from 82 to 79 and the size of the jump is 3 and we will get 79. Then we have to subtract 2, so we will start from 79 on the number line jump makes a jump from 79 to 77 and the size of the jump is 2 and we will get 77. So the subtraction of 82 – 5 is 77.

Question 10.
83 – 7 = __

Answer:
The subtraction of 83 – 7 is 76.

Explanation:
Here, we have started at 83 and subtracted 3, to subtract 3 on the number line jump makes a jump from 83 to 80 and the size of the jump is 3 and we will get 80. Then we have to subtract 4, so we will start from 80 on the number line jump makes a jump from 80 to 76 and the size of the jump is 4 and we will get 76. So the subtraction of 83 – 7 is 76.

Question 11.
72 – 7 = __

Answer:
The subtraction of 72 – 7 is 65.

Explanation:
Here, we have started at 72 and subtracted 3, to subtract 3 on the number line jump makes a jump from 72 to 69 and the size of the jump is 3 and we will get 69. Then we have to subtract 4, so we will start from 69 on the number line jump makes a jump from 69 to 65 and the size of the jump is 4 and we will get 65. So the subtraction of 72 – 7 is 65.

Question 12.
76 – 9 = __

Answer:
The subtraction of 76 – 9 is 67.

Explanation:
Here, we have started at 76 and subtracted 5, to subtract 5 on the number line jump makes a jump from 76 to 71 and the size of the jump is 5 and we will get 71. Then we have to subtract 4, so we will start from 71 on the number line jump makes a jump from 71 to 67 and the size of the jump is 4 and we will get 67. So the subtraction of 76 – 9 is 67.

Question 13.
85 – 8 = __

Answer:
The subtraction of 85 – 8 is 77.

Explanation:
Here, we have started at 85 and subtracted 4, to subtract 4 on the number line jump makes a jump from 85 to 81 and the size of the jump is 4 and we will get 81. Then we have to subtract 4, so we will start from 81 on the number line jump makes a jump from 81 to 77 and the size of the jump is 4 and we will get 77. So the subtraction of 85 – 8 is 77.

Question 14.
71 – 6 = __

Answer:
The subtraction of 71 – 6 is 65.

Explanation:
Here, we have started at 71 and subtracted 3, to subtract 3 on the number line jump makes a jump from 71 to 68 and the size of the jump is 3 and we will get 68. Then we have to subtract 3, so we will start from 68 on the number line jump makes a jump from 68 to 65 and the size of the jump is 3 and we will get 65. So the subtraction of 71 – 6 is 65.

Question 15.
THINK SMARTER
Cheryl brought 27 bagels for the bake sale. Mike brought 24 bagels. They sold all but 9 of them. How many bagels did they sell?

__ bagels

Answer:
The total number of bagels sold is 42 bagels.

Explanation:
Cheryl brought 27 bagels for the bake sale and Mike brought 24 bagels, so the total number of bagels did Mike and Cheryl bought is 27 + 24= 51 bagels. And they sold all but 9 bagels are left with them, so the number of bagels sold is 51 – 9= 42 bagels. So the total number of bagels sold is 42 bagels.

Question 16.
MATHEMATICAL PRACTICE
Analyze Lexi has 8 fewer crayons than Ken. Ken has 45 crayons. How many crayons does Lexi have?
__ crayons

Answer:
The number of crayons Lexi had is 37 crayons.

Explanation:
As Lexi has 8 fewer crayons than Ken and Ken has 45 crayons, so Lexi has 45 – 8= 37 crayons.

Problem Solving • Applications

Write or draw to explain.

Question 17.
Cheryl built a toy train with 27 train cars. Then she added 18 more train cars. How many train cars are on the toy train now?

__ train cars

Answer:
The number of train cars is on the toy train is 9 train cars.

Explanation:
Cheryl built a toy train with 27 train cars and then she added 18 more train cars, so the number of train cars are on the toy train is 27 – 18= 9 train cars.

Question 18.
MATHEMATICAL PrACTICE
Analyze
Samuel had 46 marbles. He gave some marbles to a friend and has 9 marbles left. How many marbles did Samuel give to his friend?
__ marbles

Answer:
The number of marbles did Samuel gave to his friend is 37 marbles.

Explanation:
Samuel had 46 marbles and he gave some marbles to a friend and has 9 marbles left, so the number of marbles did Samuel gave to his friend is 46 – 9= 37 marbles. So the number of marbles did Samuel gave to his friend is 37 marbles.

Question 19.
THINK SMARTER
Matthew had 73 blocks. He gave 8 blocks to his sister. How many blocks does Matthew have now? Draw or write to show how to solve the problem.

Matthew has __ blocks now.

Answer:
The total number of blocks Matthew had is 65 blocks.

Explanation:
Matthew had 73 blocks and he gave 8 blocks to his sister, so the number of blocks did Matthew had is 73 – 8= 65 blocks. So after giving 8 blocks to his sister Matthew had 65 blocks. By subtracting the number of blocks did Matthew had and the number of blocks did he gave to his sister we had solved the problem.

TAKE HOME ACTIVITY
• Ask your child to describe how to find 34 − 6.

Answer:
The subtraction of 6 from 34 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 6 from 34, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 6 from 34 is 34 – 6= 28 and there are two tens and eight ones.

Algebra • Break Apart Ones to Subtract Homework & Practice 5.1

Break apart ones to subtract. Write the difference.

Question 1.
36 – 7 = __

Answer:
The subtraction of 36 – 7 is 29.

Explanation:
Here, we have started at 36 and subtracted 3, to subtract 3 on the number line jump makes a jump from 36 to 33 and the size of the jump is 3 and we will get 33. Then we have to subtract 4, so we will start from 33 on the number line jump makes a jump from 33 to 29 and the size of the jump is 4 and we will get 29. So the subtraction of 36 – 7 is 56.

Question 2.
35 – 8 = __

Answer:
The subtraction of 35 – 8 is 27.

Explanation:
Here, we have started at 35 and subtracted 4, to subtract 4 on the number line jump makes a jump from 35 to 31 and the size of the jump is 4 and we will get 31. Then we have to subtract 4, so we will start from 31 on the number line jump makes a jump from 31 to 27 and the size of the jump is 4 and we will get 27. So the subtraction of 35 – 8 is 27.

Question 3.
37 – 9 = __

Answer:
The subtraction of 37 – 9 is 28.

Explanation:
Here, we have started at 37 and subtracted 4, to subtract 4 on the number line jump makes a jump from 37 to 33 and the size of the jump is 4 and we will get 33. Then we have to subtract 5, so we will start from 33 on the number line jump makes a jump from 33 to 28 and the size of the jump is 5 and we will get 28. So the subtraction of 37 – 9 is 28.

Question 4.
41 – 6 = __

Answer:
The subtraction of 41 – 6 is 35.

Explanation:
Here, we have started at 41 and subtracted 3, to subtract 3 on the number line jump makes a jump from 41 to 38 and the size of the jump is 3 and we will get 38. Then we have to subtract 3, so we will start from 35 on the number line jump makes a jump from 38 to 35 and the size of the jump is 3 and we will get 35. So the subtraction of 41 – 6 is 35.

Question 5.
44 – 5 = __

Answer:
The subtraction of 44 – 5 is 39.

Explanation:
Here, we have started at 44 and subtracted 3, to subtract 3 on the number line jump makes a jump from 44 to 41 and the size of the jump is 3 and we will get 41. Then we have to subtract 2, so we will start from 41 on the number line jump makes a jump from 41 to 39 and the size of the jump is 2 and we will get 39. So the subtraction of 44 – 5 is 39.

Question 6.
33 – 7 = __

Answer:
The subtraction of 33 – 7 is 26.

Explanation:
Here, we have started at 33 and subtracted 3, to subtract 3 on the number line jump makes a jump from 33 to 30 and the size of the jump is 3 and we will get 30. Then we have to subtract 4, so we will start from 30 on the number line jump makes a jump from 30 to 26 and the size of the jump is 4 and we will get 26. So the subtraction of 33 – 7 is 26.

Question 7.
32 – 4 = __

Answer:
The subtraction of 32 – 4 is 28.

Explanation:
Here, we have started at 32 and subtracted 2, to subtract 2 on the number line jump makes a jump from 32 to 30 and the size of the jump is 2 and we will get 30. Then we have to subtract 2, so we will start from 30 on the number line jump makes a jump from 30 to 28 and the size of the jump is 2 and we will get 28. So the subtraction of 32 – 4 is 28.

Question 8.
31 – 6 = __

Answer:
The subtraction of 31 – 6 is 25.

Explanation:
Here, we have started at 31 and subtracted 3, to subtract 3 on the number line jump makes a jump from 31 to 28 and the size of the jump is 3 and we will get 28. Then we have to subtract 3, so we will start from 28 on the number line jump makes a jump from 28 to 25 and the size of the jump is 3 and we will get 25. So the subtraction of 31 – 6 is 25.

Problem Solving

Choose a way to solve. Write or draw to explain.

Question 9.
Beth had 44 marbles. She gave 9 marbles to her brother. How many marbles does Beth have now?
__ marbles.

Answer:
The total number of marbles does Beth had is 35 marbles.

Explanation:
Beth had 44 marbles and she gave 9 marbles to her brother and the remaining marbles do Beth had are 44 – 9= 35 marbles.

Question 10.
WRITE Math
Draw a number line and show how to find the difference for 24 – 6 using the break apart method in this lesson.

Lesson Check

Question 1.
What is the difference?

58 – 9 = __

Answer:
The difference of 58 – 9 is 49.

Explanation:
Here, we have started at 58 and subtracted 4, to subtract 4 on the number line jump makes a jump from 58 to 54 and the size of the jump is 4 and we will get 54. Then we have to subtract 5, so we will start from 54 on the number line jump makes a jump from 54 to 49 and the size of the jump is 5 and we will get 49. So the subtraction of 58 – 9 is 49.

Spiral Review

Question 2.
What is the difference?
14 – 6 = __

Answer:
The difference of 14 – 6 is 8.

Explanation:
Here, we have started at 14 and subtracted 3, to subtract 3 on the number line jump makes a jump from 14 to 11 and the size of the jump is 3 and we will get 11. Then we have to subtract 3, so we will start from 11 on the number line jump makes a jump from 11 to 3 and the size of the jump is 3 and we will get 8. So the subtraction of 14 – 6 is 8.

Question 3.
What is the sum?
3 + 6 + 2 = ___

Answer:
The sum of the three numbers is 11.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the three numbers
3 + 6 + 2 is 11.

Question 4.
What is the sum?
64 + 7 = __

Answer:
The sum of the two numbers is 71.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 64 + 7 is 71.

Question 5.
What is the sum?
56 + 18 = __

Answer:
The sum of the two numbers is 74.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 56 + 18  is 74.

Lesson 5.2 Algebra • Break Apart Numbers to Subtract

Essential Question
How does breaking apart a number make subtracting easier?

Listen and Draw

Draw jumps on the number line to show how to break apart the number to subtract.

Math Talk
MATHEMATICAL PRACTICES
Describe a Method
For one of the problems, describe what you did.

Model and Draw

Break apart the number you are subtracting into tens and ones.
Subtract 10.
Next, subtract 2 to get to 60.
Then subtract 5 more.


So, 72 – 12 = ___

Share and Show MATH BOARD

Break apart the number you are subtracting.
Write the difference.

Question 1.

Answer:
The subtraction of 43 – 18 is 25.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 18 as 10 and 8 and we will subtract 10 and we will get the result as 33. Then we will start from 33 and subtract 3 to get to 30 and then subtract 5 more. So we will get the result as 25, and we will place it on the number line. So the subtraction of 43 – 18 is 25.

Question 2.

Answer:
The subtraction of 45 – 14 is 31.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 14 as 10 and 4 and we will subtract 10 and we will get the result as 35. Then we will start from 35 and subtract 2 to get to 33 and then subtract 2 more. So we will get the result as 31, and we will place it on the number line. So the subtraction of 45 – 14 is 31.

Question 3.
46 – 17 = __

Answer:
The subtraction of 46 – 17 is 29.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 17 as 10 and 7 and we will subtract 10 and we will get the result as 36. Then we will start from 33 and subtract 3 to get to 30 and then subtract 5 more. So we will get the result as 25, and we will place it on the number line. So the subtraction of 46 – 17 is 29.

