Vijaya Sree

Download Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables pdf for free of cost. It is very important for the students to learn the fundamentals at the secondary level. In order to help you guys, we are providing the answers to all the questions in HMH Go Math Grade 6 Chapter 9 Solution Key Independent and Dependent Variables.

Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

The Independent and Dependent Variables chapter consists of the topics like equations and tables, analyze relationships, graphs etc. It is essential for students to know the relationship between the graphs and tables in this chapter. You can know different methods of solving the problems by using Go Math Grade 6 Solution Key Chapter 9 Independent and Dependent Variables. All you have to do is to tap the below-given links.

Lesson 1: Independent and Dependent Variables

• Share and Show – Page No. 493
• Unlock the Problem – Page No. 494
• Independent and Dependent Variables – Page No. 495
• Lesson Check – Page No. 496

Lesson 2: Equations and Tables

• Share and Show – Page No. 499
• Cause and Effect – Page No. 500
• Equations and Tables – Page No. 501
• Lesson Check – Page No. 502

Lesson 3: Problem Solving • Analyze Relationships

• Share and Show – Page No. 505
• On Your Own – Page No. 506
• Problem Solving Analyze Relationships – Page No. 507
• Lesson Check – Page No. 508

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 509
• Mid-Chapter Checkpoint – Page No. 510

Lesson 4: Graph Relationships

• Share and Show – Page No. 513
• Problem Solving + Applications – Page No. 514
• Graph Relationships – Page No. 515
• Lesson Check – Page No. 516

Lesson 5: Equations and Graphs

• Share and Show – Page No. 519
• Problem Solving + Applications – Page No. 520
• Equations and Graphs – Page No. 521
• Lesson Check – Page No. 522

Chapter 9 Review/Test

• Chapter 9 Review/Test – Page No. 523
• Chapter 9 Review/Test – Page No. 524
• Chapter 9 Review/Test – Page No. 525
• Chapter 9 Review/Test – Page No. 526
• Chapter 9 Review/Test – Page No. 527
• Chapter 9 Review/Test – Page No. 528

Share and Show – Page No. 493

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 1.
An online store lets customers have their name printed on any item they buy. The total cost c in dollars is the price of the item p in dollars plus $3.99 for the name.
Type below:
________________

Answer: c = p + $3.99

Explanation:
The independent variable is c, the price of the item because it is not going to depend on anything else.
The dependent variable is p because the total cost depends on how many items there are, whether your name is marked on it, etc.
The equation would be:
c = p + $3.99

Question 2.
A raft travels downriver at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rate times the number of hours h.
Type below:
________________

Answer: d = 6 × h

Explanation:
Speed of the raft= 6 miles per hour
Total distance (d) of the raft = rate × number of hours h
The dependent variable is the number of hours h
The independent variable is distance d.
The equation would be:
d = 6 × h

Question 3.
Apples are on sale for $1.99 a pound. Sheila buys p pounds of apples for a total cost of c dollars.
Type below:
________________

Answer: c = p × $1.99

Explanation:
Apples are on sale for $1.99 a pound
p = pounds of apples
c = total cost of dollars
The equation would be:
c = p × $1.99
c is the independent variable.
p is the dependent variable.

On Your Own

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 5.
Billy has $25. His father is going to give him more money. The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.
Type below:
________________

Answer: t = m + $25

Explanation:
Billy has $25. His father is going to give him more money.
The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.
The equation would be:
t = m + $25
t is the independent variable
m is the dependent variable.

Question 6.
Connect Symbols and Words Describe a situation that can be represented by the equation c = 12b.
Type below:
________________

Answer:
Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the cost of the necklace c.
The equation is c = 12n

Question 7.
Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling. Write an equation and use it to find how much it will cost Belinda to buy 12 glasses.
Type below:
________________

Answer:
Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling.

The equation is: c = 4.25n + 9.95
Now we have to find the cost of 12 glasses.
c = 4.25(12) + 9.95
c = 60.95
It takes $60.95 to buy 12 glasses.

Unlock the Problem – Page No. 494

Question 8.
Benji decides to save $15 per week to buy a computer program. Write an equation that models the total amount t in dollars Benji will have saved in w weeks.
a. What does the variable t represent?
Type below:
________________

Answer: t represents the total amount in dollars Banji saved.

Question 8.
b. Which is the dependent variable? Which is the independent variable? How do you know?
Type below:
________________

Answer:
w is the dependent variable.
t is the independent variable.
w is dependent because it represents the number of weeks. So, we have to multiply 15 by w.
t is an independent variable because t determines the value of a dependent variable.

Question 8.
c. How can you find the total amount saved in w weeks?
Type below:
________________

Answer: We can find the total amount saved in w weeks by multiplying 15 with w.

Question 8.
d. Write an equation for the total amount that Benji will have saved.
Type below:
________________

Answer: t = 15w

Question 9.
Coach Diaz is buying hats for the baseball team. The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it. Write an equation that can be used to find the cost of the hats.
Type below:
________________

Answer: c = n + 2h

Explanation:
Coach Diaz is buying hats for the baseball team.
The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it.
c represents the total cost.
n is the number of hats
h is the price per hat.
The equation is c is equal to the number of hats plus price per hat and $2.
c = n + 2h

Question 10.
A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot. The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable. Choose the letter or equation that makes each sentence true.
The independent variable is ______________ .
The dependent variable is ______________ .
The equation that represents the relationship between the variables is ______________ .

Answer:
A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot.
The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable.
The equation would be:
w = 0.2f
f is the dependent variable
w is the dependent variable.

Independent and Dependent Variables – Page No. 495

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 2.
An online clothing store charges $6 for shipping, no matter the price of the items. The total cost c in dollars is the price of the items ordered p plus $6 for shipping.
Type below:
________________

Answer: c = p + 6

Explanation:
Given,
An online clothing store charges $6 for shipping, no matter the price of the items.
The total cost c in dollars is the price of the items ordered p plus $6 for shipping.
The equation would be:
c = p + $6
where c = cost in dollars
p is the price of items
The independent variable is c.
The dependent variable is p

Question 3.
Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the number of necklaces n.
Type below:
________________

Answer: b = 12n

Explanation:
Melinda is making necklaces. She uses 12 beads for each necklace.
The total number of beads b depends on the number of necklaces n.
b = total number of beads
n = number of necklaces
The equation would be:
b = 12n
b is the independent variable
n is the dependent variable.

Problem Solving

Question 4.
Maria earns $45 for every lawn that she mows. Her earnings e in dollars depend on the number of lawns n that she mows. Write an equation that represents this situation.
Type below:
________________

Answer: e = 45n

Explanation:
Maria earns $45 for every lawn that she mows.
Her earnings e in dollars depend on the number of lawns n that she mows.
e = earnings in dollars
n = number of lawns
The equation would be:
e = 45n
e is the independent variable.
n is the dependent variable.

Question 6.
Write a situation in which one unknown is dependent on another unknown. Write an equation for your situation and identify the dependent and independent variables.
Type below:
________________

Answer:
Byron is playing a game. He earns 10 points for each question he answers correctly. His total score s equals the number of correct answers a time a.
Answer:
Dependent variable: s
Independent variable: a
Equation: s = 10a

Lesson Check – Page No. 496

Question 1.
There are 12 boys in a math class. The total number of students s depends on the number of girls in the class g. Write an equation that represents this situation.
Type below:
________________

Answer: s = 12 + g

Explanation:
There are 12 boys in a math class.
The total number of students s depends on the number of girls in class g.
The equation would be:
s = 12 + g
s is the independent variable.
g is the dependent variable.

Spiral Review

Question 3.
The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees. Gwen measured a Celsius temperature of 35 degrees. What is this temperature in degrees Fahrenheit?
______ °F

Answer: 95 degrees

Explanation:
The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees.
C = 35
F = 9C ÷ 5 + 32
F = 9(35) ÷ 5 + 32
F = 315 ÷ 5 + 32
F = 63 + 32
F = 95 degrees

Question 4.
Write an equation to represent this sentence. The difference of a number n and 1.8 is 2.
Type below:
________________

Answer: n – 1.8 = 2

Explanation:
The difference of a number n and 1.8 is 2.
The phrase difference is nothing but subtraction.
The equation would be:
n – 1.8 = 2

Question 6.
Graph x ≤ ^–4.5 on a number line.
Type below:
________________

Answer:

Share and Show – Page No. 499

Use the equation to complete the table.

Question 1.
y = x + 3

Type below:
________________

Answer:
Substitute the value of x in the above equation.
The equation is x + 3.

Question 2.
y = 2x + 1

Type below:
________________

Answer:
Substitute the value of x in the above equation.
The equation is y = 2x + 1

On Your Own

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 3.

Type below:
________________

Answer:
The equation is y = 2x
The output is multiple of 2 and x
For x = 10
The output is y = 2x
y = 2 × 10 = 20

Question 4.

Type below:
________________

Answer:
y = x ÷ 2
The output is the quotient of x and 2.
The output for x = 40 is
y = 40 ÷ 2
y = 20

Question 5.
The table shows the current cost of buying apps for a cell phone. Next month, the price of each app will double. Write an equation you can use to find the total cost y of buying x apps next month.

Type below:
________________

Answer: y = 3x

Explanation:
The equation is multiple of 3 and x.
The equation is y = 3x

Question 6.
A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle. The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours. Use numbers and words to explain how to find the cost c of renting a bicycle for 6 hours.

Type below:
________________

Answer:
A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle.
The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours.
For x = 1
c = 1.50(1) + 4.50
c = 1.50 + 4.50
c = $6.00
For x = 2
c = 1.50(2) + 4.50
c = 3.00 + 4.50
c = $7.50
For x = 3
c = 1.50(3) + 4.50
c = 4.50 + 4.50
c = $9.00
For x = 4
c = 1.50(4) + 4.50
c = 6.00 + 4.50
c = $10.50

</aCause and Effect – Page No. 500

The reading skill cause and effect can help you understand how a change in one variable may cause a change in another variable.

In karate, a person’s skill level is often shown by the color of his or her belt. At Sara’s karate school, students must pass a test to move from one belt level to the next. Each test costs $23. Sara hopes to move up 3 belt levels this year. How will this affect her karate expenses?

Question 7.
Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.
Type below:
________________

Answer: y = 23x

Explanation:
Let x represent the number of belt levels Sara moves up and let y represent the increase in dollars in her karate expenses.
Write the equation:
y = 23x
Sara plans to move up 3 levels, so replace x with 3
y = 23 × 3
y = 69
So, if Sara moves up 3 belt levels this year, her karate expenses will increase by $69.

Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.

Question 8.
Classes at Tony’s karate school cost $29.50 per month. This year he plans to take 2 more months of classes than he did last year. How will this affect Tony’s karate expenses?
Type below:
________________

Answer:
The equation is y = 29.50x
where x is the number of additional classes
y is the increase in dollars in expenses.
Tony plans to take 2 more months of classes so his expenses will increase by y = 29.5 × 2 = $59

Equations and Tables – Page No. 501

Use the equation to complete the table.

Question 1.
y = 6x

Type below:
________________

Answer:
The equation is y = 6x
Substitute the value of x in the above equation.

Question 2.
y = x − 7

Type below:
________________

Answer:
The equation is y = x – 7
Substitute the value of x in the equation.
Use the equation to get the output y.

Question 3.
y = 3x + 4

Type below:
________________

Answer:
The equation is y = 3x + 4
Substitute the value of x in the above equation.
Use the equation to get the output y.

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 4.

Type below:
________________

Answer: y = 8x

Explanation:
The equation is the multiple of 8.
The equation is y = 8x
Substitute x = 3 in the equation.
y = 8(3) = 24
Thus the unknown value is 24.

Question 5.

Type below:
________________

Answer: y = x ÷ 2

Explanation:
The equation is divisible by 2.
The equation is y = x ÷ 2
Substitute x = 22 in the equation.
y = x ÷ 2
y = 22 ÷ 2
y = 11
Therefore the unknown value is 11.