Question 4.
44 – 16 = __

Answer:
The subtraction of 44 – 16 is 28.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 18 as 10 and 6 and we will subtract 10 and we will get the result as 34. Then we will start from 34 and subtract 4 to get to 30 and then subtract 2 more. So we will get the result as 28, and we will place it on the number line. So the subtraction of 44 – 16 is 28.

On Your Own

Break apart the number you are subtracting. Write the difference.

Question 5.

Answer:
The subtraction of 57 – 15 is 42.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 15 as 10 and 5 and we will subtract 10 and we will get the result as 47. Then we will start from 47 and subtract 3 to get to 44 and then subtract 2 more. So we will get the result as 42, and we will place it on the number line. So the subtraction of 57 – 15 is 42.

Question 6.

Answer:
The subtraction of 63 – 17 is 46.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 17 as 10 and 7 and we will subtract 10 and we will get the result as 53. Then we will start from 53 and subtract 3 to get to 50 and then subtract 4 more. So we will get the result as 46, and we will place it on the number line. So the subtraction of 63 – 17 is 46.

Question 7.
68 – 19 = __

Answer:
The subtraction of 68 – 19 is 49.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 19 as 10 and 9 and we will subtract 10 and we will get the result as 58. Then we will start from 58 and subtract 8 to get to 50 and then subtract 1 more. So we will get the result as 49, and we will place it on the number line. So the subtraction of 68 – 19 is 49.

Question 8.
61 – 18 = __

Answer:
The subtraction of 61 – 18 is 43.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 18 as 10 and 8 and we will subtract 10 and we will get the result as 51. Then we will start from 51 and subtract 1 to get to 50 and then subtract 7 more. So we will get the result as 43, and we will place it on the number line. So the subtraction of 61 – 18 is 43.

Question 9.
THINK SMARTER
Jane has 53 toys in a box. She takes some toys out. Now there are 36 toys in the box. How many toys did Jane take out of the box?

Answer:
The number of toys did Jane take out of the box is 17 toys.

Explanation:
As Jane has 53 toys in a box and she takes some toys out, so Now there are 36 toys in the box. So to find how many toys did Jane take out of the box we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So The subtraction of 36 from 53 is 53 – 36= 17. So the number of toys did Jane take out of the box is 17 toys.

Question 10.
GO DEEPER
Look at Tom’s steps to solve a problem. Solve this problem in the same way.
42 – 15 = ?

Answer:
The subtraction of 42 – 15 is 27.

Explanation:
As we can see in the above image that the subtraction is done by the break apart number process, so the given problem is 42 – 15, so here we will break the 15 into 10 and 5, and then we will break 5 apart into 3 and 2. So first we will subtract 10 then the result will be 42 – 10 is 32 and then we will 2 then the result will be 32 – 2= 30. Now we will subtract 3 then the result will be 30 – 3= 27. So the subtraction of 42 – 15 is 27.

Problem Solving • Applications

Question 11.
38 people are in the library. Then 33 more people go into the library. How many people are in the library now?
__ people

Answer:
The total number of people in the library is 71 people.

Explanation:
As there are 38 people in the library and then 33 more people go into the library, so to find the number of people in the library we will perform addition. So we will add 38 + 33 is 71. The total number of people in the library is 71 people.

Question 12.
MATHEMATICAL PRACTICE
Analyze Alex has 24 toys in a chest. He takes some toys out of the chest. Then there are 16 toys in the chest. How many toys did he take out of the chest?

__ toys

Answer:
There are 8 toys did Alex take out of the chest.

Explanation:
As Alex has 24 toys in a chest and he takes some toys out of the chest. Then there are 16 toys in the chest, so to find the number of toys did Alex has to take out of the chest we will perform subtraction. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 16 from 24 is 24 – 16= 8 and there are 8 toys did Alex take out of the chest.

Question 13.
THINK SMARTER
Gail has two piles of newspapers. There are 32 papers in the first pile. There are 19 papers in the second pile. How many more papers are in the first pile than in the second pile?
__ more papers
Write or draw to explain how you solved the problem.

Answer:
The number of papers more in the first pile than the second pile is 13 more papers.

Explanation:
As Gail has two piles of newspapers and there are 32 papers in the first pile and there are 19 papers in the second pile. So to know how many papers are in the first pile than the second pile we will perform subtraction which is 32 – 19= 13 more papers.

TAKE HOME ACTIVITY
• Ask your child to write a subtraction story that uses 2-digit numbers.

Answer:
We will perform subtraction by breaking the two-digit number into tens place digit and ones place digit. Then the other number will be placed below the number. If the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So by this, we will perform the subtraction.

Algebra • Break Apart Numbers to Subtract Homework & practice 5.2

Break apart the number you are subtracting. Write the difference.

Question 1.
81 – 14 = __

Answer:
The subtraction of 81 – 14 is 67.

Explanation:
Here, we have started at 81 and subtracted 7, to subtract 7 on the number line jump makes a jump from 81 to 74 and the size of the jump is 7 and we will get 74. Then we have to subtract 7, so we will start from 74 on the number line jump makes a jump from 74 to 67 and the size of the jump is 7 and we will get 67. So the subtraction of 81 – 14 is 67.

Question 2.
84 – 16 = __

Answer:
The subtraction of 84 – 16 is 68.

Explanation:
Here, we have started at 84 and subtracted 8, to subtract 8 on the number line jump makes a jump from 84 to 76 and the size of the jump is 8 and we will get 76. Then we have to subtract 8, so we will start from 76 on the number line jump makes a jump from 76 to 68 and the size of the jump is 8 and we will get 68. So the subtraction of 84 – 16 is 68.

Question 3.
77 – 14 = __

Answer:
The subtraction of 77 – 14 is 63.

Explanation:
Here, we have started at 77 and subtracted 7, to subtract 7 on the number line jump makes a jump from 77 to 70 and the size of the jump is 7 and we will get 70. Then we have to subtract 7, so we will start from 70 on the number line jump makes a jump from 70 to 63 and the size of the jump is 7 and we will get 63. So the subtraction of 77 – 14 is 63.

Question 4.
83 – 19 = __

Answer:
The subtraction of 83 – 19 is 64.

Explanation:
Here, we have started at 83 and subtracted 10, to subtract 10 on the number line jump makes a jump from 83 to 73 and the size of the jump is 10 and we will get 73. Then we have to subtract 9, so we will start from 73 on the number line jump makes a jump from 73 to 64 and the size of the jump is 9 and we will get 64. So the subtraction of 83 – 19 is 64.

Question 5.
81 – 17 = __

Answer:
The subtraction of 81 – 17 is 64.

Explanation:
Here, we have started at 81 and subtracted 10, to subtract 10 on the number line jump makes a jump from 81 to 71 and the size of the jump is 10 and we will get 71. Then we have to subtract 7, so we will start from 71 on the number line jump makes a jump from 71 to 64 and the size of the jump is 7 and we will get 64. So the subtraction of 81 – 17 is 64.

Question 6.
88 – 13 = __

Answer:
The subtraction of 88 – 13 is 75.

Explanation:
Here, we have started at 88 and subtracted 3, to subtract 3 on the number line jump makes a jump from 83 to 80 and the size of the jump is 3 and we will get 80. Then we have to subtract 10, so we will start from 80 on the number line jump makes a jump from 80 to 75 and the size of the jump is 10 and we will get 75. So the subtraction of 88 – 13 is 75.

Question 7.
84 – 19 = __

Answer:
The subtraction of 84 – 19 is 65.

Explanation:
Here, we have started at 84 and subtracted 10, to subtract 10 on the number line jump makes a jump from 84 to 74 and the size of the jump is 10 and we will get 74. Then we have to subtract 9, so we will start from 74 on the number line jump makes a jump from 74 to 65 and the size of the jump is 9 and we will get 65. So the subtraction of 84 – 19 is 65.

Question 8.
86 – 13 = __

Answer:
The subtraction of 86 – 13 is 73.

Explanation:
Here, we have started at 86 and subtracted 7, to subtract 7 on the number line jump makes a jump from 86 to 79 and the size of the jump is 7 and we will get 79. Then we have to subtract 6, so we will start from 79 on the number line jump makes a jump from 79 to 73 and the size of the jump is 6 and we will get 73. So the subtraction of 86 – 13 is 73.

Question 7.
84 – 19 = __

Answer:
The subtraction of 84 – 19 is 65.

Explanation:
Here, we have started at 84 and subtracted 10, to subtract 10 on the number line jump makes a jump from 84 to 74 and the size of the jump is 10 and we will get 74. Then we have to subtract 9, so we will start from 74 on the number line jump makes a jump from 74 to 65 and the size of the jump is 9 and we will get 65. So the subtraction of 84 – 19 is 65.

Question 8.
86 – 18 = __

Answer:
The subtraction of 86 – 18 is 68.

Explanation:
Here, we have started at 84 and subtracted 9, to subtract 9 on the number line jump makes a jump from 86 to 77 and the size of the jump is 9 and we will get 77. Then we have to subtract 9, so we will start from 77 on the number line jump makes a jump from 77 to 68 and the size of the jump is 9 and we will get 68. So the subtraction of 86 – 18 is 68.

Problem Solving

Solve. Write or draw to explain.

Question 9.
Mr. Pearce bought 43 plants. He gave 14 plants to his sister. How many plants does Mr. Pearce have now?
__ plants

Answer:
The number of plants does Mr. Pearce had is 29 plants.

Explanation:
Mr. Pearce bought 43 plants and he gave 14 plants to his sister. So the number of plants does Mr. Pearce has now is 43 – 14. Here, we have started at 43 and subtracted 7, to subtract 7 on the number line jump makes a jump from 43 to 36 and the size of the jump is 7 and we will get 36. Then we have to subtract 7, so we will start from 36 on the number line jump makes a jump from 7 to 29 and the size of the jump is 7 and we will get 29. So the subtraction of 43 – 14 is 29. So the number of plants does Mr. Pearce had is 29 plants.

Question 10.
WRITE Math
Draw a number line and show how to find the difference for 36 – 17 using the break apart method in this lesson.

Lesson Check

Question 1.
What is the difference?

63 – 19 = __

Answer:
The subtraction of 63 – 19 is 44.

Explanation:
Here, we have started at 63 and subtracted 10, to subtract 10 on the number line jump makes a jump from 63 to 53 and the size of the jump is 10 and we will get 53. Then we have to subtract 9, so we will start from 53 on the number line jump makes a jump from 53 to 44 and the size of the jump is 9 and we will get 44. So the subtraction of 63 – 19 is 44.

Spiral Review

Question 2.
What is the sum?

Answer:
The sum of the two numbers is 37.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 14 + 23 is 37.

Question 3.
What is the sum?
8 + 7 = _

Answer:
The sum of the two numbers is 15.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 8 + 7 is 15.

Question 4.
Write a related subtraction fact for 6 + 8 = 14.
____

Question 5.
John has 7 kites. Annie has 4 kites. How many kites do they have altogether?
__ kites

Answer:
The number of kites does they together have is 7 + 4= 11 kites.

Explanation:
John has 7 kites and Annie has 4 kites, so the number of kites do they together have is 7 + 4= 11 kites.

Lesson 5.3 Model Regrouping for Subtraction

Essential Question
When do you regroup in subtraction?

Answer:
We will regroup in subtraction when the minuend digit is less than the subtrahend digit. Then we will take carry forward to the lesser digit and then we will perform subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.

Listen and Draw

Use to model the problem. Draw quick pictures to show your model.

Math Talk
MATHEMATICAL PRACTICES

Describe why you traded a tens block for 10 ones blocks.

Model and Draw

How do you subtract 26 from 53?

Answer:
The subtraction of 53 and 26 is 27.

Explanation:
To perform subtraction for 26 from 53 we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So The subtraction of 26 from 53 is 27.

Step 1
Show 53. Are there enough ones to subtract 26?

Step 2
If there are not enough ones, regroup 1 ten as 10 ones.

Step 3
Subtract 6 ones from 13 ones.

Step 4
Subtract the tens. Write the tens and ones. Write the difference.

Share and Show MATH BOARD

Draw to show the regrouping. Write the difference two ways. Write the tens and ones. Write the number.

Question 1.
Subtract 13 from 41.

__ tens __ ones __

Answer:
The subtraction of 13 from 41 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there are four tens blocks and one one’s block. So here we need to subtract 13 from 41, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 41 is 41 – 13= 28 and there are two tens and eight ones.

Question 2.
Subtract 9 from 48.

__ tens __ ones __

Answer:
The subtraction of 9 from 48 is 39. And there are three tens and nine ones.

Explanation:
In the above image, we can see that there is four tens blocks and eight one’s block. So here we need to subtract 9 from 48, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 9 from 48 is 48 – 9= 39 and there are three tens and nine ones.

 

Question 3.
Subtract 28 from 52.

__ tens __ ones __

Answer:
The subtraction of 28 from 52 is 24. And there are two tens and four ones.

Explanation:
In the above image, we can see that there is five tens blocks and two one’s block. So here we need to subtract 28 from 48, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 52 is 52 – 28= 24 and there are two tens and four ones.

On Your Own

Draw to show the regrouping. Write the difference two ways. Write the tens and ones. Write the number.

Question 4.
Subtract 8 from 23

__ tens __ ones __

Answer:
The subtraction of 8 from 23 is 15. And there are one ten and five ones.

Explanation:
In the above image, we can see that there is one tens block and five ones block. So here we need to subtract 8 from 23, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 8 from 23 is 23 – 8= 15 and there are one ten and five ones.

Question 5.
Subtract 36 from 45.

__ tens __ ones __

Answer:
The subtraction of 36 from 45 is 9. And there are no tens and nine ones.

Explanation:
In the above image, we can see that there is five tens blocks and two one’s block. So here we need to subtract 36 from 45, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 36 from 45 is 45 – 36= 9 and there are no tens and nine ones.

Question 6.
Subtract 6 from 43.

__ tens __ ones __

Answer:
The subtraction of 6 from 43 is 37. And there are three tens and seven ones.

Explanation:
In the above image, we can see that there is four tens blocks and three one’s block. So here we need to subtract 6 from 43, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 6 from 43 is 43 – 6= 37 and there are three tens and seven ones.

Question 7.
Subtract 39 from 67

__ tens __ ones __

Answer:
The subtraction of 39 from 67 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there is six tens blocks and seven ones block. So here we need to subtract 28 from 48, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 39 from 67 is 67 – 39= 28 and there are two tens and eight ones.

Question 8.
Subtract 21 from 50.

__ tens __ ones __

Answer:
The subtraction of 21 from 50 is 29. And there are two tens and nine ones.

Explanation:
In the above image, we can see that there is five tens blocks and zero ones in ones block. So here we need to subtract 21 from 50, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 21 from 50 is 50 – 21= 29 and there are two tens and nine ones.

Question 9.
Subtract 29 from 56

__ tens __ ones __

Answer:
The subtraction of 29 from 56 is 27. And there are two tens and seven ones.

Explanation:
In the above image, we can see that there are five tens blocks and two one’s blocks. So here we need to subtract 28 from 48, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 56 is 56 – 29= 27 and there are two tens and seven ones.

Question 10.
GO DEEPER
Draw to find what number was subtracted from 53.

Subtract __ from 53.
3 tens 4 ones
34

Problem Solving • Applications

Write or draw to explain.

Question 11.
THINK SMARTER
Billy has 18 fewer marbles than Sara. Sara has 34 marbles. How many marbles does Billy have?

__ marbles

Answer:
The total number of marbles does Billy had is 16 marbles.

Explanation:
As Billy has 18 fewer marbles than Sara and Sara has 34 marbles, so here fewer marbles means we will do subtraction. So the number of marbles do Billy had is 34 – 18= 16 marbles. Here we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the total number of marbles does Billy had is 16 marbles.

Question 12.
THINK SMARTER
There are 67 toy animals in the store. Then the clerk sells 19 toy animals. How many toy animals are in the store now?
Draw to show how to find the answer.

__ toy animals

Answer:
The number of toys in the store is 48 toys.

Explanation:
As there are 67 toy animals in the store and then the clerk sells 19 toy animals, so to find how many toys in the store is we will perform subtraction. Here we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of toys in the store is 67 – 19= 48 toys.

Describe how you solved the problem.
__________________________
__________________________
__________________________

Answer:
The problem is solved by using regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.

TAKE HOME ACTIVITY
• Ask your child to write a subtraction story and then explain how to solve it.

Answer:
We will perform subtraction by breaking the two-digit number into tens place digit and ones place digit. Then the other number will be placed below the number. If the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So by this, we will perform the subtraction.

Model Regrouping for Subtraction Homework & Practice 5.3

Draw to show the regrouping. Write the difference two ways. Write the tens and ones. Write the number.

Question 1.
Subtract 9 from 35

__ tens __ ones __

Answer:
The subtraction of 9 from 35 is 26. And there are two tens and six ones.

Explanation:
In the above image, we can see that there are three tens blocks and five one’s block. So here we need to subtract 9 from 35, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 9 from 35 is 35 – 9= 26 and there are two tens and six ones.

Question 2.
Subtract 14 from 52.

__ tens __ ones __

Answer:
The subtraction of 9 from 35 is 26. And there are two tens and six ones.

Explanation:
In the above image, we can see that there are three tens blocks and five one’s block. So here we need to subtract 9 from 35, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 9 from 35 is 35 – 9= 26 and there are two tens and six ones.

Problem Solving

Choose a way to solve. Write or draw to explain.

Question 3.
Mr. Ortega made 51 cookies. He gave 14 cookies away. How many cookies does he have now?
__ cookies

Answer:
The cookies that Mr. Ortega had now are 37 cookies.

Explanation:
As Mr. Ortega made 51 cookies and he gave 14 cookies away. So to find the number of cookies does Ortega had we will do regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 51 – 14 is 37 cookies. The cookies that
Mr. Orteg had now is 37 cookies.

Question 4.
WRITE Math
Draw a quick picture for 37. Draw to show how you would subtract 19 from 37. Write to explain what you did.

__________________________
__________________________
__________________________

Answer:
The subtraction of 37 – 19 is 18. The subtraction is done by the regrouping of subtraction.

Explanation:

The subtraction of 37 – 19 is 18. The subtraction is done by the regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 37 – 19 is 18.

Lesson Check

Question 1.
Subtract 9 from 36. What is the difference?

Answer:
The subtraction of 9 from 36 is 27. And there are two tens and seven ones.

Explanation:
In the above image, we can see that there are three tens blocks and six one’s blocks. So here we need to subtract 9 from 36, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 9 from 36 is 36 – 9= 27 and there are two tens and seven ones.

Question 2.
Subtract 28 from 45. What is the difference?

Answer:
The subtraction of 28 from 45 is 17. And there are one ten and seven ones.

Explanation:
In the above image, we can see that there are four tens blocks and five one’s blocks. So here we need to subtract 28 from 45, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 45 is 45 – 28= 17 and there are one ten and seven ones.

Spiral Review

Question 3.
What is the difference?
51 – 8 = __

Answer:
The subtraction of 8 from 51 is 43. And there are four tens and three ones.

Explanation:
In the above image, we can see that there are three tens blocks and six one’s blocks. So here we need to subtract 8 from 51, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 8 from 51 is 51 – 8= 43 and there are four tens and three ones.

Question 4.
What is the sum?
38 + 35 = __

Answer:
The sum of the two numbers is 73.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 38 + 35 is 73.

Question 5.
What is the sum?

Answer:
The sum of the three numbers is 90.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the three numbers 63 + 18 + 9 is 90.

Lesson 5.4 Model and Record 2-Digit Subtraction

Essential Question
How do you record 2-digit subtraction?

Answer:
We will perform subtraction by breaking the two-digit number into tens place digit and ones place digit. Then the other number will be placed below the number. If the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So by this, we will perform the subtraction.

Listen and Draw
Use to model the problem. Draw quick pictures to show your model.

Math Talk
MATHEMATICAL PRACTICE
Explain a Method
Did you trade blocks in your model? Explain why or why not.

Model and Draw

Trace over the quick pictures in the steps. Subtract.

Share and Show MATH BOARD

Draw a quick picture to solve. Write the difference.

Question 1.

Answer:
The subtraction of 15 from 47 is 32. And there are three ten and two ones.

Explanation:
In the above image, we can see that there are four tens and seven ones. So here we need to subtract 15 from 47, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 15 from 47 is 47 – 15= 32 and there are three ten and two ones.

Question 2.

Answer:
The subtraction of 18 from 32 is 14. And there are one ten and four ones.

Explanation:
In the above image, we can see that there are three tens and five ones. So here we need to subtract 18 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 32 is 32 – 18= 14 and there are one ten and four ones.

On Your Own

Draw a quick picture to solve. Write the difference.

Question 3.

Answer:
The subtraction of 29 from 35 is 6. And there are zero tens and six ones.

Explanation:
In the above image, we can see that there are three tens and five ones. So here we need to subtract 29 from 35, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 35 is 35 – 29= 6 and there are zero tens and six ones.

Question 4.

Answer:
The subtraction of 5 from 28 is 23. And there are two tens and three ones.

Explanation:
In the above image, we can see that there are two tens and eight ones. So here we need to subtract 5 from 28, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 5 from 28 is 28 – 5= 23 and there are two ten and three ones.

Question 5.

Answer:
The subtraction of 26 from 53 is 27. And there are two tens and seven ones.

Explanation:
In the above image, we can see that there are five tens and three ones. So here we need to subtract 26 from 53, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 26 from 53 is 53 – 26= 27 and there are two tens and seven ones.

Question 6.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 7.
GO DEEPER
There are 16 robins in the trees. 24 more fly in. Then 28 robins fly away. How many robins are still in the trees?

__ robbins

Answer:
The total number of robins are still on the trees is 12 robins.

Explanation:
As there are 16 robins on the tree and 24 more fly-ins. So the number of robins is 24 + 16= 40. Now 28 robins fly away, so the total number of robins are still on the trees is 40 – 28= 12 robins.

Problem Solving • Applications

Question 8.
THINK SMARTER
Claire’s puzzle has 85 pieces. She has used 46 pieces so far. How many puzzle pieces have not been used yet?

__ puzzle pieces

Answer:
The number of puzzle pieces that have not been used is 39 puzzle pieces.

Explanation:
As Claire’s puzzle has 85 pieces and she has used 46 pieces so far. So the number of puzzle pieces that have not been used is
85 – 46= 39 puzzle pieces.

Question 9.
MATHEMATICAL PRACTICE
Analyze There were some people at the park. 24 people went home. Then there were 19 people at the park. How many people were at the park before?
__ people

Answer:
The total number of people at the park before is 43 people.

Explanation:
As there were some people at the park and 24 people went home. Then there were 19 people at the park, so the total number of people at the park before is 24 + 19= 43 people.

Question 10.
THINK SMARTER
Mr. Sims has a box of 44 erasers. He gives 28 erasers to his students. How many erasers does Mr. Sims have now? Show how you solved the problem.

__ erasers

Answer:
The number of erasers does Mr. Sims has now is 16 erasers.

Explanation:
As Mr. Sims has a box of 44 erasers and he gives 28 erasers to his students. So the number of erasers does Mr. Sims has now is
44 – 28= 16 erasers. Here we have solved by using regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 44 is 44 – 28= 16 erasers. The number of erasers does Mr. Sims has now is 16 erasers.

TAKE HOME ACTIVITY
• Write 73 − 28 on a sheet of paper. Ask your child if he or she would regroup to find the difference.

Answer:
The subtraction of 73 – 28 is 45.

Explanation:
The subtraction of 73 – 28 is 45. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 73 – 28 is 45.

Model and Record 2-Digit Subtraction Homework & Practice 5.4

Draw a quick picture to solve. Write the difference.

Question 1.

Answer:
The subtraction of 17 from 43 is 26. And there are two tens and six ones.

Explanation:
In the above image, we can see that there are four tens and three ones. So here we need to subtract 17 from 43, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 17 from 43 is 43 – 17= 26 and there are two tens and six ones.

Question 2.

Answer:
The subtraction of 29 from 38 is 9. And there are zero tens and nine ones.

Explanation:
In the above image, we can see that there are three tens and eight ones. So here we need to subtract 29 from 38, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 38 is 38 – 29= 9 and there are zero tens and nine ones.

Problem Solving

Solve. Write or draw to explain.

Question 3.
Kendall has 63 stickers. Her sister has 57 stickers. How many more stickers does Kendall have than her sister?
__ more stickers.