Problem Solving

Question 7.
Write an equation for the relationship shown in the table. Then use the equation to find the estimated number of shrimp in a 5-pound bag.

Type below:
________________

Answer: y = 24x

Explanation:
The equation is the multiple of 24.
The equation is y = 24x

Question 8.
Write a word problem that can be represented by a table and equation. Solve your problem and include the table and equation.
Type below:
________________

Answer:
Susie ran a race. She ran 5 miles an hour and the race took her x hours to complete.
y = 5x
Use the equation to get the output y.

Lesson Check – Page No. 502

Question 1.
Write an equation that represents the relationship shown in the table.

Type below:
________________

Answer: y = x – 4

Explanation:
The relationship between x and y is y = x – 4.
We get the output when we subtract 4 from x.

Question 2.
There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18. Write an equation for the relationship that gives the total cost y in dollars of joining the gym and using it for x months.
Type below:
________________

Answer: y = 18x + 27

Explanation:
Given,
There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18.
Here y represents the total coast in dollars of joining the gym.
x represents months.
So, the equation would be: y = 18x + 27

Spiral Review

Question 3.
Mindy wants to buy several books that each cost $10. She has a coupon for $6 off her total cost. Write an expression to represent her total cost in dollars for b books.
Type below:
________________

Answer: 10b – 6

Explanation:
Given,
Mindy wants to buy several books that each cost $10.
She has a coupon for $6 off her total cost.
b represents the total cost in dollars for b books.
So, the equation to represent the total cost is 10b – 6.

Question 5.
Which of the following are solutions to the inequality n > ^–7?
n = ^–7 n = ^–6.9 n = ^–7.2 n = ^–6\(\frac{1}{2}\)
Type below:
________________

Answer: n = -7

Explanation:
Substitute the value of n in the inequality.
n > ^–7
n = -7
-7 > -7
Thus -7 is the solution.
n = ^–6.9
-6.9 > -7
-6.9 is not the solution.
n = ^–7.2
-7.2 > -7
-7.2 is less than – 7
Thus -7.2 is not the solution.
n = ^–6\(\frac{1}{2}\)
^–6\(\frac{1}{2}\) > -7
^–6\(\frac{1}{2}\) is not the solution.

Question 6.
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies. He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation.
Type below:
________________

Answer: p = d – 5.50

Explanation:
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies.
He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings.
p represents the total profit in dollars.
d is the dollars worth of brownies.
The equation is p = d – 5.50

Share and Show – Page No. 505

Question 1.
A soccer coach is ordering shirts for the players. The table shows the total cost based on the number of shirts ordered. How much will it cost the coach to order 18 shirts?

$ _______

Answer: 270

Explanation:
First, find a pattern and write an equation.
The cost is $15 multiplied by the number of shirts.
c = $15 × n
Next, use the equation to find the cost of 18 shirts.
c = $15 × n
c = $15 × 18
c = $270
So, the cost of 18 shirts is $270.

Question 2.
What if the coach spent $375 to purchase a number of shirts? Could you use the same equation to find how many shirts the coach bought? Explain.
Type below:
________________

Answer:
Yes, I could use the same equation.
I could substitute 375 for the variable c and solve for n.

Question 3.
The table shows the number of miles the Carter family drove over time. If the pattern continues, will the Carter family have driven more than 400 miles in 8 hours? Explain.

Type below:
________________

Answer: 376 miles

Explanation:
First, find a pattern and write an equation.
The distance is 47 miles multiplied by the number of hours.
y = 47 × x
Next, use the equations to find the distance for 8 hours.
y = 47x
y = 47 × 8
y = 376
So, the family will have driven 376 miles in 8 hours, which is less than 400 miles.

On Your Own – Page No. 506

Question 5.
A group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June. If the pattern continues, how many hours will they practice in November?
_______ hours

Answer: 36 hours

Explanation:
Given that, a group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June.
The equation would be h = 4m
m = 9
h = 4 × 9 = 36
Thus the group practiced 36 hours in the month of November.

Question 6.
The table shows the number of hours Jacob worked and the amount he earned each day.

At the end of the week, he used his earnings to buy a new pair of skis. He had $218 left over. How much did the skis cost?
$ _______

Answer: 142

Explanation:
First, add the total amount he earned.
60 + 84 + 72 + 96 + 48 = 360
Jacob earned $360 for the week.
If he has $218 leftover, this means that the cost of the skis is 360 – 218 = 14
Therefore the cost of the skis is $142.

Question 7.
Pose a Problem Look back at Problem 6. Use the data in the table to write a new problem in which you could use the strategy to find a pattern. Then solve the problem.
Type below:
________________

Answer:
How much money would Jacob earn if he worked for 10 hours?
From the table, we can see that the pattern is that Jacob earns $12 per hour.
The equation is s = 12h
Where s is the total pay and h is the number of hours worked.
s = 12h
s = 12 × 10
s = 120
Thus Jacob earned $120 for 10 hours.

Question 8.
Draw Conclusions Marlon rode his bicycle 9 miles the first week, 18 miles the second week, and 27 miles the third week. If the pattern continues, will Marlon ride exactly 100 miles in a week at some point? Explain how you determined your answer.
Type below:
________________

Answer: No, Marlon will not ride exactly 100 miles in a week at some point.
Each number in the pattern is a multiple of 9 and 100 is not a multiple of 9.

Question 9.
A diving instructor ordered snorkels. The table shows the cost based on the number of snorkels ordered.

If the diving instructor spent $1,024, how many snorkels did he order? Use numbers and words to explain your answer.
_______ snorkels

Answer: 32

Explanation:
Use the table to find the equation.
c represents the cost based on the number of snorkels.
s represents the number of snorkels
The equation would be:
c = 32s
The diving instructor spent $1,024
c = 1024
1024 = 32s
s = 1024/32
s = 32
Thus the diving instructor gets 32 snorkels for $1024.

Problem Solving Analyze Relationships – Page No. 507

The table shows the number of cups of yogurt needed to make different amounts of a fruit smoothie. Use the table for 1–3.

Question 1.
Write an equation to represent the relationship.
Type below:
________________

Answer: c = 3b

Explanation:
c represents number of cups of yogurt
b represents the batches
From the table, we can observe that b is multiplied with 3 to get cups of yogurt.
So, the equation to find the number of cups of yogurt is c = 3b

Question 2.
How much yogurt is needed for 9 batches of smoothie?
_______ cups

Answer: 27

Explanation:
Given that there are 9 batches of smoothie.
By using the above equation we can find the number of cups.
c = 3b
c = 3 × 9 = 27 cups
Thus 27 cups of yogurt is need to make 9 batches of smoothie.

Question 3.
Jerry used 33 cups of yogurt to make smoothies. How many batches did he make?
_______ batches

Answer: 11 batches

Explanation:
Jerry used 33 cups of yogurt to make smoothies.
Use the equation to find the batches.
c = 3b
33 = 3b
b = 33/3
b = 11
Therefore jerry made 11 batches of smoothie.

The table shows the relationship between Winn’s age and his sister’s age. Use the table for 4–5.

Question 4.
Write an equation to represent the relationship.
Type below:
________________

Answer: s = w + 4

Explanation:
By using the table we can find the relationship between wine’s age and wine’s sister’s age.
Winn’s sister’s age will be the sum of Winn’s age and 4.
So, the equation is s = w + 4

Question 5.
When Winn is 14 years old, how old will his sister be?
_______ years old

Answer: 18

Explanation:
Use the equation s = w + 4
W = 14 years
s = 14 + 4
s = 18 years
Thus winn’s sister’s age is 18 years.

Question 6.
Write a problem for the table. Use a pattern and an equation to solve your problem.

Type below:
________________

Answer: m = 16h

Explanation:
Jerry runs 16 miles per hour. How many miles he can run in 5 hours?
The equation is m = 16h
m = 16 × 5 = 80 miles
Therefore jerry runs 80 miles in 5 hours.

Lesson Check – Page No. 508

Question 1.
The table shows the total cost c in dollars of n gift baskets. What will be the cost of 9 gift baskets?

Answer: $108

Explanation:
By seeing the above we can say that the equation is
c = 12n
n = 9
Use the equation to find the cost of 9 gift baskets.
c = 12 × 9
c = $108
Thus the cost of 9 gift baskets is $108.

Question 2.
The table shows the number of minutes m that Tara has practiced after d days. If Tara has practiced for 70 minutes, how many days has she practiced?

_______ days

Answer: 2 days

Explanation:
The table shows the number of minutes m that Tara has practiced after d days.
The equation would be
m = 35d
If Tara has practiced for 70 minutes
m = 70
Use the equation to find the number of days she practiced.
70 = 35d
d = 70/35
d = 2 days
Thus Tara has practiced 2 days.

Spiral Review

Question 3.
Soccer shirts cost $15 each, and soccer shorts cost $18 each. The expression 15n + 18n represents the total cost in dollars of n uniforms. Simplify the expression by combining like terms.
Type below:
________________

Answer: 33n

Explanation:
Soccer shirts cost $15 each, and soccer shorts cost $18 each.
The expression 15n + 18n represents the total cost in dollars of n uniforms.
Now combine the like terms.
15n + 18n = 33n

Question 4.
What is an equation that represents the relationship in the table?

Type below:
________________

Answer: y = x ÷ 2

Explanation:
By seeing the above table we can find the relationship between x and y.
y is the quotient of x and 2.
We get the value of y when you divide x by 2.
The equation is y = x ÷ 2

Question 6.
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to Marisol’s ratio.
Type below:
________________

Answer: 9:2

Explanation:
Given that, Marisol plans to make 9 mini-sandwiches for every 2 people attending her party.
The ratio will be 9:2
Now we need to write the equivalent ratio for the 9 sandwiches for every 2 people i.e, 9:2
We know that the equivalent ratio can be written as
9/2 × 3/3 = 27/6
9/2 × 5/5 = 45/6
Thus the equivalent fractions are 27/6 and 45/6.

Mid-Chapter Checkpoint – Vocabulary – Page No. 509

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

Question 1.
A(n) _____ has a value that determines the value of another quantity.
Type below:
________________

Answer: Independent variable
An Independent variable has a value that determines the value of another quantity.

Question 2.
A variable whose value is determined by the value of another quantity is called a(n) _____.
Type below:
________________

Answer: Dependent variable
A variable whose value is determined by the value of another quantity is called a Dependent variable.

Concepts and Skills

Identify the independent and dependent variables.

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 5.

Type below:
________________

Answer: 49

Explanation:
The equation is y = 7x
x = 7
y = 7 × 7 = 49
Thus the unknown value y is 49.

Question 6.

Type below:
________________

Answer: 12

Explanation:
The equation for the above table is
y = x ÷ 5
Use the equation to find the value of y where x = 60
y = 60 ÷ 5
y = 12
Thus the unknown value is 12.

Write an equation that describes the pattern shown in the table.

Question 7.
The table shows how the number of pepperoni slices used depends on the number of pizzas made.

Type below:
_______________

Answer: y = 17x

Explanation:
The table shows how the number of pepperoni slices used depends on the number of pizzas made.
y is 17 times of x.
The equation for the above table is y = 17x

Question 8.
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.

Type below:
________________

Answer: m = w + 5

Explanation:
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.
m is equal to the sum of w and 5.
Thus the equation is m = w + 5.

Page No. 510

Question 9.
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band. Write an equation that models how many marching band members m there are if there are c concert band members.
Type below:
________________

Answer: m = 152 – c

Explanation:
Given,
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band.
m is equal to the difference of 152 and c.
The equation is m = 152 – c

Question 11.
Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
_______ hours

Answer: 28 hours

Explanation:
Amy volunteers at an animal shelter.
She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June.
As she started working from the march. December will be the 10th month.
Keep on adding 2 hours for each month you get 28 hours for December.
Thus she worked 28 hours in December.

Question 12.
Aaron wants to buy a new snowboard. The table shows the amount that he has saved. If the pattern in the table continues, how much will he have saved after 1 year?

$ _______

Answer: $540

Explanation:
Aaron wants to buy a new snowboard. The table shows the amount that he has saved.
The equation will be s = 45m
s is the money saved
m is the number of months
1 year = 12 months
s = 45 × 12
s = 540
Thus he saved $540 after 1 year.

Share and Show – Page No. 513

Graph the relationship represented by the table.

Question 1.

Type below:
________________

Answer: y = 50x

Question 2.

Type below:
________________

Answer: y = 5x

Graph the relationship represented by the table to find the unknown value of y.

Question 3.

Type below:
________________

Answer: 3

Question 4.

Type below:
________________

Answer: 6

On Your Own

Practice: Copy and Solve Graph the relationship represented by the table to find the unknown value of y.

Question 5.

Type below:
________________

Answer: 5

Question 6.

Type below:
________________

Answer: 7

Problem Solving + Applications – Page No. 514

The table at the right shows the typical price of a popular brand of corn cereal over time. Use the table for 7–8.

Question 7.
Use Graphs Complete the table below to show the cost of buying 1 to 5 boxes of corn cereal in 1988. Then graph the relationship on the coordinate plane at right.

Type below:
________________

Answer:

Question 8.
Suppose you graphed the cost of buying 1 to 5 boxes of corn cereal using the 1968 price and the 2008 price. Explain how those graphs would compare to the graph you made using the 1988 price.
Type below:
________________

Answer:
The points on both graphs would lie on a line, but the line for the 1968 costs would rise less steeply than the line for 1988 costs and the line for the 2008 costs would rise more steeply than the line for 1988 costs.

Question 10.
Graph the relationship represented by the table to find the unknown value of y.

Type below:
________________

Answer: 3

Graph Relationships – Page No. 515

Graph the relationship represented by the table.

Question 1.

Type below:
________________

Answer: y = 25x

Question 2.

Type below:
________________

Answer:

Graph the relationship represented by the table to find the unknown value of y.

Question 3.

Type below:
________________

Answer: 6

Question 4.

Type below:
________________

Answer: 2

Problem Solving

Question 5.
Graph the relationship represented by the table.

Type below:
________________

Answer: y = 15x

Question 6.
Use the graph to find the cost of purchasing 5 DVDs.
$ ______

Answer:
The above graph shows that the cost of 5 DVDs is $75.

Question 7.
Both tables and graphs can be used to represent relationships between two variables. Explain how tables and graphs are similar and how they are different.
Type below:
________________

Answer:
Tables and graphs can be useful tools for helping people make decisions. However, they only provide part of a story. Inferences often have to be made from the data shown. As well as being able to identify clearly what the graph or table is telling us, it is important to identify what parts of the story are missing.

Lesson Check – Page No. 516

Question 1.
Mei wants to graph the relationship represented by the table. Write an ordered pair that is a point on the graph of the relationship.

Type below:
________________

Answer: y = 8x

Question 2.
An online bookstore charges $2 to ship any book. Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars. Name an ordered pair that is a point on the graph of the relationship.
Type below:
________________

Answer:
An online bookstore charges $2 to ship any book.
Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars.
y = x + 2
x = 4
y = 4 + 2
y = 6
The ordered pair is (4,6)

Spiral Review

Question 3.
Write an expression that is equivalent to 6(g + 4).
Type below:
________________

Answer:
6(g + 4)
6 × g + 6 × 4
6g + 24

Question 5.
Graph n > ^–2 on a number line.
Type below:
________________

Answer:

Question 6.
Sam is ordering lunch for the people in his office. The table shows the cost of lunch based on the number of people. How much will lunch cost for 35 people?

$ _____

Answer: 280

Explanation:
Sam is ordering lunch for the people in his office.
The table shows the cost of lunch based on the number of people.
The equation is c = 8n
c = 8 × 35
c = 280
Thus the lunch cost for 35 people is $280.

Share and Show – Page No. 519

Graph the linear equation.

Question 1.
y = x + 2
Type below:
________________

Answer:

Question 2.
y = 3x
Type below:
________________

Answer:

Write the linear equation for the relationship shown by the graph.

Question 3.

Type below:
________________

Answer: y = x – 1

Question 4.
Type below:
________________

On Your Own

Graph the linear equation.

Question 5.
y = x + 1
Type below:
________________

Answer:

Question 6.
y = 2x − 1
Type below:
________________

Answer:

Question 7.
Identify Relationships The graph shows the number of loaves of bread y that Kareem bakes in x hours. Write the linear equation for the relationship shown by the graph.

Type below:
________________

Answer:
The ordered pairs are (1,1), (2,2), (4,4), (5,5)
Look for a pattern among the pairs: each y value is the same as the corresponding x-value.
The equation is y = x
y = x

Problem Solving + Applications – Page No. 520

The graph shows the growth of a bamboo plant. Use the graph for 8–9.

Question 8.
Write a linear equation for the relationship shown by the graph. Use your equation to predict the height of the bamboo plant after 7 days.
Type below:
________________

Answer:
Write the ordered pairs from the graph: (1,50), (2,100), (3,150), (4,200), (5,250).
Look for a pattern among the pairs: each y value is 50 times the corresponding x value.
The equation is y = 50x
For x = 7, the solution is y = 50 × 7 = 350.
So, the height of the bamboo plant after 7 days will be 350 centimeters.

Question 10.
Maria graphed the linear equation y = x + 3. Then she used her ruler to draw a vertical line through the point (4, 0). At what point do the two lines intersect?
Type below:
________________

Answer:
y = x + 3
y = 4 + 0 = 4
y = 4 + 3 = 7
The coordinate is (4, 7)

Question 11.
Antonio claims the linear equation for the relationship shown by the graph is y = \(\frac{1}{2}\)x + 2. Use numbers and words to support Antonio’s claim.

Type below:
________________

Answer:
The ordered pairs (2,3) and (6,5) on the line make the equation.
y = \(\frac{1}{2}\)x + 2
y = 1/2 × 2 + 2
y = 1 + 2 = 3
y = 1/2 × 6 + 2
y = 3 + 2 = 5

Equations and Graphs – Page No. 521

Graph the linear equation.

Question 1.
y = x − 3
Type below:
________________

Answer:

Question 2.
y = x ÷ 3
Type below:
________________

Answer:

Write a linear equation for the relationship shown by the graph.

Question 3.

Type below:
________________

Answer:
By seeing the above graph we can say that the equation is
y = x + 1

Question 4.

Type below:
________________

Answer:
The ordered pairs are (1,4), (1.5,6), (2,8)
By seeing the above pairs we can say that the equation is y = 4x

Problem Solving

Question 5.
Dee is driving at an average speed of 50 miles per hour. Write a linear equation for the relationship that gives the distance y in miles that Dee drives in x hours.
Type below:
________________

Answer: y = 50x

Explanation:
Dee is driving at an average speed of 50 miles per hour.
y represents the distance in miles
x is the number of hours.
y is equal to the product of 50 and x.
y = 50x

Question 6.
Graph the relationship from Exercise 5.
Type below:
________________

Answer:

Question 7.
Explain how to write a linear equation for a line on a graph.
Type below:
________________

Answer:
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope.

Lesson Check – Page No. 522

Question 1.
A balloon rises at a rate of 10 feet per second. What is the linear equation for the relationship that gives the height y in feet of the balloon after x seconds?
Type below:
________________

Answer: The linear equation for the relationship is y = 10x

Question 2.
Write the linear equation that is shown by the graph.

Type below:
________________

Answer:
Write the ordered pairs from the graph: (3,3), (5,5), (8,8)
Look for a pattern among the pairs: each y value is the same as the corresponding x-value.
The equation is y = x

Spiral Review

Question 4.
Which of the following are solutions of j ≥ 0.6?
j = 1      j = ^–0.6       j = \(\frac{3}{5}\)       j = 0.12        j = 0.08
Type below:
________________

Answer: j = \(\frac{3}{5}\)

Explanation:
Substitute the values of j in the inequality.
j = 1
1 ≥ 0.6
1 is greater than 0.6 but not equal.
Thus 1 is not the solution of j ≥ 0.6.
j = ^–0.6
-0.6 ≥ 0.6
-0.6 is less than 0.6
Thus -0.6 is not the solution of j ≥ 0.6.
j = \(\frac{3}{5}\)
\(\frac{3}{5}\) ≥ 0.6
\(\frac{3}{5}\) = 0.6
0.6 ≥ 0.6
Thus \(\frac{3}{5}\) is the solution.
j = 0.12
0.12 ≥ 0.6
0.12 is less than 0.6.
Thus 0.12 is not the solution of j ≥ 0.6.
j = 0.08
0.08 ≥ 0.6
0.08 is less than 0.6.
Thus 0.08 is not the solution of j ≥ 0.6.

Question 5.
Red grapes cost $2.49 per pound. Write an equation that shows the relationship between the cost c in dollars and the number of pounds of grapes p.
Type below:
________________

Answer: c = 2.49p

Explanation:
Given,
Red grapes cost $2.49 per pound.
c is the cost in dollars.
p is the number of pounds of grapes.
The equation c is equal to the product of the number of pounds of grapes and $2.49
c = 2.49p

Chapter 9 Review/Test – Page No. 523

Question 1.
A box of peanut butter crackers contains 12 individual snacks. The total number of individual snacks s is equal to 12 times the number of boxes of crackers b.
The independent variable is _____.
The dependent variable is _____.
The equation that represents the relationship between the variables is _____.

Answer:
The independent variable is b.
The dependent variable is s.
The equation that represents the relationship between the variables is s = 12b.

Question 2.
A stationery store charges $8 to print logos on paper purchases. The total cost c is the price of the paper p plus $8 for printing the logo.
For numbers 2a–2d, select True or False for each statement.
2a. The total cost c depends on the price of the paper.
2b. c is the dependent variable.
2c. p is the independent variable.
2d. The equation that represents the relationship between the variables is c = 8p.
2a. ____________
2b. ____________
2c. ____________
2d. ____________

Answer:
2a. True
2b. True
2c. True
2d. False

Explanation:
2a. c represents the relationship between the two quantities.
So, the statement “The total cost c depends on the price of the paper” is true.
2b. c is the total cost so the statement “c is the dependent variable” is true.
2c. p represents the price to print logos
So, the statement “p is the independent variable” is true.
2d. The total cost c is the price of the paper p plus $8 for printing the logo.
The equation would be:
c = 8 + p
Thus the statement “The equation that represents the relationship between the variables is c = 8p” is false.

Question 3.
An electrician charges $75 an hour for labor and an initial fee of $65. The total cost c equals 75 times the number of hours x plus 65. Write an equation for the relationship and use the equation to complete the table.

Type below:
________________

Answer: c = 75x + 65
Substitute the value of x in the equation.

Page No. 524

Question 4.
The community center offers classes in arts and crafts. There is a registration fee of $125 and each class costs $79. The total cost c in dollars equals 79 times the number of classes n plus 125.

For numbers 4a–4d, select True or False for each statement.
4a. The registration fee is $120.
4b. n is the independent variable.
4c. c is the dependent variable.
4d. The cost for 7 classes is $678.
4a. ____________
4b. ____________
4c. ____________
4d. ____________

Answer:
4a. False
4b. True
4c. True
4d. True

Explanation:
4a. The registration fee is $120.
The registration fee is $125, not $120.
So, the statement is false.
4b. n is the independent variable.
n represents the number of classes.
The statement is true.
4c. c is the dependent variable.
c depends on the registration fee.
Thus the statement is true.
4d. The cost for 7 classes is $678
79 × 7 + 125 = $678
Thus the statement is true.