Answer:
The number of stickers does Kendall has than her sister is 6 more stickers.

Explanation:
As Kendall has 63 stickers and her sister has 57 stickers, so the number of stickers does Kendall has than her sister is 63 – 57= 6 more stickers. Here we will perform regrouping of subtraction. Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 57 from 63 is 63 – 57= 9 stickers.

Question 4.
WRITE Math
Draw a quick picture to show the number 24. Then draw a quick picture to show 24 after you have regrouped 1 ten as 1-ones. Explain how both pictures show the same number, 24.
__________________________
__________________________
__________________________

Lesson Check

Question 1.
What is the difference?

Answer:
The subtraction of 18 from 47 is 29. And there are two tens and nine ones.

Explanation:
In the above image, we can see that there are four tens and seven ones. So here we need to subtract 18 from 47, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 47 is 47 – 18= 29 and there are two tens and nine ones.

Question 2.
What is the difference?

Answer:
The subtraction of 29 from 33 is 4. And there are zero tens and four ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 29 from 33, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 33 is 33 – 29= 4 and there are zero tens and four ones.

Spiral Review

Question 3.
What is the difference?
10 – 6 = __

Answer:
The difference is 4.

Explanation:
The difference between 10 and 6 is 4.

Question 4.
What is the sum?
16 + 49 = __

Answer:
The sum of the two numbers is 65.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 16 + 49  is 65.

Question 5.
What is the sum?
28 + 8 = __

Answer:
The sum of the two numbers is 36.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 28 + 8  is 36.

Question 6.
What is the difference?
52 – 6 = __

Answer:
The difference is 46.

Explanation:
The difference between 52 and 6 is 46.

Lesson 5.5 2-Digit Subtraction

Essential Question
How do you record the steps when subtracting 2-digit numbers?

Answer:
We will perform subtraction by breaking the two-digit number into tens place digit and ones place digit. Then the other number will be placed below the number. If the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So by this, we will perform the subtraction.

Listen and Draw

Draw a quick picture to model each problem.

Math Talk
MATHEMATICAL PRACTICES
Use Reasoning Explain how you know when to regroup.

Answer:
We will perform regrouping when the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. And Regrouping in subtraction is a process of exchanging one ten into ten ones.

Model and Draw

Share and Show MATH BOARD

Regroup if you need to. Write the difference.

Question 1.

Answer:
The subtraction of 14 from 31 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and one in ones place. So here we need to subtract 14 from 31, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 14 from 31 is 31 – 14= 19 and there are one ten and nine ones.

Question 2.

Answer:
The subtraction of 21 from 56 is 35. And there are three tens and five ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 21 from 56, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 21 from 56 is 56 – 21= 35 and there are three tens and five ones.

Question 3.

Answer:
The subtraction of 35 from 72 is 37. And there are three tens and seven ones.

Explanation:
In the above image, we can see that there are seven tens and two ones. So here we need to subtract 35 from 72, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 35 from 72 is 72 – 35= 37 and there are three tens and seven ones.

On Your Own
Regroup if you need to. Write the difference.

Question 4.

Answer:
The subtraction of 14 from 23 is 9. And there are zero tens and nine ones.

Explanation:
In the above image, we can see that there are two tens and three one’s. So here we need to subtract 14 from 23, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 14 from 23 is 23 – 14= 9 and there are zero tens and nine ones.

Question 5.

Answer:
The subtraction of 57 from 87 is 30. And there are three ten and zero ones.

Explanation:
In the above image, we can see that there are eight tens and seven one’s. So here we need to subtract 57 from 87, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 57 from 87 is 87 – 57= 30 and there are three ten and zero ones.

Question 6.

Answer:
The subtraction of 18 from 34 is 16. And there are one ten and six ones.

Explanation:
In the above image, we can see that there are three tens and four one’s. So here we need to subtract 18 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 34 is 34 – 18= 16 and there are one ten and six ones.

Question 7.

Answer:
The subtraction of 13 from 61 is 48. And there are four ten and eight ones.

Explanation:
In the above image, we can see that there are six tens and one ones. So here we need to subtract 13 from 61, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 61 is 61 – 13= 48 and there are four ten and eight ones.

Question 8.

Answer:
The subtraction of 18 from 45 is 27. And there are two tens and seven ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 45 is 45 – 18= 27 and there are two ten and nine ones.

Question 9.

Answer:
The subtraction of 36 from 52 is 16. And there are one ten and six ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 36 from 52, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 36 from 52 is 52 – 36= 16 and there are one ten and six ones.

Question 10.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 11.

Answer:
The subtraction of 43 from 75 is 32. And there are three tens and two ones.

Explanation:
In the above image, we can see that there are seven tens and five ones. So here we need to subtract 43 from 75, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 43 from 75 is 75 – 43= 32 and there are three tens and two ones.

Question 12.

Answer:
The subtraction of 27 from 56 is 29. And there are two tens and nine ones.

Explanation:
In the above image, we can see that there are five tens and six ones. So here we need to subtract 27 from 56, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 27 from 56 is 56 – 27= 29 and there are two tens and nine ones.

Question 13.

Answer:
The subtraction of 29 from 94 is 65. And there are six tens and five ones.

Explanation:
In the above image, we can see that there are nine tens and four one’s. So here we need to subtract 29 from 94, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 94 is 94 – 29= 65 and there are six tens and five ones.

Question 14.

Answer:
The subtraction of 39 from 87 is 48. And there are four tens and eight ones.

Explanation:
In the above image, we can see that there are eight tens and seven one’s. So here we need to subtract 39 from 87, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 39 from 87 is 87 – 39= 48 and there are four tens and eight ones.

Question 15.

Answer:
The subtraction of 46 from 83 is 37. And there are three tens and seven ones.

Explanation:
In the above image, we can see that there are eight tens and three one’s. So here we need to subtract 46 from 83, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 46 from 83 is 83 – 46= 37 and there are three tens and seven ones.

Question 16.
THINK SMARTER
Spencer wrote 5 fewer stories than Katie. Spencer wrote 18 stories. How many stories did Katie write?

__ stories

Answer:
The number of stories written by Katie is 13 stories.

Explanation:
As Spencer wrote 5 fewer stories than Katie and Spencer wrote 18 stories. As Spencer wrote 5 fewer stories than Katie so we will perform subtraction. So the number of stories written by Katie is 18 – 5= 13 stories.

Problem Solving • Applications

Question 17.
MATHEMATICAL PRACTICE
Explain a Method Circle the problems below that you could use mental math to solve.
54 – 10 = __
63 – 27 = __
93 – 20 = __
39 – 2 = __
41 – 18 = __
82 – 26 = __
Explain your choices
__________________________
__________________________
__________________________

Answer:

Explanation:

Question 18.
THINK SMARTER
There are 34 chickens in the barn. If 16 chickens go outside into the yard, how many chickens will still be in the barn?
Circle the number from the box to make the sentence true.

Answer:
The number of chickens will be in the barn will be 18 chickens.

Explanation:
As there are 34 chickens in the barn and if 16 chickens go outside into the yard then the number of chickens will be in the barn will be 34 – 16= 18 chickens. Here we have performed regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of chickens will be in the barn will be 34 – 16= 18 chickens.

TAKE HOME ACTIVITY
• Ask your child to write a 2-digit subtraction problem with no regrouping needed. Have your child explain why he or she chose those numbers.

Answer:
The subtraction of 56 – 23 is 33.

Explanation:
Given that we need to perform the subtraction without regrouping, so we need to take the minuend number greater than the subtrahend. Then we need not perform the regrouping, so we will take the numbers to be subtracted be 56 – 23= 33.

2-Digit Subtraction Homework & practice 5.5

Regroup if you need to. Write the difference.

Question 1.

Answer:
The subtraction of 28 from 47 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 28 from 47, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 47 is 47 – 28= 19 and there are one ten and nine ones.

Question 2.

Answer:
The subtraction of 18 from 33 is 15. And there are one ten and five ones.

Explanation:
In the above image, we can see that there are three tens and three ones. So here we need to subtract 18 from 33, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 33 is 33 – 18= 15 and there are one ten and five ones.

Question 3.

Answer:
The subtraction of 14 from 28 is 19. And there are one ten and four ones.

Explanation:
In the above image, we can see that there are two tens and eight ones. So here we need to subtract 14 from 28, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 14 from 28 is 28 – 14= 14 and there are one ten and four ones.

Question 4.

Answer:
The subtraction of 19 from 66 is 47. And there are four ten and seven ones.

Explanation:
In the above image, we can see that there are six tens and six ones. So here we need to subtract 19 from 66, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 19 from 66 is 66 – 19= 47 and there are four ten and seven ones.

Question 5.

Answer:
The subtraction of 26 from 77 is 51. And there are five tens and one in one’s place.

Explanation:
In the above image, we can see that there are seven tens and seven ones. So here we need to subtract 26 from 77, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 26 from 77 is 77 – 26= 51 and there are five tens and nine one in one’s place.

Question 6.

Answer:
The subtraction of 34 from 58 is 24. And there are two tens and four ones.

Explanation:
In the above image, we can see that there are five tens and eight ones. So here we need to subtract 34 from 58, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 34 from 58 is 58 – 34= 24 and there are two tens and four ones.

Question 7.

Answer:
The subtraction of 25 from 52 is 27. And there are two tens and seven ones.

Explanation:
In the above image, we can see that there are five tens and five ones. So here we need to subtract 25 from 52, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 25 from 52 is 52 – 25= 27 and there are two tens and seven ones.

Question 8.

Answer:
The subtraction of 49 from 87 is 38. And there are three tens and eight ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 49 from 87, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 49 from 87 is 87 – 49= 38 and there are three tens and eight ones.

Problem Solving

Solve. Write or draw to explain.

Question 9.
Mrs. Paul bought 32 erasers. She gave 19 erasers to students. How many erasers does she still have?

Answer:
The number of erasers Mrs. Paul had is 13 erasers.

Explanation:
As Mrs. Paul bought 32 erasers and she gave 19 erasers to students. So to find how many erasers does she still has is we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of erasers Mrs. Paul had is
32 – 9= 13 erasers.

Question 10.
WRITE Math
Write a few sentences about different ways to show subtraction for a problem like 32 – 15.
__________________________
__________________________

Lesson Check

Question 1.
What is the difference?

Answer:
The subtraction of 39 from 48 is 9. And there are zero tens and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 39 from 48, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 39 from 48 is 48 – 39= 9 and there are zero tens and nine ones.

Question 2.
What is the difference?

Answer:
The subtraction of 66 from 84 is 18. And there are one ten and eight ones.

Explanation:
In the above image, we can see that there are eight tens and four ones. So here we need to subtract 66 from 84, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 66 from 84 is 84 – 66= 18 and there are one ten and eight ones.

Spiral Review

Question 3.
What is the difference?

Answer:
The subtraction of 19 from 32 is 13. And there are one ten and three ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 19 from 32 is 32 – 19= 13 and there are one ten and three ones.

Question 4.
Write an addition fact that will give the same sum as 8 + 7.
10 + __

Answer:
The number to get the sum as 15 is we should add 5 to the number 10.

Explanation:
The sum of 8 + 7 is 15. So to get the 15 as a result of the given number, we will add 5 to the number 10. So we will get the result as 15.

Question 5.
27 boys and 23 girls go on a field trip to the museum. How many children go to the museum?
__ children

Answer:
The number of children who went to the museum is 50 children.

Explanation:
As there are 27 boys 23 girls on the field trip to the museum, so the number of children who went to the museum is 27 + 23= 50 children

Question 6.
There were 17 berries in the basket. Then 9 berries are eaten. How many berries are there now?
__ berries

Answer:
The number of berries will be 8 berries.

Explanation:
As there are 17 berries in the basket and 9 berries are eaten, then the number of berries will be 17 – 9= 8 berries. Here we have performed regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of berries will be 17 – 9= 8 berries

Lesson 5.6 Practice 2-Digit Subtraction

Essential Question
How do you record the steps when subtracting 2-digit numbers?

Answer:
We will perform subtraction by breaking the two-digit number into tens place digit and ones place digit. Then the other number will be placed below the number. If the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So by this, we will perform the subtraction.

Listen and Draw

Choose one way to solve the problem.
Draw or write to show what you did.

Math Talk
MATHEMATICAL PRACTICES
Describe a different way that you could have solved the problem.