Question 5.
Ms. Walsh is buying calculators for her class. The table shows the total cost based on the number of calculators purchased.

If Ms. Walsh spent a total of $525, how many calculators did she buy? Use numbers and words to explain your answer.
Type below:
________________

Answer:
She bought 35 calculators. I found a pattern and wrote the equation c = 15n.
Since I know that Mrs.Walsh spent a total of $525, I can substitute 525 for c and solve for n
525 = 15n
n = 35

Chapter 9 Review/Test – Page No. 525

Question 6.
The table shows the number of cups of lemonade that can be made from cups of lemon juice.

Mary Beth says the number of cups of lemon juice j depends on the number of cups of lemonade l. She says the equation j = 7l represents the relationship between the cups of lemon juice j and the cups of lemonade l. Is Mary Beth correct? Use words and numbers to explain why or why not.
Type below:
________________

Answer:
Mary Beth is not correct. The number of cups of lemonade l depends on the number of cups of lemon juice j.
So l is the dependent variable and j is the independent variable.
The equation showing the relationship is l = 7j

Question 7.
For numbers 7a–7d, choose Yes or No to indicate whether the points, when graphed, would lie on the same line.
7a. (1, 6), (2, 4), (3, 2), (4, 0)
7b. (1, 1), (2, 4), (3, 9), (4, 16)
7c. (1, 3), (2, 5), (3, 7), (4, 9)
7d. (1, 8), (2, 10), (3, 12), (4, 14)
7a. ____________
7b. ____________
7c. ____________
7d. ____________

Answer:
7a. Yes

7b. No

7c. Yes

7d. Yes

Question 8.
Graph the relationship represented by the table to find the unknown value.

Type below:
________________

Answer: 10

Chapter 9 Review/Test – Page No. 526

Question 9.
Graph the relationship represented by the table.

Type below:
________________

Answer:

Question 10.
Miranda’s wages are $15 per hour. Write a linear equation that gives the wages w in dollars that Miranda earns in h hours.
Type below:
________________

Answer: w = 15h

Question 11.
The table shows the number of miles m that Lucinda could walk in h hours.

Graph the relationship between hours h and miles m. Then write the equation that shows the relationship.
Type below:
________________

Answer: m = 4h

Chapter 9 Review/Test – Page No. 527

Question 13.
Lacy is staying at a hotel that costs $85 per night. The total cost c in dollars of Lacy’s stay is 85 times the number of nights n she stays.
For numbers, 13a–13d, select True or False for each statement.
13a. The number of nights n is dependent on the cost c.
13b. n is the independent variable.
13c. c is the dependent variable.
13d. The equation that represents the total cost is c = 85n.
13a. ____________
13b. ____________
13c. ____________
13d. ____________

Answer:
13a. False
13b. True
13c. True
13d. True

Explanation:
13a. The number of nights n is dependent on the cost c.
n is independent on the cost c.
So, the statement is false.
13b. n is the independent variable.
The statement is true.
13c. c is the dependent variable.
c is dependent because it depends on the cost c.
So, the statement is true.
13d. The equation that represents the total cost is c = 85n.
The equation is true.

Question 14.
A taxi cab company charges an initial fee of $5 and then $4 per mile for a ride. Use the equation c = 4x + 5 to complete the table.

Type below:
________________

Answer:
Substitute the value of x in the equation.
We get,

Chapter 9 Review/Test – Page No. 528

Question 15.
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row. The total number of cans c equals 2 times the row r minus 1. Use the equation c = 2r − 1 to complete the table.

Type below:
________________

Answer:
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row.
c = 2r − 1
Substitute r in the equation.

Question 16.
The graph shows the number of words Mason read in a given amount of minutes. If Mason continues to read at the same rate, how many words will he have read in 5 minutes?

______ words

Answer: 1000 words
By seeing the above graph we can say that Mason can read 1000 words in 5 minutes.

Question 17.
Casey claims the linear equation for the relationship shown by the graph is c = 25j. Use numbers and words to support Casey’s claim.

Type below:
________________

Answer: The ordered pairs (1,25), (3,75), (5,125) and (7,175) each make the equation c = 25j

Conclusion:

I wish the details prevailed in the Go Math Grade 6 Answer Key Chapter 9 is helpful for you. Share this pdf link with your friends and help them to overcome the difficulties. If you have any doubts regarding the solutions you can leave a comment in the comment section.

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CANBK Pivot Calculator

Detailed and Step-by-step explanation of Chapter 5 concepts is provided in this Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers. Assure that you should practice with the help of Go math HMH grade 4 chapter 5 solution key and improve mathematical and logical skills. Learning & practicing the fundamentals of math chapter 5 concepts is very important to score more marks in the exams. So, download online Go Math Grade 4 Solution Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers pdf and overcome all the difficulties in math.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers

Consistent practice helps students to gain more knowledge and overcome their weak points. So, grab these Concept-wise Chapter 4 Go math Grade 4 Answer Key pdf and practice regularly for securing good scores in the exams. Some of the topics covered in Go Math Solution Key Grade 4 Homework Practice FL Chapter 4 Divide by 1-Digit Numbers are Estimate Quotients Using Multiples, Remainders, Divide Tens, Hundreds, and Thousands, etc. Solve the questions provided at the end of the page and test your subject knowledge.

Lesson: 1 – Estimate Quotients Using Multiples

• Common Core – Divide by 1-Digit Numbers – Page No. 69
• Common Core – Divide by 1-Digit Numbers – Page No. 70

Lesson: 2 – Remainders

• Common Core – Divide by 1-Digit Numbers – Page No. 71
• Common Core – Divide by 1-Digit Numbers – Page No. 72

Lesson: 3 – Interpret the Remainder

• Common Core – Divide by 1-Digit Numbers – Page No. 73
• Common Core – Divide by 1-Digit Numbers – Page No. 74

Lesson: 4 – Divide Tens, Hundreds, and Thousands

• Common Core – Divide by 1-Digit Numbers – Page No. 75
• Common Core – Divide by 1-Digit Numbers – Page No. 76

Lesson: 5 – Estimate Quotients Using Compatible Numbers

• Common Core – Divide by 1-Digit Numbers – Page No. 77
• Common Core – Divide by 1-Digit Numbers – Page No. 78

Lesson: 6 – Division and the Distributive Property

• Common Core – Divide by 1-Digit Numbers – Page No. 79
• Common Core – Divide by 1-Digit Numbers – Page No. 80

Lesson: 7 – Divide Using Repeated Subtraction

• Common Core – Divide by 1-Digit Numbers – Page No. 81
• Common Core – Divide by 1-Digit Numbers – Page No. 82

Lesson: 8 – Divide Using Partial Quotients

• Common Core – Divide by 1-Digit Numbers – Page No. 83
• Common Core – Divide by 1-Digit Numbers – Page No. 84

Lesson: 9 – Model Division with Regrouping

• Common Core – Divide by 1-Digit Numbers – Page No. 85
• Common Core – Divide by 1-Digit Numbers – Page No. 86

Lesson: 10 – Place the First Digit

• Common Core – Divide by 1-Digit Numbers – Page No. 87
• Common Core – Divide by 1-Digit Numbers – Page No. 88

Lesson: 11 – Divide by 1-Digit Numbers

• Common Core – Divide by 1-Digit Numbers – Page No. 89
• Common Core – Divide by 1-Digit Numbers – Page No. 90

Lesson: 12 – Problem Solving Multistep Division Problems

• Common Core – Divide by 1-Digit Numbers – Page No. 91

Lesson: 13

• Common Core – Divide by 1-Digit Numbers – Page No. 93
• Common Core – Divide by 1-Digit Numbers – Page No. 94

Common Core – Divide by 1-Digit Numbers – Page No. 69

Estimate Quotients Using Multiples

Find two numbers the quotient is between. Then estimate the quotient.

Question 1.
175 ÷ 6
Think: 6 × 20 = 120 and 6 × 30 = 180. So, 175 ÷ 6 is between 20 and 30. Since 175 is closer to 180 than to 120, the quotient is about 30.
between 20 and 30
about 30

Question 2.
53 ÷ 3
between ____ and ____
about ____

Answer: About 18

Explanation:
17 × 3= 51 and 18 × 3 = 54. 53 is between 51 and 54. 53 ÷ 3 is closest to 17 and 18. So, 53 ÷ 3 is between 17 and 18. So, 53 ÷ 3 will be about 18.

Question 3.
75 ÷ 4
between ____ and ____
about ____

Answer: About 19

Explanation:
18 × 4= 72 and 19 × 4= 76. 75 is between 72 and 76. 75 ÷ 4 is closest to 18 and 19. So, 75÷ 4 is between 18 and 19. So, 75 ÷ 4 will be about 19.

Question 4.
215 ÷ 9
between ____ and ____
about ____

Answer: About 24

Explanation:
23 × 9= 207 and 24 × 9 = 216. 24 is between 207 and 216. 215 ÷ 9 is closest to 23 and 24. So, 215 ÷ 9 is between 23 and 24. So, 215 ÷ 9 will be about 24.

Question 5.
284 ÷ 5
between ____ and ____
about ____

Answer: About 57

Explanation:
56 × 5 = 280 and 57 × 5 = 285. 284 is between 280 and 285. 284 ÷ 5 is closest to 56 and 57. So, 284 ÷ 5 is between 56 and 57. So, 175 ÷ 6 will be about 57.

Question 6.
191 ÷ 3
between ____ and ____
about ____

Answer: About 64

Explanation:
63 × 3 = 189 and 64 × 3 = 192. 191 is between 189 and 192. 191 ÷ 3 is closest to 63 and 64. So, 191 ÷ 3 is between 63 and 64. So, 175 ÷ 6 will be about 64.

Question 7.
100 ÷ 7
between ____ and ____
about ____

Answer: About 14

Explanation:
14 × 7 = 98 and 15 × 7 = 105. 100 is between 98 and 105. 100 ÷ 7 is closest to 14 and 15.
So, 100 ÷ 7 is between 14 and 15. So, 100 ÷ 7 will be about 14.

Question 8.
438 ÷ 7
between ____ and ____
about ____

Answer: About 63

Explanation:
63 × 7 = 441 and 62 × 7 = 434. 438 is between 434 and 441. 438 ÷ 7 is closest to 62 and 63. So, 438 ÷ 7 is between 62 and 63. So, 438 ÷ 7 will be about 63.

Question 9.
103 ÷ 8
between ____ and ____
about ____

Answer: About 13

Explanation:
13 × 8 = 104 and 12 ×8 = 96. 103 is between 96 and 104. 103 ÷ 8 is closest to 12 and 13. So, 103 ÷ 8 is between 12 and 13. So, 103 ÷ 8 will be about 13.

Question 10.
255 ÷ 9
between ____ and ____
about ____

Answer: About 28

Explanation:
28 × 9 = 252 and 29 × 9 = 261. 255 is between 252 and 261. 255 ÷ 9 is closest to 28 and 29.
So, 255 ÷ 9 is between 28 and 29. So, 255 ÷ 9 will be about 28.

Problem Solving

Question 11
Joy collected 287 aluminum cans in 6 hours. About how many cans did she collect per hour?
about ____ cans

Answer: About 48 cans

Explanation:
47 × 6 = 282 and 48 × 6 = 288. 287 is between 282 and 288. 287 ÷ 6 is closest to 47 and 48. So, 287 ÷ 6 is between 47 and 48. So, 287 ÷6 will be about 48.

Question 12.
Paul sold 162 cups of lemonade in 5 hours. About how many cups of lemonade did he sell each hour?
about ____ cups

Answer: About 32 cups of lemonade he sold in each hour

Explanation:
32 × 5 = 160 and 33 × 5 = 165. 162 is between 160 and 165. 162 ÷ 5 is closest to 32 and 33. So, 162 ÷ 5 is between 32 and 33. So, 162 ÷ 5 will be about 32.

Common Core – Divide by 1-Digit Numbers – Page No. 70

Lesson Check

Question 1.
Abby did 121 sit-ups in 8 minutes. Which is the best estimate of the number of sit-ups she did in 1 minute?
Options:
a. about 12
b. about 15
c. about 16
d. about 20

Answer: About 15

Explanation:
15 × 8 = 120 and 16 × 8 = 128. 121 is between 120 and 128. 121 ÷ 8 is closest to 120 and 128. So, 121 ÷ 8 is between 15 and 16.
So, 121 ÷ 8 will be about 15.
Thus the correct answer is option b.

Question 2.
The Garibaldi family drove 400 miles in 7 hours. Which is the best estimate of the number of miles they drove in 1 hour?
Options:
a. about 40 miles
b. about 50 miles
c. about 60 miles
d. about 70 miles

Answer: about 60 miles

Explanation:
Given,
The Garibaldi family drove 400 miles in 7 hours.
57 × 7 = 399 and 58 × 7 = 406.
400 is between 399 and 406. 400 ÷ 7 is closest to 57 and 58.
So, 400 ÷ 7 is between 57 and 58.
So, 400 ÷ 7 will be about 57.
Thus the correct answer is option c.

Spiral Review

Question 3.
Twelve boys collected 16 aluminum cans each. Fifteen girls collected 14 aluminum cans each. How many more cans did the girls collect than the boys?
Options:
a. 8
b. 12
c. 14
d. 18

Answer: 18

Explanation:
Given that,
Twelve boys collected 16 aluminum cans each.
Fifteen girls collected 14 aluminum cans each.
Number of aluminium cans boys had= 12 × 16=192
Number of aluminium cans girls had = 15 × 14=210
Girls collected more cans compared to boys,
Number of more cans collected by girls= 210 – 192=18
Thus the correct answer is option d.

Question 4.
George bought 30 packs of football cards. There were 14 cards in each pack. How many cards did George buy?
Options:
a. 170
b. 320
c. 420
d. 520

Answer: 420

Explanation:
Given,
George bought 30 packs of football cards.
There were 14 cards in each pack.
Number of packs of football cards= 30
Number of cards in each pack= 14
Total number of cards George bought=30×14=420
Thus the correct answer is option c.

Question 5.
Sarah made a necklace using 5 times as many blue beads as white beads. She used a total of 30 beads. How many blue beads did Sarah use?
Options:
a. 5
b. 6
c. 24
d. 25

Answer: 25

Explanation:
Given,
Sarah made a necklace using 5 times as many blue beads as white beads.
She used a total of 30 beads.
Let the number of white beads be x while the number of blue beads are 5x.
Total number of beads in the necklace=30 beads
According to the problem,
5x+x=30
6x=30
x=30/6=5
Therefore the number of blue beads in the necklace are 5x= 5×5=25
Thus the correct answer is option d.

Question 6.
This year, Ms. Webster flew 145,000 miles on business. Last year, she flew 83,125 miles on business. How many more miles did Ms. Webster fly on business this year?
Options:
a. 61,125 miles
b. 61,875 miles
c. 61,985 miles
d. 62,125 miles

Answer: 61,875 miles

Explanation:
Given,
This year, Ms. Webster flew 145,000 miles on business.
Last year, she flew 83,125 miles on business.
Number of miles Ms Webster flew in this year = 145,000 miles
Number of miles Ms Webster flew in the last year = 83,125 miles
Number of more miles travelled by Ms Webster =145,000 – 83,125 = 61,875
Thus the correct answer is option b.

Common Core – Divide by 1-Digit Numbers – Page No. 71

Remainders

Use counters to find the quotient and remainder.

Question 1.
13 ÷ 4
3 r1

Explanation:
Quotient:
A. Use 13 counters to represent the 13 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 13 ÷ 4
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 3.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 1
For 13 ÷ 4, the quotient is 3 and the remainder is 1, or 3 r1.

Question 2.
24 ÷ 7
_____ R _____

Answer: 3 r3

Explanation:
Quotient:
A. Use 24 counters to represent the 24 dominoes. Then draw 7 circles to represent the divisor.
B. Share the counters equally among the 7 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 24 ÷ 7
D. Number of circles are equally filled with 3 counters, therefore, the quotient is 3
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 24 ÷ 7, the quotient is 3 and the remainder is 3, or 3 r3.

Question 3.
39 ÷ 5
_____ R _____

Answer: 7 r4

Explanation:
Quotient:
A. Use 39 counters to represent the 39dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of counters formed in each group = quotient 39 ÷ 5
D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 39 ÷ 5, the quotient is 7 and the remainder is 4, or 7 r4.

Question 4.
36 ÷ 8
_____ R _____

Answer: 4 r4

Explanation:
Quotient:
A. Use 36 counters to represent the 36 dominoes. Then draw 8 circles to represent the divisor.
B. Share the counters equally among the 8 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 36 ÷ 8
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 36 ÷ 8, the quotient is 4 and the remainder is 4, or 4 r4.

Question 5.
6)\(\overline { 27 } \)
_____ R _____

Answer: 4 r3

Explanation:
Quotient:
A. Use 27 counters to represent the 27 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 6 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 27 ÷6
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 27 ÷ 6, the quotient is 4 and the remainder is 3, or 4 r3.

Question 6.
25 ÷ 9
_____ R _____

Answer: 2 r7

Explanation:
Quotient:
A. Use 25 counters to represent the 25 dominoes. Then draw 9 circles to represent the divisor.
B. Share the counters equally among the 9 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 25 ÷ 9
D. Number of circles are equally filled with 2 counters, therefore, the quotient is 2
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 7
For 25 ÷ 7, the quotient is 2 and the remainder is 7, or 2 r7.

Question 7.
3)\(\overline { 17 } \)
_____ R _____

Answer: 5 r2

Explanation:
Quotient:
A. Use 17 counters to represent the 17 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 17 ÷ 3
D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 17 ÷ 3, the quotient is 5 and the remainder is 2, or 5 r2.

Question 8.
26 ÷ 4
_____ R _____

Answer: 6 r2

Explanation:
Quotient:
A. Use 26 counters to represent the 26 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 26 ÷ 4
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 26 ÷ 4, the quotient is 6 and the remainder is 2, or 6 r2.

Divide. Draw a quick picture to help.

Question 9.
14 ÷ 3
_____ R _____

Answer: Quotient: 4 Remainder: 2

Explanation:
Quotient:
A. Use 14 counters to represent the 14 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of circles filled= quotient of 14 ÷ 3 = 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2

Question 10.
5)\(\overline { 29 } \)
_____ R _____

Answer: Quotient: 5 Remainder: 4

Explanation:
Quotient:
A. Use 29 counters to represent the 29 dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of circles filled= quotient of 29 ÷ 5 = 5
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4

Problem Solving

Question 11.
What is the quotient and remainder in the division problem modeled below?

_____ R _____

Answer: quotient:6 remainder2

Explanation:
Quotient:
A. Use 20 counters to represent the 20 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 20 ÷ 3
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 20 ÷ 3, the quotient is 6 and the remainder is 2, or 6 r2.

Question 12.
Mark drew the following model and said it represented the problem 21 ÷ 4. Is Mark’s model correct? If so, what is the quotient and remainder? If not, what is the correct quotient and remainder?

_____ : _____ r _____

Answer: 4 r5

Explanation:
Quotient:
A. Use 21 counters to represent the 21 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 21 ÷ 4
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 5
For 21 ÷ 4, the quotient is 4 and the remainder is 5, or 4 r5.

Common Core – Divide by 1-Digit Numbers – Page No. 72

Lesson Check

Question 1.
What is the quotient and remainder for 32 ÷ 6?
Options:
a. 4 r3
b. 5 r1
c. 5 r2
d. 6 r1

Answer: 5 r2

Explanation:
Quotient:
A. Use 32 counters to represent the 32 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 32 ÷ 6
D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 32 ÷ 6, the quotient is 5 and the remainder is 2, or 5 r2.
Thus the correct answer is option c.

Question 2.
What is the remainder in the division problem modeled below?

Options:
a. 8
b. 4
c. 3
d. 1

Answer: 3

Explanation:
When a number cannot be divided evenly, the amount left over is called the remainder.
The number of counters that are left = remainder = 3
Thus the correct answer is option c.

Spiral Review

Question 3.
Each kit to build a castle contains 235 parts. How many parts are in 4 of the kits?
Options:
a. 1,020
b. 940
c. 920
d. 840

Answer: 940

Explanation:
Number of parts used to build a castle in each kit=235 parts
Number of kits= 4
Total number of parts in 4 of the kits= 235 x 4=940 parts

Thus the correct answer is option b.

Question 4.
In 2010, the population of Alaska was about 710,200. What is this number written in word form?
Options:
a. seven hundred ten thousand, two
b. seven hundred twelve thousand
c. seventy-one thousand, two
d. seven hundred ten thousand, two hundred

Answer: seven hundred ten thousand, two hundred

Explanation:
The ones and tens place of the number are zeroes, so the next place which is hundreds is considered and the value is 7 so, it can be written as seven hundred and in the thousands period, it can be written as seven hundred ten thousand.
Thus the correct answer is option d.

Question 5.
At the theater, one section of seats has 8 rows with 12 seats in each row. In the center of the first 3 rows are 4 broken seats that cannot be used. How many seats can be used in the section?
Options:
a. 84
b. 88
c. 92
d. 96

Answer: 92

Explanation:
Given,
Number of rows at the theatre = 8
Number of seats in each row= 12
Number of seats broken and that cannot be used to sit= 4
Total number of seats that can be used= 12 × 8 – 4 = 96 – 4 = 92
Thus the correct answer is option c.

Question 6.
What partial products are shown by the model below?

Options:
a. 300, 24
b. 300, 600, 40, 60
c. 300, 60, 40, 24
d. 300, 180, 40, 24

Answer: 300, 180, 40, 24

Explanation:
The whole rectangle is divided into four small rectangles the areas of these rectangles are:

Area of yellow rectangle= 30 x 10=300
Area of green rectangle= 4 x 10 = 40
Area of pink rectangle= 6 x 30= 180
Area of blue rectangle= 4 x 6= 24
Thus the correct answer is option d.

Common Core – Divide by 1-Digit Numbers – Page No. 73

Interpret the Remainder

Interpret the remainder to solve.

Question 1.
Hakeem has 100 tomato plants. He wants to plant them in rows of 8. How many full rows will he have?
Think: 100 ÷ 8 is 12 with a remainder of 4. The question asks “how many full rows,” so use only the quotient.
12 full rows

Explanation:
Quotient:
A. Use 100 counters to represent the 100 dominoes. Then draw 8 circles to represent the divisor.
B. Share the counters equally among the 8 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 100 ÷ 8
D. Number of circles are equally filled with 12 counters, therefore, the quotient is 12
Therefore, the tomatoes placed in full rows are 12

Question 2.
A teacher has 27 students in her class. She asks the students to form as many groups of 4 as possible. How many students will not be in a group?
______ students

Answer: 3 students will not be in the group

Explanation:
Total number of students in the class= 27
Number of students who make a group=4
Number of groups that can be made =Quotient of 27÷ 4=6
Number of students who do not come under a group= Remainder of 27÷ 4=3

Question 3.
A sporting goods company can ship 6 footballs in each carton. How many cartons are needed to ship 75 footballs?
______ cartons

Answer: 12 full cartons and 0.5 or 1/2 carton to ship all the 75 footballs

Explanation:
Total number of footballs that should be shipped= 75
Number of footballs placed in each carton = 6
Number of cartons required=Quotient of 75÷ 6=12

Since each carton carries 6 balls, half carton contains 3 balls because 6÷3=2, therefore, each half of the carton contains 3 balls.