Model and Draw

Carmen had 50 game cards. Then she gave 16 game cards to Theo. How many game cards does Carmen have now?

Answer:
The number of game cards will be 50 – 16= 34 game cards.

Explanation:
As the Carmen had 50 game cards and she gave 16 game cards to Theo, then the number of game cards will be 50 – 16= 34 game cards. Here we have performed regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of game cards will be 50 – 16= 34 game cards.
Step 1
Look at the ones. There are not enough ones to subtract 6 from 0. So, regroup

Step 2
Subtract the ones.
10 – 6 = 4

Step 3
Subtract the tens.
4 – 1 = 3

Share and Show MATH BOARD

Write the difference.

Question 1.

Answer:
The subtraction of 19 from 38 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and eight ones. So here we need to subtract 19 from 38, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 19 from 38 is 38 – 19= 19 and there are one ten and nine ones.

Question 2.

Answer:
The subtraction of 32 from 65 is 33. And there are three tens and three ones.

Explanation:
In the above image, we can see that there are six tens and five ones. So here we need to subtract 32 from 65, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 32 from 65 is 65 – 32= 33 and there are three tens and three ones.

Question 3.

Answer:
The subtraction of 12 from 50 is 38. And there are three tens and eight ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 12 from 50, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 12 from 50 is 50 – 12= 38 and there are three tens and eight ones.

Question 4.

Answer:
The subtraction of 4 from 23 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are two tens and three ones. So here we need to subtract 4 from 23, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 4 from 23 is 23 – 4= 19 and there are one ten and nine ones.

Question 5.

Answer:
The subtraction of 38 from 70 is 32. And there are three tens and two ones.

Explanation:
In the above image, we can see that there are seven tens and zero one. So here we need to subtract 38 from 70, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 38 from 70 is 70 – 38= 32 and there are three tens and two ones.

Question 6.

Answer:
The subtraction of 17 from 52 is 35. And there are three tens and five ones.

Explanation:
In the above image, we can see that there are five tens and two one. So here we need to subtract 17 from 52, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 17 from 52 is 52 – 17= 35 and there are three tens and five ones.

On Your Own

Write the difference.

Question 7.

Answer:
The subtraction of 24 from 41 is 17. And there are one ten and seven ones.

Explanation:
In the above image, we can see that there are four tens and one in ones place. So here we need to subtract 24 from 41, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 24 from 41 is 41 – 24= 17 and there are one ten and nine ones.

Question 8.

Answer:
The subtraction of 16 from 58 is 42. And there are four tens and two ones.

Explanation:
In the above image, we can see that there are five tens and eight ones. So here we need to subtract 16 from 58, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 16 from 58 is 58 – 16= 42 and there are four tens and two ones.

Question 9.

Answer:
The subtraction of 13 from 60 is 47. And there are four tens and seven ones.

Explanation:
In the above image, we can see that there are six tens and zero ones. So here we need to subtract 13 from 60, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 60 is 60 – 13= 47 and there are four tens and seven ones.

Question 10.

Answer:
The subtraction of 47 from 52 is 5. And there are zero tens and five ones.

Explanation:
In the above image, we can see that there are five tens and two ones. So here we need to subtract 47 from 52, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 47 from 52 is 52 – 47= 5 and there are zero tens and five ones.

Question 11.

Answer:
The subtraction of 46 from 72 is 26. And there are two tens and six ones.

Explanation:
In the above image, we can see that there are seven tens and two ones So here we need to subtract 46 from 72, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 46 from 72 is 72 – 46= 26 and there are two tens and six ones.

Question 12.

Answer:
The subtraction of 6 from 37 is 31. And there are three tens and one in ones place.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 6 from 37, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 6 from 37 is 37 – 6= 31 and there are three tens and one in ones place.

Question 13.

Answer:
The subtraction of 46 from 74 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 46 from 74, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 46 from 74 is 74 – 46= 28 and there are two tens and eight ones.

Question 14.

Answer:
The subtraction of 18 from 90 is 72. And there are seven tens and two ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 18 from 90, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 90 is 90 – 18= 72 and there are seven tens and two ones.

Question 15.
GO DEEPER
Write the missing numbers in the subtraction problems. The regrouping for each problem is shown.

Answer:
The missing values is 75 and 28 and 83 and 58.

Explanation:

Here, to find the missing values we will find with the help of the carry forward numbers. As the carry forward are 6 and 15 so the minuend is 75 as the result is 47, so the other number will be 75 – 47= 28. As the carry forward are 7 and 13 so the minuend is 83 as the result is 25, so the other number will be 83 – 58= 25.

Question 16.
THINK SMARTER
Adam takes 38 rocks out of a box. There are 23 rocks left in the box. How many rocks were in the box to start?

__ rocks

Answer:
The number of rocks were in the box to start is 61 rocks.

Explanation:
Adam takes 38 rocks out of a box and there are 23 rocks left in the box. So to find the number of rocks were in the box we will add the rocks that adam had took and the number of rocks left in the box. So the number of rocks were in the box to start is
38 + 28= 61 rocks.

TAKE HOME ACTIVITY
• Ask your child to show you one way to find 80 − 34.

Answer:
The subtraction of 34 from 80 is 46. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are eight tens and zero ones. So here we need to subtract 34 from 80, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 34 from 80 is 80 – 34= 46 and there are four tens and six ones.

Practice 2-Digit Subtraction Homework & Practice 5.6

Write the difference.

Question 1.

Answer:
The subtraction of 18 from 50 is 32. And there are three tens and two ones.

Explanation:
In the above image, we can see that there are five tens and zero ones. So here we need to subtract 18 from 50, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 18 from 50 is 50 – 18= 32 and there are three tens and two ones.

Question 2.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 3.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 4.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 5.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 6.

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Problem Solving

Solve. Write or draw to explain.

Question 7.
Julie has 42 sheets of paper. She gives 17 sheets to Kari. How many sheets of paper does Julie have now?
__ sheets of paper

Question 8.
WRITE Math
Draw and write to explain how these two problems are different: 35 – 15 = ________ and 43 – 26 = _______
__________________________

Lesson Check

Question 1.
What is the difference?

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Question 2.
What is the difference?

Answer:
The subtraction of 13 from 32 is 19. And there are one ten and nine ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 32 is 32 – 13= 19 and there are one ten and nine ones.

Spiral Review

Question 3.
What is the sum?
9 + 9 = __

Answer:
The sum of the two numbers is 18.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 9 + 9 is 18.

Question 4.
What is the difference?
14 – 7 = __

Answer:
The subtraction of 7 from 14 is 7. And there are zero tens and seven ones.

Explanation:
In the above image, we can see that there are one ten and four ones. So here we need to subtract 7 from 14, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 7 from 14 is 14 – 7= 7 and there are zero tens and seven ones.

Question 5.
What is the sum?
36 + 25 = __

Answer:
The sum of the two numbers is 61.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 36 + 25 is 61.

Question 6.
What is the sum?
7 + 2 + 3 = __

Answer:
The sum of the three numbers is 12.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the three numbers 7 + 2 + 3 is 12.

2-Digit Subtraction Mid-Chapter Checkpoint

Concepts and Skills

Break apart the number you are subtracting. Use the number line to help. Write the difference.

Question 1.
34 – 8 = __

Answer:
The subtraction of 8 from 34 is 26. And there are two tens and six ones.

Explanation:
In the above image, we can see that there are three tens and four ones. So here we need to subtract 8 from 34, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 8 from 34 is 34 – 8= 26 and there are two tens and six ones.

Question 2.
45 – 17 = __

Answer:
The subtraction of 17 from 45 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there are four tens and five ones. So here we need to subtract 17 from 45, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 17 from 45 is 45 – 17= 28 and there are two tens and eight ones.

Draw a quick picture to solve. Write the difference.

Question 3.

Answer:
The subtraction of 29 from 42 is 13. And there are one ten and three ones.

Explanation:
In the above image, we can see that there are four tens and two ones. So here we need to subtract 29 from 42, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 42 is 42 – 29= 13 and there are one ten and three ones.

Question 4.

Answer:
The subtraction of 23 from 54 is 31. And there are three tens and one in ones place.

Explanation:
In the above image, we can see that there are five tens and four ones. So here we need to subtract 23 from 54, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 23 from 54 is 54 – 23= 31 and there are three tens and one in ones place

Write the difference.

Question 5.

Answer:
The subtraction of 43 from 78 is 35. And there are three tens and five ones.

Explanation:
In the above image, we can see that there are seven tens and eight ones. So here we need to subtract 43 from 78, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 43 from 78 is 78 – 43= 35 and there are three tens and five ones.

Question 6.

Answer:
The subtraction of 26 from 60 is 34. And there are three tens and four ones.

Explanation:
In the above image, we can see that there are six tens and zero ones. So here we need to subtract 26 from 60, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 26 from 60 is 60 – 26= 34 and there are three tens and four ones.

Question 7.

Answer:
The subtraction of 37 from 85 is 48. And there are four tens and eight ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 37 from 85, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 37 from 85 is 85 – 37= 48 and there are four tens and eight ones.

Question 8.
THINK SMARTER
Marissa had 51 toy dinosaurs. She gave 14 toy dinosaurs to her brother. How many toy dinosaurs does she have now?

__ toy dinosaurs

Answer:
The number of dinosaurs does Marissa has is 37 dinosaurs.

Explanation:
Marissa had 51 toy dinosaurs and she gave 14 toy dinosaurs to her brother. So to how many toy dinosaurs does she have we will perform regrouping of subtraction. Here we have solved by using regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of dinosaurs does Marissa has is 51 – 14= 37 dinosaurs.

Lesson 5.7 Rewrite 2-Digit Subtraction

Essential Question
What are two different ways to write subtraction problems?

Math Talk
MATHEMATICAL PRACTICES
Explain why it is important to line up the digits of the numbers in columns.

Model and Draw

What is 81 – 36?
Rewrite the subtraction problem.
Then find the difference.

Step 1
For 81, write the tens digit in the tens column. Write the ones digit in the ones column.

Step 2
Look at the ones. Regroup if you need to.

Share and Show MATH BOARD

Rewrite the subtraction problem. Then find the difference.

Question 1.

Answer:
The subtraction of 37 from 4 is 33. And there are three tens and three ones.

Explanation:
In the above image, we can see that there are three tens and four ones. So here we need to subtract 4 from 37, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 4 from 37 is 37 – 4= 33 and there are three tens and three ones.

Question 2.

Answer:
The subtraction of 24 from 48 is 24. And there are two tens and four ones.

Explanation:
In the above image, we can see that there are four tens and eight ones. So here we need to subtract 24 from 48, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 24 from 48 is 48 – 24= 24 and there are two tens and four ones.

Question 3.

Answer:
The subtraction of 37 from 85 is 48. And there are four tens and eight ones.

Explanation:
In the above image, we can see that there are eight tens and five ones. So here we need to subtract 37 from 85, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 37 from 85 is 85 – 37= 48 and there are four tens and eight ones.

Question 4.

Answer:
The subtraction of 19 from 63 is 44. And there are four tens and four ones.

Explanation:
In the above image, we can see that there are six tens and three ones. So here we need to subtract 19 from 63, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 19 from 63 is 63 – 19= 44 and there are four tens and four ones.

Question 5.

Answer:
The subtraction of 37 from 62 is 25. And there are two tens and five ones.

Explanation:
In the above image, we can see that there are six tens and two ones. So here we need to subtract 37 from 62, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 37 from 62 is 62 – 37= 25 and there are two tens and five ones.

Question 6.

Answer:
The subtraction of 27 from 51 is 24. And there are two tens and four ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 27 from 51, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 27 from 51 is 51 – 27= 24 and there are two tens and four ones.

Question 7.

Answer:
The subtraction of 3 from 76 is 73. And there are seven tens and three ones.

Explanation:
In the above image, we can see that there are seven tens and three ones. So here we need to subtract 3 from 76, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 3 from 76 is 76 – 3= 73 and there are seven tens and three ones.

Question 8.

Answer:
The subtraction of 48 from 95 is 47. And there are four tens and seven ones.

Explanation:
In the above image, we can see that there are nine tens and five ones. So here we need to subtract 48 from 95, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 48 from 95 is 95 – 48= 47 and there are four tens and seven ones.

On Your Own

Rewrite the subtraction problem. Then find the difference.

Question 9.

Answer:
The subtraction of 8 from 49 is 41. And there are four tens and one in one’s place.

Explanation:
In the above image, we can see that there are four tens and nine ones. So here we need to subtract 8 from 49, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 8 from 49 is 49 – 8= 41 and there are four tens and one in one’s place.

Question 10.

Answer:
The subtraction of 47 from 85 is 38. And there are three tens and eight ones.

Explanation:
In the above image, we can see that there are eight tens and five ones. So here we need to subtract 47 from 85, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 47 from 85 is 85 – 47= 38 and there are three tens and eight ones.

Question 11.

Answer:
The subtraction of 23 from 63 is 40. And there are four tens and zero ones.

Explanation:
In the above image, we can see that there are six tens and three ones. So here we need to subtract 23 from 63, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 23 from 63 is 63 – 23= 40 and there are four tens and zero ones.

Question 12.

Answer:
The subtraction of 23 from 51 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there are five tens and one in one’s place. So here we need to subtract 23 from 51, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 23 from 51 is 51 – 23= 28 and there are two tens and eight ones.

Question 13.

Answer:
The subtraction of 15 from 60 is 45. And there are four tens and five ones.

Explanation:
In the above image, we can see that there are six tens and zero ones. So here we need to subtract 15 from 60, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 15 from 60 is 60 – 15= 45 and there are four tens and four ones.

Question 14.

Answer:
The subtraction of 58 from 94 is 36. And there are three tens and six ones.

Explanation:
In the above image, we can see that there are nine tens and four ones. So here we need to subtract 58 from 94, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 58 from 94 is 94 – 58= 36 and there are three tens and six ones.

Question 15.

Answer:
The subtraction of 20 from 47 is 27. And there are two tens and seven ones.

Explanation:
In the above image, we can see that there are four tens and seven ones. So here we need to subtract 20 from 47, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 20 from 47 is 47 – 20= 27 and there are two tens and seven ones.

Question 16.

Answer:
The subtraction of 9 from 35 is 26. And there are two tens and six ones.

Explanation:
In the above image, we can see that there are three tens and five ones. So here we need to subtract 9 from 35, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 9 from 35 is 35 – 9= 26 and there are two tens and six ones.

Question 17.

Answer:
The subtraction of 10 from 78 is 68. And there are six tens and eight ones.

Explanation:
In the above image, we can see that there are seven tens and eight ones. So here we need to subtract 10 from 78, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 10 from 78 is 78 – 10= 68 and there are six tens and eight ones.

Question 18.

Answer:
The subtraction of 38 from 54 is 16. And there are one ten and six ones.

Explanation:
In the above image, we can see that there are five tens and four one. So here we need to subtract 38 from 54, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 38 from 54 is 54 – 38= 16 and there are one ten and six ones.

Question 19.

Answer:
The subtraction of 39 from 92 is 53. And there are five tens and three ones.

Explanation:
In the above image, we can see that there are nine tens and two ones. So here we need to subtract 39 from 92, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 39 from 92 is 92 – 39= 53 and there are five tens and three ones.

Question 20.

Answer:
The subtraction of 28 from 87 is 59. And there are five tens and nine ones.

Explanation:
In the above image, we can see that there are eight tens and seven ones. So here we need to subtract 28 from 87, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 87 is 87 – 28= 59 and there are eight tens and nine ones.

Question 21.
THINK SMARTER
For which of the problems above could you find the difference without rewriting it? Explain.

___________________________
___________________________
___________________________

Problem Solving • Applications

Read about the class trip. Then answer the questions.

Question 22.
How many more paintings were done by adults than by children?
__ more paintings

Answer:
The number of paints which were more by adults than the children is 53 – 26= 27 paintings.

Explanation:
As Pablo’s class went to the art museum, and they saw 26 paintings done by the children. After that, they saw 53 paintings done by the adults. So the number of paints which were more by adults than the children is 53 – 26= 27 paintings.

Question 23.
GO DEEPER
How many more paintings than sculptures did they see?
__ more paintings

Answer:
The number of paints that were more than the sculptures is 61 more paintings.

Explanation:
As Pablo’s class went to the art museum, and they saw 26 paintings done by the children. After that they saw 53 paintings done by the adults. So the total number of paintings is 53 + 26 = 79 paintings. And they saw 18 sculptures, so the number of paints which were more than the sculptures is 79 – 18= 61 more paintings.

Question 24.
THINK SMARTER
Tom drew 23 pictures last year. Beth drew 14 pictures. How many more pictures did Tom draw than Beth?
Fill in the bubble next to all the ways to show the problem.

Answer:
The number of more pictures did Tom draw than Beth is 23 – 14= 9 pictures.

Explanation:
As Tom draw 23 pictures last year and Beth draw 14 pictures, so the number of more pictures did Tom draw than Beth is 23 – 14= 9 pictures.

TAKE HOME ACTIVITY
• Ask your child to write and solve a subtraction problem about a family trip.

Rewrite 2-Digit Subtraction Homework & Practice 5.7

Rewrite the subtraction problem. Then find the difference.

Question 1.

Answer:
The subtraction of 19 from 35 is 16. And there are one ten and six ones.

Explanation:
In the above image, we can see that there are three tens and five ones. So here we need to subtract 19 from 35, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 19 from 35 is 35 – 19= 16 and there are one ten and six ones.

Question 2.

Answer:
The subtraction of 23 from 47 is 24. And there are two tens and four ones.

Explanation:
In the above image, we can see that there are four tens and seven ones. So here we need to subtract 23 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 23 from 47 is 47 – 23= 24 and there are two tens and four ones.

Question 3.

Answer:
The subtraction of 28 from 58 is 30. And there are three tens and zero ones.

Explanation:
In the above image, we can see that there are three tens and five one’s blocks. So here we need to subtract 28 from 58, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 58 is 58 – 28= 30 and there are three tens and zero ones.

Problem Solving

Solve. Write or draw to explain.

Question 4.
Jimmy went to the toy store. He saw 23 wooden trains and 41 plastic trains. How many more plastic trains than wooden trains did he see?
___ more plastic trains

Answer:
There are 18 more plastic trains than wooden trains.

Explanation:
Jimmy went to the toy store and he saw 23 wooden trains and 41 plastic trains, so to find how many more plastic trains than wooden trains did he see is we will perform subtraction. So there will be 41 – 23= 18 more plastic trains than wooden trains.

Question 5.
WRITE Math
Is it easier to subtract when the numbers are written above and below each other? Explain your answer
__________________________
__________________________
__________________________
__________________________

Answer:
Yes, it is easier to subtract the numbers that are written above and below each other. As we can easily borrow from the place in front of the number and we can rewrite without a problem. It also helps to keep the math problems more organized so by writing the numbers above and below we will be confused.

Lesson Check

Question 1.
What is the difference for 43 − 17?

Answer:
The subtraction of 17 from 43 is 26. And there are one ten and nine ones.

Explanation:
In the above, we can see that there are four tens and three ones. So here we need to subtract 13 from 32, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 17 from 43 is 43 – 16= 26 and there are two tens and six ones.

Question 2.
What is the difference for 50 − 16?

Answer:
The subtraction of 16 from 50 is 34. And there are three tens and four ones.

Explanation:
In the above, we can see that there are five tens and zero ones. So here we need to subtract 16 from 50, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 16 from 50 is 50 – 16= 34 and there are three tens and four ones.

Spiral Review

Question 3.
What is the sum?

Answer:
The sum of the given numbers is 74.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the given numbers
29 + 4 + 25 + 16  is 74.

Question 4.
What is the sum of 41 + 19?
_______

Answer:
The sum of the given numbers is 60.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the given numbers
41 + 19 is 60.

Question 5.
Write an addition fact that will give the same sum as 5 + 9?
10 + ___

Answer:
The sum of the two numbers is 14.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 5 + 9 is 14. So to get the same sum we need to add 4, so the sum of the 10 + 4= 14, which is same as 5 + 9 sum.

Question 6.
What is the difference?
45 – 13 = ___

Answer:
The subtraction of 13 from 45 is 32. And there are three tens and two ones.

Explanation:
In the above, we can see that there are four tens and three ones. So here we need to subtract 13 from 45, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 13 from 45 is 45 – 13= 32 and there are three tens and two ones.

Lesson 5.8 Add to Find Differences

Essential Question
How can you use addition to solve subtraction problems?
_______ ____ markers

Now draw pictures to show the next part of the problem. Write a number sentence for your drawing.
_______ ____ markers

Math Talk
MATHEMATICAL PRACTICES
Describe what happens when you add back the number that you had subtracted.

Model and Draw

Count up from the number you are subtracting to find the difference.

Start at 38. Count up to 40.

Then count up 5 more to 45.

So, 45 − 38 = __.

Share and Show MATH BOARD

Use the number line. Count up to find the difference.

Question 1.
36 – 27 = ___

Answer:
The subtraction of 27 from 36 is 9. And there are zero tens and nine ones.

Explanation:
Here we need to subtract 27 from 36, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 27 from 36 is 36 – 27= 9 and there are zero tens and nine ones.

Question 2.
56 – 49 = __

Answer:
The subtraction of 49 from 56 is 7. And there are zero tens and seven ones.

Explanation:
Here we need to subtract 49 from 56, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 49 from 56 is 56 – 49= 7 and there are zero tens and seven ones.

Question 3.
64 – 58 = __

Answer:
The subtraction of 58 from 64 is 6. And there are zero tens and six ones.

Explanation:
Here we need to subtract 58 from 64, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 58 from 64 is 64 – 58= 6 and there are zero tens and six ones.

On Your Own

Use the number line. Count up to find the difference.

Question 4.
33 – 28 = __

Answer:
The subtraction of 28 from 33 is 5. And there are zero tens and five ones.

Explanation:
In the above image, we can see that there are three tens and three ones. So here we need to subtract 28 from 33, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 33 is 33 – 28= 5 and there are zero tens and five ones.

Question 5.
45 – 37 = __

Answer:
The subtraction of 37 from 45 is 8. And there are zero tens and eight ones.

Explanation:
In the above image, we can see that there are four tens and five ones. So here we need to subtract 37 from 45, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 37 from 45 is 45 – 37= 8 and there are zero tens and eight ones.

Question 6.
58 – 49 = __

Answer:
The subtraction of 49 from 58 is 9. And there are zero tens and nine ones.

Explanation:
In the above image, we can see that there are five tens and eight ones. So here we need to subtract 49 from 58, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 49 from 58 is 58 – 49= 49 and there are zero tens and nine ones.

Question 7.
THINK SMARTER
There were 55 books on the table. Sandra picked up some of the books. Now there are 49 books on the table. How many books did Sandra pick up?

__ books

Answer:
The number of books picked up by the Sandra is 6 books.

Explanation:
As there were 55 books on the table and Sandra picked up some of the books. And Now there are 49 books on the table, so to find how many books did Sandra pick up is we will perform subtraction. So the number of books picked up by the Sandra is 55 – 49= 6 books.

Problem Solving • Applications

Solve. You may wish to use the number line to help.

Question 8.
There are 46 game pieces in a box. Adam takes 38 game pieces out of the box. How many game pieces are still in the box?

__ game pieces

Answer:
The number of game pieces is still in the box is 8 game pieces.

Explanation:
As there are 46 game pieces in a box and Adam takes 38 game pieces out of the box. So there will be 46 – 38= 8 game pieces.

Question 9.
THINK SMARTER
Rachel had 27 craft sticks. Then she gave 19 craft sticks to Theo. How many craft sticks does Rachel have now?
Circle the number from the box to make the sentence true.
Rachel has craft sticks now.
Explain how you can use addition to solve the problem.
__________________________
__________________________

Answer:
The number of craft sticks Rachel has now is 27 – 19 = 8 craft sticks.

Explanation:
As Rachel had 27 craft sticks and then she gave 19 craft sticks to Theo. So the number of craft sticks Rachel has now is 27 – 19 = 8 craft sticks.

TAKE HOME ACTIVITY
• Have your child describe how he or she used a number line to solve one problem in this lesson.

Answer:
The number line is used by performing we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. Then we will make the number of jumps by the difference what we had got and we will make jump from minuend number to the subtrahend and will count the number of jumps.

Add to Find Differences Homework & practice 5.8

Use the number line. Count up to find the difference.