Question 4.
A carpenter has a board that is 10 feet long. He wants to make 6 table legs that are all the same length. What is the longest each leg can be?
______ foot

Answer: The length of the longest leg = 4 foot-long

Explanation:
According to the question,
Length of the board the carpenter has= 10 foot long
Number of table legs that are to be made = 6
Length of the 6 table legs are equal
then,
Length of each table leg = Quotient of 10 ÷ 6 =1 foot
Length of the longest table leg = Remainder of 10 ÷ 6 = 4 foot.

Question 5.
Allie wants to arrange her flower garden in 8 equal rows. She buys 60 plants. What is the greatest number of plants she can put in each row?
______ plants

Answer: 7

Explanation:
Total number of plants Allie bought = 60
Number of rows = 8
Number of plants in each row= Quotient of 60 ÷ 8 = 7
Thus the greatest number of plants she can put in a row is 7.

Problem Solving

Question 6.
Joanna has 70 beads. She uses 8 beads for each bracelet. She makes as many bracelets as possible. How many beads will Joanna have left over?
______ beads

Answer: 6 beads

Explanation:
Total number of beads Joanna has= 70 beads
Number beads used for each bracelet= 8 beads
Number of bracelets made with these beads= Quotient of 70÷8= 7 bracelets
then,
The number of beads leftover= Remainder of 70÷8= 6 beads

Question 7.
A teacher wants to give 3 markers to each of her 25 students. Markers come in packages of 8. How many packages of markers will the teacher need?
______ packages

Answer: 10 packages

Explanation:
Total number of students= 25
Number of markers each student got= 3
Total number of markers the teacher needs to distribute= 25 x 3= 75
Number of markers in each package= 8
Number of packages the teacher required= Quotient of 75÷8=9
While the remainder = 3
Therefore the total number of packages = 10

Common Core – Divide by 1-Digit Numbers – Page No. 74

Lesson Check

Question 1.
Marcus sorts his 85 baseball cards into stacks of 9 cards each. How many stacks of 9 cards can Marcus make?
Options:
a. 4
b. 8
c. 9
d. 10

Answer: 10

Explanation:
Total number of baseball cards=85
Number of cards in each stack=9
Number of stacks sorted= Quotient of 85÷9=9
While the remainder=4
So the total number of stacks required= 10
Thus the correct answer is option d.

Question 2.
A minivan can hold up to 7 people. How many minivans are needed to take 45 people to a basketball game?
Options:
a. 3
b. 5
c. 6
d. 7

Answer: 7

Explanation:
A minivan can hold up to 7 people.
Total number of people who want to hire the minivan= 45 people
Number of minivans required= Quotient of 45÷7= 6 vans
While the remainder is 3.
Total number of minivans required to take the people to the baseball game= 7 minivans
Thus the correct answer is option d.

Spiral Review

Question 3.
Mrs. Wilkerson cut some oranges into 20 equal pieces to be shared by 6 friends. How many pieces did each person get and how many pieces were left over?
Options:
a. 2 pieces with 4 pieces left over
b. 3 pieces with 2 pieces left over
c. 3 pieces with 4 pieces left over
d. 4 pieces with 2 pieces left over

Answer: 3 pieces with 2 pieces left over

Explanation:
Total number of orange pieces= 20
Number of friends= 6
Number of pieces each friend got= Quotient of 20÷6= 3 pieces
Number of pieces leftover= Remainder of 20÷6= 2 pieces
Thus the correct answer is option b.

Question 4.
A school bought 32 new desks. Each desk cost $24. Which is the best estimate of how much the school spent on the new desks?
Options:
a. $500
b. $750
c. $1,000
d. $1,200

Answer: $750

Explanation:
Total number of desks= 32
Cost of each desk= $24
Total cost spent on the desks= 32 x 24=$768

So the estimated value can be $768.
Thus the correct answer is option b.

Question 5.
Kris has a box of 8 crayons. Sylvia’s box has 6 times as many crayons as Kris’s box. How many crayons are in Sylvia’s box?
Options:
a. 48
b. 42
c. 36
d. 4

Answer: 48

Explanation:
Number of crayons in Kris box=8
Number of crayons in Sylvia’s box= 6 times as many crayons as Kris’s box= 6 x 8=48
Thus the correct answer is option a.

Question 6.
Yesterday, 1,743 people visited the fair. Today, there are 576 more people at the fair than yesterday. How many people are at the fair today?
Options:
a. 1,167
b. 2,219
c. 2,319
d. 2,367

Answer: 2,319

Explanation:
Number of people in the fair yesterday= 1,743
Number of more people at the fair than yesterday= 576
Total number of people in the fair today=2,319

Thus the correct answer is option c.

Common Core – Divide by 1-Digit Numbers – Page No. 75

Divide Tens, Hundreds, and Thousands

Use basic facts and place value to find the quotient.

Question 1.
3,600 ÷ 4 = 900
Think: 3,600 is 36 hundreds.
Use the basic fact 36 ÷ 4 = 9.
So, 36 hundreds ÷ 4 = 9 hundreds, or 900.

Question 2.
240 ÷ 6 = ______

Answer: 40

Explanation:
STEP 1 Identify the basic fact. 24 ÷ 6
STEP 2 Use place value. 240 = 24 tens
STEP 3 Divide. 24 tens ÷ 6 = 4 tens
240 ÷ 6 = 40

Question 3.
5,400 ÷ 9 = ______

Answer: 600

Explanation:
STEP 1 Identify the basic fact. 54 ÷ 9
STEP 2 Use place value. 5,400 = 54 hundreds
STEP 3 Divide. 54 hundreds ÷ 9 = 6 hundreds
5,400 ÷ 9 = 600

Question 4.
300 ÷ 5 = ______

Answer: 60

Explanation:
STEP 1 Identify the basic fact. 30 ÷ 5
STEP 2 Use place value. 300 = 30 tens
STEP 3 Divide. 30 tens ÷ 5 = 60 tens
300 ÷ 5 = 60

Question 5.
4,800 ÷ 6 = ______

Answer: 800

Explanation:
STEP 1 Identify the basic fact. 48 ÷ 6
STEP 2 Use place value. 4,800 = 48 hundreds
STEP 3 Divide. 48 hundreds ÷ 6 = 80 hundreds
4,800 ÷ 6 = 800

Question 6.
420 ÷ 7 = ______

Answer: 60

Explanation:
STEP 1 Identify the basic fact. 42 ÷ 7
STEP 2 Use place value. 420 = 42 tens
STEP 3 Divide. 42 tens ÷ 7 = 60 tens
420 ÷ 7 = 60

Question 7.
150 ÷ 3 = ______

Answer: 50

Explanation:
STEP 1 Identify the basic fact. 15 ÷ 3
STEP 2 Use place value. 150 = 15 tens
STEP 3 Divide. 15 tens ÷ 3 = 5 tens
150 ÷ 3 = 50

Question 8.
6,300 ÷ 7 = ______

Answer: 900

Explanation:
STEP 1 Identify the basic fact. 63 ÷ 7
STEP 2 Use place value. 6,300 = 63 hundreds
STEP 3 Divide. 63 hundreds ÷ 7 = 9 hundreds
6,300 ÷ 7 = 900

Question 9.
1,200 ÷ 4 = ______

Answer: 300

Explanation:
STEP 1 Identify the basic fact. 12 ÷ 4
STEP 2 Use place value. 1,200 = 12 hundreds
STEP 3 Divide. 12 hundreds ÷ 4 = 3 hundreds
1,200 ÷ 4 = 300

Question 10.
360 ÷ 6 = ______

Answer: 60

Explanation:
STEP 1 Identify the basic fact. 36 ÷ 6
STEP 2 Use place value. 360 = 36 tens
STEP 3 Divide. 36 tens ÷ 6 = 6 tens
360 ÷ 6 = 60

Find the quotient.

Question 11.
28 ÷ 4 = ______
280 ÷ 4 = ______
2,800 ÷ 4 = ______

Answer: 7, 70, 700

Explanation:
Quotient:
A. Use 28 counters to represent the 28 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 28 ÷ 4
D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7

STEP 1 Identify the basic fact. 28 ÷ 4
STEP 2 Use place value. 280 = 28 tens
STEP 3 Divide. 28 tens ÷ 4 = 7 tens
280 ÷ 4 = 70

STEP 1 Identify the basic fact. 28 ÷ 4
STEP 2 Use place value. 2,800 = 28 hundreds
STEP 3 Divide. 28 hundreds ÷ 4 = 7 hundreds
2,800 ÷ 4 = 700

Question 12.
18 ÷ 3 = ______
180 ÷ 3 = ______
1,800 ÷ 3 = ______

Answer: 6, 60, 600

Explanation:
Quotient:
A. Use 18 counters to represent the 18 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 18 ÷ 3
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6

STEP 1 Identify the basic fact. 18 ÷ 3
STEP 2 Use place value. 180 = 18 tens
STEP 3 Divide. 18 tens ÷ 3 = 6 tens
180 ÷ 6 = 60

STEP 1 Identify the basic fact. 18 ÷ 3
STEP 2 Use place value. 1,800 = 18 hundreds
STEP 3 Divide. 18 hundreds ÷ 3 = 6 hundreds
1,800 ÷ 3 = 600

Question 13.
45 ÷ 9 = ______
450 ÷ 9 = ______
4,500 ÷ 9 = ______

Answer: 5, 50, 500

Explanation:
Quotient:
A. Use 45 counters to represent the 45 dominoes. Then draw 9 circles to represent the divisor.
B. Share the counters equally among the 9 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 45 ÷ 9
D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5

STEP 1 Identify the basic fact. 45 ÷ 9
STEP 2 Use place value. 450 = 45 tens
STEP 3 Divide. 45 tens ÷ 9 = 5 tens
450 ÷ 9 = 50

STEP 1 Identify the basic fact. 45 ÷ 9
STEP 2 Use place value. 4,500 = 45 hundreds
STEP 3 Divide. 45 hundred ÷ 9 = 5 hundred
4,500 ÷ 9 = 500

Problem Solving

Question 14.
At an assembly, 180 students sit in 9 equal rows. How many students sit in each row?
______ students

Answer: 20

Explanation:
Total number of students= 180
Number of rows= 9
Number of students in each row= 180 ÷ 9 = 20

Question 15.
Hilary can read 560 words in 7 minutes. How many words can Hilary read in 1 minute?
______ words

Answer: 80

Explanation:
Total number of words Hilary can read in 7 minutes = 560
Number of words Hilary can read in 1 minute= 560 ÷ 7= 80
Therefore Hilary can read 80 words in 1 minute.

Question 16.
A company produces 7,200 gallons of bottled water each day. The company puts 8 one-gallon bottles in each carton. How many cartons are needed to hold all the one-gallon bottles produced in one day?
______ cartons

Answer: 900

Explanation:
Total number of gallons bottled in each day= 7,200
Number of gallons bottled in each carton= 8
Number of cartons used= 7,200 ÷ 8= 900

Question 17.
An airplane flew 2,400 miles in 4 hours. If the plane flew the same number of miles each hour, how many miles did it fly in 1 hour?
______ miles

Answer: 600

Explanation:
Total number of miles flew in 4 hours= 2,400
Number of miles flew in 1 hour= 2,400 ÷ 4 = 600

Common Core – Divide by 1-Digit Numbers – Page No. 76

Lesson Check

Question 1.
A baseball player hits a ball 360 feet to the outfield. It takes the ball 4 seconds to travel this distance. How many feet does the ball travel in 1 second?
Options:
a. 9 feet
b. 40 feet
c. 90 feet
d. 900 feet

Answer: 90 feet

Explanation:
The height to which the player hits a ball=360 feet
Height to which the ball travels in 1 second= 360÷4= 90 feet
The correct answer is option c.

Question 2.
Sebastian rides his bike 2,000 meters in 5 minutes. How many meters does he bike in 1 minute?
Options:
a. 4 meters
b. 40 meters
c. 50 meters
d. 400 meters

Answer: 400 meters

Explanation:
Total number of meters travelled in 5 minutes= 2,000
Number of meters travelled in 1 minute= 2,000÷5= 400
The correct answer is option d.

Spiral Review

Question 3.
A full container of juice holds 64 ounces. How many 7-ounce servings of juice are in a full container?
Options:
a. 1
b. 8
c. 9
d. 10

Answer: 9

Explanation:
A full container of juice holds= 63 ounces
Quantity of servings of juice in one glass=7 ounce
The number of servings of the juice are= 63÷7=9
The correct answer is option c.

Question 4.
Paolo pays $244 for 5 identical calculators. Which is the best estimate of how much Paolo pays for one calculator?
Options:
a. $40
b. $50
c. $60
d. $245

Answer: $50

Explanation:
Amount Paolo pays for the identical calculators = $244
Number of identical calculators=5
The best-estimated value of each identical calculator=$244 ÷ 5is approximately $50.
The correct answer is option b.

Question 5.
A football team paid $28 per jersey. They bought 16 jerseys. How much money did the team spend on jerseys?
Options:
a. $44
b. $196
c. $408
d. $448

Answer: $448

Explanation:
Cost of each jersey=$28
Number of jerseys= 16
Total cost of the jerseys= $28 x 16= $448
The correct answer is option d.

Question 6.
Suzanne bought 50 apples at the apple orchard. She bought 4 times as many red apples as green apples. How many more red apples than green apples did Suzanne buy?
Options:
a. 10
b. 25
c. 30
d. 40

Answer: 40

Explanation:
Let the number of green apples be x and the number of red apples be 4x
4x + x = 50
x = 50 ÷ 5= 10
Number of red balls = 4x = 4 x 10 = 40
The correct answer is option d.

Common Core – Divide by 1-Digit Numbers – Page No. 77

Estimate Quotients Using Compatible Numbers

Use compatible numbers to estimate the quotient.

Question 1.
389 ÷ 4
400 ÷ 4 = 100

Question 2.
358 ÷ 3
_____ ÷ 3 = _____

Answer: 120

Explanation:
What number close to358 is easy to divide by 3?
360 is close to 358. What basic fact can you use?
360 ÷ 3
Choose 360 because it is close to 358 and can easily be divided by 3.
36 ÷3 = 12
360 ÷ 3 =120
358 ÷ 3 is about 120

Question 3.
784 ÷ 8
_____ ÷ 8 = _____

Answer: 100

Explanation:
What number close to 784 is easy to divide by 8?
800 is close to 784. What basic fact can you use?
800 ÷ 8
Choose 800 because it is close to 784 and can easily be divided by 8.
80 ÷ 8 = 10
800 ÷ 8 = 100
784 ÷ 8 is about 100.

Question 4.
179 ÷ 9
_____ ÷ 9 = _____

Answer: 20

Explanation:
What number close to 179 is easy to divide by 9?
180 is close to 179. What basic fact can you use?
180 ÷ 9
Choose 180 because it is close to 179 and can easily be divided by 9.
18 ÷ 9 = 2
180 ÷ 9 = 20
179 ÷ 9 is about 20

Question 5.
315 ÷ 8
_____ ÷ 8 = _____

Answer: 40

Explanation:
What number close to 315 is easy to divide by 8?
320 is close to 315. What basic fact can you use?
320 ÷ 8
Choose 320 because it is close to 315 and can easily be divided by 8.
32 ÷ 8 = 4
320 ÷ 8 =40
315 ÷ 8 is about 40.

Question 6.
2,116 ÷ 7
_____ ÷ 7 = _____

Answer: 300

Explanation:
What number close to 2,116 is easy to divide by 7?
2,100 is close to 2,116. What basic fact can you use?
2,100 ÷ 7
Choose 2,100 because it is close to 2,116 and can easily be divided by 7.
21 ÷ 7= 3
2,100 ÷ 7 = 300
2,116 ÷ 7 is about 300

Question 7.
4,156 ÷ 7
_____ ÷ 7 = _____

Answer: 600

Explanation:
What number close to 4,156 is easy to divide by 7?
4,200 is close to 4,156. What basic fact can you use?
4,200 ÷7
Choose 4,200 because it is close to 4,156 and can easily be divided by 7.
42 ÷ 7 = 6
4,200 ÷ 7 = 600
4,156 ÷ 7 is about 600.

Question 8.
474 ÷ 9
_____ ÷ 9 = _____

Answer: 50

Explanation:
What number close to 474 is easy to divide by 9?
450 is close to 474. What basic fact can you use?
450 ÷ 9
Choose 450 because it is close to 474 and can easily be divided by 9.
45 ÷ 9 = 5
450 ÷ 9 = 50
474 ÷ 9 is about 50.

Use compatible numbers to find two estimates that the quotient is between.

Question 9.
1,624 ÷ 3
_____ ÷ 3 = _____
_____ ÷ 3 = _____

Answer: The quotient is between 500 and 600

Explanation:
What number close to 1,624 is easy to divide by 3?
1,500 is close to 1,624. What basic fact can you use?
1,500 ÷ 3
Choose 1,500 because it is close to 1,624 and can easily be divided by 3.
15 ÷ 3 = 5
1,500 ÷ 3 = 500
1,624 ÷ 3 is about 500

What number close to 1,624 is easy to divide by 3?
1,800 is close to 1,624. What basic fact can you use?
1,800 ÷ 3
Choose 1,800 because it is close to 1,624 and can easily be divided by 3.
18 ÷ 3 = 6
1,800 ÷ 3 = 600
1,624 ÷ 3 is about 600

Question 10.
2,593 ÷ 6
_____ ÷ 6 = _____
_____ ÷ 6 = _____

Answer: The quotient is between 400 and 500

Explanation:
What number close to 2,593 is easy to divide by 6?
2,400 is close to 2,593. What basic fact can you use?
2,400 ÷ 6
Choose 2,400 because it is close to 2,593 and can easily be divided by 6.
24 ÷ 6 = 4
2,400 ÷ 6 = 400
2,593 ÷ 6 is about 400

What number close to 2,593 is easy to divide by 6?
3,000 is close to 2,593. What basic fact can you use?
3000 ÷ 6
Choose 3,000 because it is close to 2,593 and can easily be divided by 6.
30 ÷ 6 = 5
3,000 ÷ 6 = 500
2,593 ÷ 6 is about 500

Question 11.
1,045 ÷ 2
_____ ÷ 2 = _____
_____ ÷ 2 = _____

Answer: The quotient is between 520 and 525

Explanation:
What number close to 1,045 is easy to divide by 2?
1,040 is close to 1,045. What basic fact can you use?
1,040 ÷ 2
Choose 1,040 because it is close to 1,045 and can easily be divided by 2.
1,04 ÷ 2 = 52
1,040 ÷ 2 = 520
1,045 ÷ 2 is about 520

What number close to 1,045 is easy to divide by 2?
1,050 is close to 1,045. What basic fact can you use?
1,050 ÷ 2
Choose 1,050 because it is close to 1,045 and can easily be divided by 2.
1,050 ÷ 2 = 525
1,045 ÷ 2 is about 525

Question 12.
1,754 ÷ 9
_____ ÷ 9 = _____
_____ ÷ 9 = _____

Answer: The quotient is between 195 and 200

Explanation:
What number close to 1,754 is easy to divide by 9?
1,755 is close to 1,754. What basic fact can you use?
1,755 ÷ 9
Choose 1,755 because it is close to 1,754 and can easily be divided by 9.
1,755 ÷ 9 = 195
1,754 ÷ 9 is about 195

What number close to 1,754 is easy to divide by 9?
1,800 is close to 1,754. What basic fact can you use?
1,800 ÷ 9
Choose 1,800 because it is close to 1,754 and can easily be divided by 9.
18 ÷ 9 = 2
1,800 ÷ 9 = 200
1,754 ÷ 9 is about 200

Question 13.
2,363 ÷ 8
_____ ÷ 8 = _____
_____ ÷ 8 = _____

Answer: The quotient is between 295 and 300

Explanation:
What number close to 2,363 is easy to divide by 8?
2,360 is close to 2,363. What basic fact can you use?
2,360 ÷ 8
Choose 2,360 because it is close to 2,363 and can easily be divided by 8.
2,360 ÷ 8 = 295
2,363 ÷ 8 is about 295

What number close to 2,363 is easy to divide by 8?
2,400 is close to 2,363. What basic fact can you use?
2,400 ÷ 8
Choose 2,400 because it is close to 2,363 and can easily be divided by 8.
24 ÷ 8 = 3
2,400 ÷ 8= 300
2,363 ÷ 8 is about 300.

Question 14.
1,649 ÷ 5
_____ ÷ 5 = _____
_____ ÷ 5 = _____

Answer: The quotient is between 329 and 330

Explanation:
What number close to 1,649 is easy to divide by 5?
1,645 is close to 1,649. What basic fact can you use?
1,645 ÷ 5
Choose 1,645 because it is close to 1,649 and can easily be divided by 5.
1,645 ÷ 5 = 329
1,649 ÷ 5 is about 329

What number close to 1,650 is easy to divide by 5?
1,650 is close to 1,649. What basic fact can you use?
1,650 ÷ 5
Choose 1,650 because it is close to 1,649 and can easily be divided by 5.
1,650 ÷ 5 = 330
1,649 ÷ 5 is about 330

Question 15.
5,535 ÷ 7
_____ ÷ 7 = _____
_____ ÷ 7 = _____

Answer: The quotient is between 790 and 791

Explanation:
What number close to 5,535 is easy to divide by 7?
5,530 is close to 5,535. What basic fact can you use?
5,530 ÷ 7
Choose 5,530 because it is close to 5,535 and can easily be divided by 7.
553 ÷ 7 = 79
5,530 ÷ 7 = 790
5,535 ÷ 7 is about 790

What number close to 5,535 is easy to divide by 7?
5,537 is close to 5,535. What basic fact can you use?
5,537 ÷ 7
Choose 5,537 because it is close to 5,535 and can easily be divided by 7.
553 ÷ 7 = 79
5,537 ÷ 7 = 791
5,535 ÷ 7 is about 791

Question 16.
3,640 ÷ 6
_____ ÷ 6 = _____
_____ ÷ 6 = _____

Answer: The quotient is between 606 and 607

Explanation:
What number close to 3,640 is easy to divide by 6?
3,636 is close to 3,640. What basic fact can you use?
3,636 ÷ 6
Choose 3,636 because it is close to 3,640 and can easily be divided by 6.
36 ÷ 6 = 6
3,636 ÷ 6 = 606
3,640 ÷ 6 is about 606

What number close to 3,640 is easy to divide by 6?
3,642 is close to 3,640. What basic fact can you use?
3,642 ÷ 6
Choose 3,642 because it is close to 3,640 and can easily be divided by 6.
3,642 ÷ 6 = 607
3,640 ÷ 6 is about 607

Problem Solving

Question 17.
A CD store sold 3,467 CDs in 7 days. About the same number of CDs were sold each day. About how many CDs did the store sell each day?
about _____ CDs

Answer: 495(approx)

Explanation:
Total number of CDs in the store= 3,467
Number of days= 7
Number of CDs sold on one day= 3,467 ÷ 7=495(approx)

Question 18.
Marcus has 731 books. He puts about the same number of books on each of 9 shelves in his a bookcase. About how many books are on each shelf?
about _____ books

Answer: 81 books(approx)

Explanation:
Total number of books Marcus has= 731
Number of shelves= 9
Number of books on each shelf= 731÷9= 81 (approx)

Common Core – Divide by 1-Digit Numbers – Page No. 78

Lesson Check

Question 1.
Jamal is planting seeds for a garden nursery. He plants 9 seeds in each container. If Jamal has 296 seeds to plant, about how many containers will he use?
Options:
a. about 20
b. about 30
c. about 200
d. about 300

Answer: about 30

Explanation:
Total number of seeds Jamal has= 296
Number of seeds placed in each container= 9
Number of containers Jamal used= 296÷9= 32.8=33 (approx)
Therefore, the number of containers used is about 30
The correct answer is option b.