Question 1.
36 – 29 = __

Answer:
The subtraction of 29 from 36 is 7. And there are zero tens and seven ones.

Explanation:
In the above image, we can see that there are three tens and six ones. So here we need to subtract 29 from 36, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 29 from 36 is 36 – 29= 7 and there are zero tens and seven ones.

Question 2.
43 – 38 = __

Answer:
The subtraction of 38 from 43 is 5. And there are zero tens and five ones.

Explanation:
In the above image, we can see that there are three tens blocks and six one’s blocks. So here we need to subtract 8 from 51, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 38 from 43 is 43 – 38= 5 and there are zero tens and five ones.

Problem Solving

Solve. You may wish to use the number line.

Question 3.
Jill has 63 index cards. She uses 57 of them for a project. How many index cards does Jill have now?
__ index cards

Answer:
The number of index cards does Jill has now is 6 index cards.

Explanation:
As Jill has 63 index cards and she uses 57 of them for a project, so the number of index cards does Jill have now is 63 – 57 = 6 index cards.

Question 4.
WRITE Math
Explain how a number line can be used to find the difference for 34 – 28.
__________________________
__________________________

Answer:

Lesson Check

Use the number line. Count up to find the difference.

Question 1.
82 − 75 = __

Answer:
The subtraction of 75 from 82 is 7. And there are zero tens and seven ones.

Explanation:
In the above image, we can see that there are eight tens and two ones. So here we need to subtract 75 from 82, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 75 from 82 is 82 – 75= 7 and there are zero tens and seven ones.

Question 2.
90 − 82 = __

Answer:
The subtraction of 82 from 90 is 8. And there are zero tens and eight ones.

Explanation:
In the above image, we can see that there are nine tens and zero ones. So here we need to subtract 82 from 90, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 82 from 90 is 90 – 82= 8and there are zero tens and eight ones.

Spiral Review

Question 3.
Jordan has 41 toy cars at home. He brings 24 cars to school. How many cars are at home?
__ cars

Answer:
The number of cars is at home is 17 cars.

Explanation:
As Jordan has 41 toy cars at home and he brings 24 cars to school, so the number of cars are at home is 41 – 24= 17 cars.

Question 4.
Pam has 15 fish. 9 are goldfish and the rest are guppies. How many fish are guppies?
__ guppies

Answer:
The number of fishes is guppies is 6 guppies.

Explanation:
As Pam has 15 fishes and 9 are gold fishes and the rest are guppies, so the number of fishes are guppies is 15 – 9= 6 guppies.

Question 5.
What is the sum?

Answer:
The sum of the two numbers is 54.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 35 + 19 is 54.

Question 6.
Each table has 5 pencils. There are 3 tables. How many pencils are there altogether?
__ pencils.

Answer:
The total number of pencils will be 15 pencils are there altogether.

Explanation:
As each table has 5 pencils and there are 3 tables, so the total number of pencils will be 5 × 3= 15 pencils are there altogether.

Lesson 5.9 Problem Solving • Subtraction

Essential Question
How can drawing a diagram help when solving subtraction problems?

Jane and her mom made 33 puppets for the craft fair. They sold 14 puppets. How many puppets do they still have?

Answer:
The total number of puppets do they left is 19 puppets.

Explanation:
As Jane and her mom made 33 puppets for the craft fair and they sold 14 puppets, so they still have 33 – 14= 19 puppets. Here we need to subtract 14 from 33, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 14 from 33 is 33 – 14= 19 and there are one ten and nine ones. So they will have 19 puppets left.

Unlock the Problem

What do I need to find?
they still have

What information do I need to use?

They made __ puppets.
They sold __ puppets.

Show how to solve the problem.

HOME CONNECTION
• Your child used a bar model and a number sentence to represent the problem. Using a bar model helps show what is known and what is needed to solve the problem.

Try Another Problem

Label the bar model. Write a number sentence with a for the missing number. Solve.

Question 1.
Carlette had a box of 46 craft sticks. She used 28 craft sticks to make a sailboat. How many craft sticks were not used?

Answer:
They will have 18 craft sticks left.

Explanation:
As Carlette had a box of 46 craft sticks and she used 28 craft sticks to make a sailboat. So the number of craft sticks that are not used is 46 – 28= 18 craft sticks. Here we need to subtract 28 from 46, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 28 from 46 is 46 – 28= 18 and there are one ten and eight ones. So they will have 18 craft sticks left.

Question 2.
Rob’s class made 31 clay bowls. Sarah’s class made 15 clay bowls. How many more clay bowls did Rob’s class make than Sarah’s class?

______ ___ more clay bowls

Answer:
The number of more clay bowls did Rob’s class make than Sarah’s class is 31 – 15= 16 clay bowls.

Explanation:
As Rob’s class made 31 clay bowls and Sarah’s class made 15 clay bowls. So the number of more clay bowls did Rob’s class make than Sarah’s class is 31 – 15= 16 clay bowls. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of more clay bowls did Rob’s class make than Sarah’s class is 16 clay bowls.

Share and Show MATH BOARD

Label the bar model. Write a number sentence with a for the missing number. Solve.

Question 3.
Mr. Hayes makes 32 wooden frames. He gives away 15 frames as gifts. How many frames does he still have?

Answer:
The number of many frames does he still have now is 32 – 15= 17 frames.

Explanation:
As Mr. Hayes makes 32 wooden frames and he gives away 15 frames as gifts. So the number of many frames does he still have now is 32 – 15= 17 frames. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of many frames does he still have now is 17 frames.

Question 4.
Wesley has 21 ribbons in a box. He has 15 ribbons on the wall. How many more ribbons does he have in the box than on the wall?

__ more ribbons

_____

Answer:
The number of many more ribbons does he have in the box than on the wall is 6 more ribbons.

Explanation:
As Wesley has 21 ribbons in a box and he has 15 ribbons on the wall. So the number of many more ribbons does he have in the box than on the wall is 21 – 15= 6 more ribbons. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of many more ribbons does he have in the box than on the wall is 6 more ribbons.

Question 5.
THINK SMARTER
Jennifer wrote 9 poems at school and 11 poems at home. She wrote 5 more poems than Nell. How many poems did Nell write?

__ poems

Answer:

Explanation:

On Your Own

Question 6.
GO DEEPER
There are 70 children. 28 children are hiking and 16 are at a picnic. The rest of the children are playing soccer. How many children are playing soccer?
Draw a model with bars for the problem. Describe how your drawing shows the problem. Then solve the problem.
__________________________
__________________________
__________________________

Question 7.
THINK SMARTER
There are 48 crackers in a bag. The children eat 25 crackers. How many crackers are still in the bag? Circle the bar model that can be used to solve the problem.

Write a number sentence with a for the missing number. Solve.
__________________________
___ crackers

TAKE HOME ACTIVITY
• Ask your child to explain how he or she solved one of the problems on this page.

Answer:
We will perform subtraction by breaking the two-digit number into tens place digit and ones place digit. Then the other number will be placed below the number. If the minuend number is less than the subtrahend number then we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So by this, we will perform the subtraction.

Problem Solving • Subtraction Homework & Practice 5.9

Label the bar model. Write a number sentence with a for the missing number. Solve.

Question 1.
Megan picked 34 flowers. Some of the flowers are yellow and 18 flowers are pink. How many of the flowers are yellow?
___ yellow flowers

___

Question 2.
Alex had 45 toy cars. He put 26 toy cars in a box. How many toy cars are not in the box?
___ toy cars

Question 3.
WRITE Math
Explain how bar models show a problem in a different way.
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Lesson Check

Question 1.
There were 39 pumpkins at the store. Then 17 of the pumpkins were sold. How many pumpkins are still at the store?
__ pumpkins

Question 2.
There were 48 ants on a hill. Then 13 of the ants marched away. How many ants are still on the hill?
__ ants

Spiral Review

Question 3.
Ashley had 26 markers. Her friend gave her 17 more markers. How many markers does Ashley have now?
__ markers

Question 4.
What is the sum?

Question 5.
Write a subtraction fact that will give the same difference as 15 − 7.
10 – __

Question 6.
What is the sum?
34 + 5 = __

Lesson 5.10 Algebra • Write Equations to Represent Subtraction

Essential Question
How do you write a number sentence to represent a problem?

Listen and Draw

Draw to show the problem. Write a number sentence. Then solve.
_______________

Math Talk
MATHEMATICAL PRACTICES
Describe how your drawing shows the problem.

Model and Draw

You can write a number sentence to
show a problem.
Liza has 65 postcards. She gives 24 postcards to Wesley. How many postcards does Liza have now?

Liza has __ postcards now.

Share and Show MATH BOARD

Write a number sentence for the problem. Use a for the missing number. Then solve.

Question 1.
There were 32 birds in the trees. Then 18 birds flew away. How many birds are in the trees now?

__ birds

Question 2.
Carla read 43 pages in her book. Joe read 32 pages in his book. How many more pages did Carla read than Joe?
________
__ more pages

On Your Own

Write a number sentence for the problem. Use a for the missing number. Then solve.

Question 3.
There were 40 ants on a rock. Some ants moved to the grass. Now there are 26 ants on the rock. How many ants moved to the grass?
___
__ ants

Question 4.
THINK SMARTER
Keisha had a bag of ribbons. She took 29 ribbons out of the bag. Then there were 17 ribbons still in the bag. How many ribbons were in the bag to start?

_______
__ ribbons

Question 5.
GO DEEPER
There are 50 bees in a hive. Some bees fly out. If fewer than 20 bees are still in the hive, how many bees could have flown out?
__ bees

Problem Solving • Applications

Question 6.
MATHEMATICAL PRACTICE
Make Connections Brendan made this number line to find a difference. What was he subtracting from 100? Explain your answer.

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Question 7.
THINK SMARTER
There are 52 pictures on the wall. 37 are wild cats and the rest are birds. How many of the pictures are birds? Use the numbers and symbols on the tiles to complete the number sentence for the problem.

_______________
___ birds

TAKE HOME ACTIVITY
• Have your child explain how he or she solved one problem in this lesson.

Algebra • Write Equations to Represent Subtraction Homework & Practice 5.10

Write a number sentence for the problem. Use a for the missing number. Then solve.

Question 1.
29 children rode their bikes to school. After some of the children rode home, there were 8 children with bikes still at school. How many children rode their bikes home?
________
__ children

Answer:
The number of students who rode their bikes home is 29 – 8= 21 children rode their bike home.

Explanation:
As 29 children rode their bikes to school and after that some of the children rode home, there were 8 children with bikes still at school. So the number of students who rode their bikes home is 29 – 8= 21 children rode their bike home. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of students who rode their bikes home is 21 children rode their bike home.

Problem Solving

Solve. Write or draw to explain.

Question 2.
There were 21 children in the library. After 7 children left the library, how many children were still in the library?
__ children

Question 3.
WRITE Math
Describe different ways that you can show a story problem. Use one of the problems in this lesson as your example.
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Lesson Check

Question 1.
Cindy had 42 beads. She used some beads for a bracelet. She has 14 beads left. How many beads did she use for the bracelet?
__ beads

Question 2.
Jake had 36 baseball cards. He gave 17 cards to his sister. How many baseball cards does Jake have now?
__ cards

Spiral Review

Question 3.
What is the sum?
6 + 7 = __

Question 4.
What is the difference?
16 – 9 = __

Answer:
The subtraction of 9 from 16 is 7. And there are zero tens and seven ones.

Explanation:
In the above image, we can see that there are nine tens and zero ones. So here we need to subtract 9 from 16, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 9 from 16 is 16 – 9= 7 and there are zero tens and seven ones.

Question 5.
What is the difference?

Answer:
The subtraction of 39 from 46 is 7. And there are zero tens and seven ones.

Explanation:
In the above image, we can see that there are four tens and six ones. So here we need to subtract 39 from 46, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 39 from 46 is 46 – 39= 7 and there are zero tens and seven ones.

Question 6.
Write an addition fact that will give the same sum as 6 + 8.
10 + ___

Answer:
The sum of the two numbers is 14.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 6 + 8 is 14. So to get the same sum we need to add 4, so the sum of the 10 + 4= 14, which is same as 6 + 8 sum.

Lesson 5.11 Solve Multistep Problems

Essential Question
How do you decide what steps to do to solve a problem?

Listen and Draw

Label the bar model to show each problem. Then solve.

Math Talk
MATHEMATICAL PRACTICES

Describe how the two bar models are different.

Model and Draw

Bar models help you know what to do to solve a problem.
Ali has 27 stamps. Matt has 38 stamps. How many more stamps are needed so they will have 91 stamps?

They need __ more stamps

Share and Show MATH BOARD

Complete the bar models for the steps you do to solve the problem.

Question 1.
Jen has 93 beads. Ana has 46 red beads and 29 blue beads. How many more beads does Ana need to have 93 beads also?


__ more beads

Answer:
Ana needs 18 beads to have 93 beads.

Explanation:
As Jen has 93 beads and Ana has 46 red beads and 29 blue beads, so the total number of beads does Ana had is 46 + 29= 75 beads. So the number of many more beads does Ana need to have 93 beads is 93 – 75= 18 beads. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So Ana needs 18 beads to have 93 beads.

On Your Own

Complete the bar models for the steps you do to solve the problem.

Question 2.
Max has 35 trading cards. He buys 22 more cards. Then he gives 14 cards to Rudy. How many cards does Max have now?

Answer:
The number of many cards does Max have now is 43 trading cards.

Explanation:
As Max has 35 trading cards and he buys 22 more cards, so the total number of cards will be 35 + 22= 57 trading cards. Then he gives 14 cards to Rudy. So the number of trading cards will be 57 – 14= 43 trading cards. So the number of many cards does Max have now is 43 trading cards.

Question 3.
Drew has 32 toy cars. He trades 7 of those cars for 11 other toy cars. How many toy cars does Drew have now?

Question 4.
Marta and Debbie each have 17 ribbons. They buy 1 package with 8 ribbons in it. How many ribbons do they have now?

Answer:
The total number of ribbons do they had now is 42 ribbons.

Explanation:
As Marta and Debbie each have 17 ribbons, so the total number of ribbons did Marta and Debbie had together is 17 + 17= 34 ribbons. And they bought 1 package with 8 ribbons in it. So the total number of ribbons do they had now is 34 + 8= 42 ribbons.

Problem Solving • Applications WRITE Math

Question 5.
Shelby had 32 rocks. She finds 33 more rocks at the park and gives 28 rocks to George. How many rocks does she have now?


__ rocks

Answer:
So the number of many rocks does she have now is 37 rocks.

Explanation:
As Shelby had 32 rocks and she finds 33 more rocks at the park, so the total number of rocks did Shelby had now is 32 + 33= 65 rocks. And Shelby gives 28 rocks to George. So the number of many rocks does she have now is 65 – 28= 37 rocks. so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of many rocks does she have now is 37 rocks.

Question 6.
Benjamin finds 31 pinecones at the park. Together, Jenna and Ellen find the same number of pinecones as Benjamin. How many pinecones could each girl have found?

Jenna: __ pinecones
Ellen: __ pinecones

Answer:

Explanation:
As Benjamin finds 31 pinecones at the park and Jenna and Ellen together finds the same number of pinecones as Benjamin. How many pinecones could each girl have found

Question 7.
THINK SMARTER
Tanya finds 22 leaves. Maurice finds 5 more leaves than Tanya finds. How many leaves do the children find? Draw to show how you solve the problem.

__ leaves

Answer:
The number of many leaves do the children finds together is 22 + 5=  27 leaves.

Explanation:
As Tanya finds 22 leaves and Maurice finds 5 more leaves than Tanya finds. So the number of many leaves do the children finds together is 22 + 5=  27 leaves.

TAKE HOME ACTIVITY
• Have your child explain how he or she would solve Exercise 6 if the number 31 was changed to 42.

Solve Multistep Problems Homework & Practice 5.11

Complete the bar models for the steps you do to solve the problem

Question 1.
Greg has 60 building blocks. His sister gives him 17 more blocks. He uses 38 blocks to make a tower. How many blocks are not used in the tower?

__ blocks

Answer:
The number of many blocks are not used in the tower is 5 blocks.

Explanation:
As Greg has 60 building blocks and his sister gives him 17 more blocks, so the number of blocks did Greg had now is 60 – 17= 43 blocks and he uses 38 blocks to make a tower so the number of many blocks are not used in the tower is 43 – 38= 5 blocks. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of many blocks are not used in the tower is 5 blocks.

Problem Solving

Solve. Write or draw to explain.

Question 2.
Ava has 25 books. She gives away 7 books. Then Tom gives her 12 books. How many books does Ava have now?
__ books

Answer:
The number of many books does Ava have now is 6 books.

Explanation:
As Ava has 25 books and she gives away 7 books, then Ava will have 25 – 7= 18 books and then Tom gives her 12 books, so the number of books did Ava have now is 18 – 12= 6 books. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the number of many books does Ava have now is 6 books.

Question 3.
WRITE Math
Choose one of the problems on this page. Describe how you decided what steps were needed to solve the problem.
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Lesson Check

Question 1.
Sara has 18 crayons. Max has 19 crayons. How many more crayons do they need to have 50 crayons altogether?
__ crayons

Answer:
They need 13 crayons more do they need to have 50 crayons altogether.

Explanation:
As Sara has 18 crayons and Max has 19 crayons, so the total number of crayons do they have together is 18 + 19= 37 crayons. So to get 50 crayons altogether we need to perform subtraction. So we need 50 – 37= 13 crayons more do they need to have 50 crayons altogether. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So They need 13 crayons more do they need to have 50 crayons altogether.

Question 2.
Jon has 12 pennies. Lucy has 17 pennies. How many more pennies do they need to have 75 pennies altogether?
__ pennies

Answer:
They need 46 pennies more to have 75 pennies altogether.

Explanation:
As Jon has 12 pennies and Lucy has 17 pennies, so the total number of pennies together they have is 29 pennies. So to 75 pennies together we need to perform subtraction 75 – 29= 46 pennies. So the number of many frames does he still have now is 32 – 15= 17 frames. So we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the total number of pennies together they have is 29 pennies. So to 75 pennies together we need to perform subtraction 75 – 29= 46 pennies.

Spiral Review

Question 3.
What is the difference?
58 – 13 = __

Answer:
The subtraction of 8 from 51 is 43. And there are four tens and three ones.

Explanation:
In the above image, we can see that there are three tens blocks and six one’s blocks. So here we need to subtract 8 from 51, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 8 from 51 is 51 – 8= 43 and there are four tens and three ones.

Question 4.
What is the sum?

Answer:
The sum of the two numbers is 62.

Explanation:
The sum can be defined as the resulting of two or more numbers by adding. So here the sum of the two numbers 47 + 15 is 62.

Question 5.
There are 26 cards in a box. Bryan takes 12 cards. How many cards are still in the box?
__ cards

Answer:
The number of cards still in the box is 14 cards.

Explanation:
As there are 26 cards in a box and Bryan takes 12 cards, so the number of cards still in the box is 26 – 12= 14 cards. we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 12 from 26 is 26 – 12= 14 and there are zero tens and four ones.

2-Digit Subtraction Chapter 5 Review Test

Question 1.
Do you need to regroup to subtract? Choose Yes or No.

Question 2.
Use the number line. Count up to find the difference.
52 – 48 = __

Answer:
The subtraction of 48 from 52 is 4. And there are zero tens and four ones.

Explanation:
Here we need to subtract 48 from 52, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 48 from 52 is 52 – 48= 4 and there are zero tens and four ones.

Question 3.
Ed has 28 blocks. Sue has 34 blocks. Who has more blocks? How many more? Label the bar model. Solve.

Circle the word and number from each box to make the sentence true.

Break apart the number you are subtracting. Write the difference?

Answer:
Sue has more number of blocks tha Ed. And had 6 more blocks than Ed.

Explanation:
Ed has 28 blocks and Sue has 34 blocks. As 34 is greater than 28, so Sue has more number of blocks and has 34 – 28= 6 more blocks than the Ed. So to perform Break apart the number subratction for 34 – 28 first we will break into tens and ones. So here we will break 28 as 20 and 8 and we will subtract 20 and we will get the result as 14. Then we will start from 14 and subtract 8 to get to 6. So we will get the result as 6. The subtraction of 34 – 28 is 6.

Question 4.

Answer:
The subtraction of 42 – 8 is 34.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 8 as 2 and 6 and we will subtract 2 and we will get the result as 42. Then we will start from 42 and subtract 6 to get to 34 and then. So we will get the result as 34. The subtraction of 42 – 8 is 34.

Question 5.

Answer:
The subtraction of 53 – 16 is 37.

Explanation:
Here, we will break apart the number that we are subtracting. So first we will break into tens and ones. So here we will break 10 as 6 and we will subtract 10 and we will get the result as 43. Then we will start from 43 and subtract 6 to get to 37 and then. So we will get the result as 37. The subtraction of 53 – 16 is 37.

Question 6.
What is 33 − 19? Use the numbers on the tiles to rewrite the subtraction problem. Then find the difference.

Answer:
The subtraction of 19 from 33 is 14. And there are one ten and four ones.

Explanation:
In the above image, we can see that there are three tens and three ones. So here we need to subtract 19 from 33, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 19 from 33 is 33 – 19= 14 and there are one ten and four ones.

Question 7.
GO DEEPER
Jacob’s puzzle has 84 pieces. Jacob puts together 27 pieces in the morning. He puts together 38 more pieces in the afternoon. How many pieces does Jacob need to put together to finish the puzzle?

Complete the bar models for the steps you do to solve the problem.
__ more pieces

Answer:
Jacob needs 19 pieces to complete the puzzle.

Explanation:
Jacob’s puzzle has 84 pieces and Jacob puts together 27 pieces in the morning and he puts together 38 more pieces in the afternoon. So the total number of puzzles kept by Jacob together in the morning and the afternoon is 27 + 38= 65 pieces. So Jacob needs 84 – 65= 19 pieces to complete the puzzle.

Regroup if you need to. Write the difference.

Question 8.

Answer:
The subtraction of 5 from 28 is 23. And there are two tens and three ones.

Explanation:
In the above image, we can see that there are two tens and eight ones. So here we need to subtract 5 from 28, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 5 from 28 is 28 – 5= 23 and there are two ten and three ones.

Question 9.

Answer:
The subtraction of 12 from 32 is 23. And there are two tens and three ones.

Explanation:
In the above image, we can see that there are two tens and eight ones. So here we need to subtract 5 from 28, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 5 from 28 is 28 – 5= 23 and there are two ten and three ones.

Question 10.
Find the difference.

Answer:
The subtraction of 62 from 90 is 28. And there are two tens and eight ones.

Explanation:
In the above image, we can see that there are nine tens and zero ones. So here we need to subtract 62 from 90, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 62 from 90 is 90 – 62= 28 and there are two tens and eight ones.

Fill in the bubble next to one number from each column to show the difference.

Question 11.
There are 22 children at the park. 5 children are on the swings. The rest of the children are playing ball. How many children are playing ball?

Answer:
The number of children is playing ball is 17 children.

Explanation:
As there are 22 children at the park and 5 children are on swings and the rest of the children are playing ball. So the number of children are playing ball is 22 – 15= 17 children.

Question 12.
THINK SMARTER
Subtract 27 from 43. Draw to show the regrouping.
Fill in the bubble next to all the ways to write the difference.

Answer:
The subtraction of 27 from 43 is 16. And there are one ten and six ones.

Explanation:
In the above image, we can see that there are two tens and eight ones. So here we need to subtract 27 from 43, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 27 from 43 is 43 – 27= 43 and there are one ten and six ones.

Question 13.
Jill collects stamps. Her stamp book has space for 64 stamps. She needs 18 more stamps to fill the book. How many stamps does Jill have now?
Write a number sentence for the problem.
Use a for the missing number. Then solve.
________
Jill has __ stamps.

Answer:
The number of does Jill have now is 46 stamps.

Explanation:
Jill collects stamps and her stamp book has space for 64 stamps then she needs 18 more stamps to fill the book. So the number of does Jill have now is 64 – 18= 46 stamps.

Question 14.
Draw a quick picture to solve. Write the difference.

Explain what you did to find the difference.
_______________
_______________

Answer:
The subtraction of 25 from 62 is 37. And there are three tens and seven ones.

Explanation:
In the above image, we can see that there are two tens and eight ones. So here we need to subtract 25 from 62, so we will perform regrouping of subtraction. Here Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So the subtraction of 25 from 62 is 62 – 25= 37 and there are three tens and seven ones.

Conclusion:

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