Question 2.
Winona purchased a set of vintage beads. There are 2,140 beads in the set. If she uses the beads to make bracelets that have 7 beads each, about how many bracelets can she make?
Options:
a. about 30
b. about 140
c. about 300
d. about 14,000

Answer: about 300

Explanation:
Total number of beads Winona has= 2,140
Number of beads in each bracelet= 7
Number of bracelets made= 2,140÷7=305.7=306(approx)
Therefore, the number of bracelets made are about 30
The correct answer is option c.

Spiral Review

Question 3.
A train traveled 360 miles in 6 hours. How many miles per hour did the train travel?
Options:
a. 60 miles per hour
b. 66 miles per hour
c. 70 miles per hour
d. 600 miles per hour

Answer: 60 miles per hour

Explanation:
Total number of miles traveled by train= 360
Time taken by the train to cover 360 miles= 6 hours
Number of miles traveled in each hour= 360÷6=60 miles
The correct answer is option a.

Question 4.
An orchard has 12 rows of pear trees. Each row has 15 pear trees. How many pear trees are there in the orchard?
Options:
a. 170
b. 180
c. 185
d. 190

Answer: 180

Explanation:
Number of rows of pear trees in an orchard= 12
Number of pear trees in each row=15
Total number of pear trees in the orchard= 12 x 15=180
The correct answer is option b.

Question 5.
Megan rounded 366,458 to 370,000. To which place did Megan round the number?
Options:
a. hundred thousands
b. ten thousands
c. thousands
d. hundreds

Answer: ten thousands

Explanation:
The given number is 366,458, the ten thousand place digit has 6 which while rounding off should be changed to the next consecutive number and the digits in the other places should be written as zeroes.
The correct answer is option b.

Question 6.
Mr. Jessup, an airline pilot, flies 1,350 miles a day. How many miles will he fly in 8 days?
Options:
a. 1,358 miles
b. 8,400 miles
c. 10,800 miles
d. 13,508 miles

Answer: 10,800 miles

Explanation:
Number of miles flew by Mr.Jessup in one day= 1,350 miles
Number of days=8
Total number of miles flew by Mr.Jessup in 8 days= 1,350 x 8= 10,800 miles.
The correct answer is option c.

Common Core – Divide by 1-Digit Numbers – Page No. 79

Division and the Distributive Property

Find the quotient.

Question 1.
54 ÷ 3 = ( 30 ÷ 3) + ( 24 ÷ 3)
= 10 + 8
= 18

Question 2.
81 ÷ 3 = ______

Answer: 27

Explanation:
81 ÷ 3
STEP1 Find the nearest estimates of the number 81
STEP2 We can break the number 81 into 21 + 60
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (60 ÷ 3) + (21 ÷ 3)
STEP5 Add quotients of the above 20 +7= 27

Question 3.
232 ÷ 4 = ______

Answer: 58

Explanation:
232 ÷ 4
STEP1 Find the nearest estimates of the number 232
STEP2 We can break the number 232 into 200 + 32
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (200 ÷ 4) + (32 ÷ 4)
STEP5 Add quotients of the above 50 +8= 58

Question 4.
305 ÷ 5 = ______

Answer: 61

Explanation:
305 ÷ 5
STEP1 Find the nearest estimates of the number 305
STEP2 We can break the number 305 into 300 + 5
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (300 ÷ 5) + (5 ÷ 5)
STEP5 Add quotients of the above 60 +1= 61

Question 5.
246 ÷ 6 = ______

Answer: 41

Explanation:
246 ÷ 6
STEP1 Find the nearest estimates of the number 246
STEP2 We can break the number 246 into 240 + 6
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (240 ÷ 6) + (6 ÷ 6)
STEP5 Add quotients of the above 40 +1= 41

Question 6.
69 ÷ 3 = ______

Answer: 23

Explanation:
69 ÷ 3
STEP1 Find the nearest estimates of the number 69
STEP2 We can break the number 69 into 60 + 9
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (60 ÷ 3) + (9 ÷ 3)
STEP5 Add quotients of the above 20 +3= 23

Question 7.
477 ÷ 9 = ______

Answer: 53

Explanation:
477 ÷ 9
STEP1 Find the nearest estimates of the number 477
STEP2 We can break the number 477 into 450 + 27
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (450 ÷ 9) + (27 ÷ 9)
STEP5 Add quotients of the above 50 +3= 53

Question 8.
224 ÷ 7 = ______

Answer: 32

Explanation:
224 ÷ 7
STEP1 Find the nearest estimates of the number 224
STEP2 We can break the number 224 into 210 + 14
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (210 ÷ 7) + (14 ÷ 7)
STEP5 Add quotients of the above 30 +2= 32

Question 9.
72 ÷ 4 = ______

Answer: 18

Explanation:
72 ÷ 4
STEP1 Find the nearest estimates of the number 72
STEP2 We can break the number 72 into 40 + 32
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (40 ÷ 4) + (32 ÷ 4)
STEP5 Add quotients of the above 10 +8= 18

Question 10.
315 ÷ 3 = ______

Answer: 105

Explanation:
315 ÷ 3
STEP1 Find the nearest estimates of the number 315
STEP2 We can break the number 315 into 300 + 15
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (300 ÷ 3) + (15 ÷3)
STEP5 Add quotients of the above 100 +5= 105

Problem Solving

Question 11.
Cecily picked 219 apples. She divided the apples equally into 3 baskets. How many apples are in each basket?
______ apples

Answer: 73 apples

Explanation:
The total number of apples Cecily picked= 219 apples
Number of parts into which she wanted to divide the apples= 3
Number of apples in each part = Quotient of 147 ÷ 7
STEP1 Find the nearest estimates of the number 219
STEP2 We can break the number 219 into 210 + 9
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (210 ÷ 3) + (9 ÷ 3)
STEP5 Add quotients of the above 70 +3= 73

Question 12.
Jordan has 260 basketball cards. He divides them into 4 equal groups. How many cards are in each group?
______ cards

Answer: 65 cards

Explanation:
The total number of basketball cards Jordan has= 260 basketball cards
Number of parts into which he wanted to divide the cards= 4
Number of apples in each part = Quotient of 260 ÷ 4
STEP1 Find the nearest estimates of the number 260
STEP2 We can break the number 260 into 240 + 20
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (240 ÷ 4) + (20 ÷ 4)
STEP5 Add quotients of the above 60 +5= 65

Question 13.
The Wilsons drove 324 miles in 6 hours. If they drove the same number of miles each hour, how many miles did they drive in 1 hour?
______ miles

Answer: 54 miles

Explanation:
The total number of miles drove by Wilson= 324 miles
Number of hours he drove = 6
Number of miles drove in each hour = Quotient of 324 ÷ 6
STEP1 Find the nearest estimates of the number 324
STEP2 We can break the number 324 into 300 + 24
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (300 ÷ 6) + (24 ÷ 6)
STEP5 Add quotients of the above 50 +4= 54

Question 14.
Phil has 189 stamps to put into his stamp album. He puts the same number of stamps on each of 9 pages. How many stamps does Phil put on each page?
______ stamps

Answer: 21 stamps

Explanation:
The total number of stamps Phil has= 189 stamps
Number of pages= 9
Number of stamps put on each page = Quotient of 189 ÷ 9
STEP1 Find the nearest estimates of the number 189
STEP2 We can break the number 189 into 180 + 9
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (180 ÷ 9) + (9 ÷ 9)
STEP5 Add quotients of the above 20 +1= 21

Common Core – Divide by 1-Digit Numbers – Page No. 80

Lesson Check

Question 1.
A landscaping company planted 176 trees in 8 equal rows in the new park. How many trees did the company plant in each row?
Options:
a. 18
b. 20
c. 22
d. 24

Answer: 22

Explanation:
The total number of trees in the landscaping= 176 trees
Number of rows= 8
Number of trees in each row = Quotient of 176 ÷ 8
STEP1 Find the nearest estimates of the number 176
STEP2 We can break the number 176 into 160 + 16
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (160 ÷ 8) + (16 ÷ 8)
STEP5 Add quotients of the above 20 +2= 22

Question 2.
Arnold can do 65 pushups in 5 minutes. How many pushups can he do in 1 minute?
Options:
a. 11
b. 13
c. 15
d. 17

Answer: 13

Explanation:
The total number of pushups done by Arnold = 65
Number of minutes spent on pushups= 5
Number of pushups done in each minute = Quotient of 65 ÷ 5
STEP1 Find the nearest estimates of the number 65
STEP2 We can break the number 65 into 60 + 5
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (60 ÷ 5) + (5 ÷ 5)
STEP5 Add quotients of the above 12 +1= 13

Spiral Review

Question 3.
Last Saturday, there were 1,486 people at the Cineplex. There were about the same number of people in each of the 6 theaters. Which is the best estimate of the number of people in each theater?
Options:
a. between 20 and 30
b. between 80 and 90
c. between 100 and 200
d. between 200 and 300

Answer: between 200 and 300

Explanation:
Total number of people at the Cineplex= 1,486 people
Number of theatres = 6
Number of people at each theatre= estimate of the number of people 1,486 ÷ 6

What number close to 1,486 is easy to divide by 6?
1,488 is close to 1,486. What basic fact can you use?
1,488 ÷ 6
Choose 1,488 because it is close to 1,486 and can easily be divided by 6.
1,488 ÷ 6 = 248
1,486 ÷ 6 is about 248

What number close to 1,486 is easy to divide by 6?
1,482 is close to 1,486 . What basic fact can you use?
1,482 ÷ 6
Choose 1,482 because it is close to 1,486 and can easily be divided by 6.
1,482 ÷ 6 = 247
1,486 ÷ 6 is about 247

Question 4.
Nancy walked 50 minutes each day for 4 days last week. Gillian walked 35 minutes each day for 6 days last week. Which statement is true?
Options:
a. Gillian walked 10 minutes more than Nancy.
b. Gillian walked 20 minutes more than Nancy.
c. Nancy walked 10 minutes more than Gillian.
d. Nancy walked 15 minutes more than Gillian.

Answer: Nancy walked 15 minutes more than Gillian.

Explanation:
Time walked by Nancy= 50 minutes
Time walked by Gillian= 35 minutes
Nancy walked more time compared to Gillian
50-35=15 minutes
Therefore, Nancy walked 15 minutes more than Gillian.

Question 5.
Three boys share 28 toy cars equally. Which best describes how the cars are shared?
Options:
a. Each gets 3 cars with 1 left over.
b. Each gets 8 cars with 2 left over.
c. Each gets 9 cars with 1 left over.
d. Each gets 10 cars with 2 left over.

Answer: Each gets 9 cars with 1 left over.

Explanation:
Total number of toys three boys have= 28
Number of toys each boy got= 28 ÷3=9.33
Therefore we can say that each gets 9 cars with 1 leftover.

Question 6.
An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly in 5 hours?
Options:
a. 2,070 miles
b. 2,140 miles
c. 2,370 miles
d. 2,730 miles

Answer: 2,370 miles

Explanation:
Number of miles flew by airplane in one hour= 474
Number of hours the airplane flew= 5 hours
Total number of miles flew in 5 hours= 474 x 5= 2,370 miles

Common Core – Divide by 1-Digit Numbers – Page No. 81

Divide Using Repeated Subtraction

Use repeated subtraction to divide.

Question 1.
42 ÷ 3 = 14
3)\(\overline { 42 } \)
-30 ← 10 × 3 | 10
——-
12
-12 ← 4 × 3 | +4
——-             ———
0                     14

Question 2.
72 ÷ 4 = ______

Answer: 18

Explanation:
A. Begin with 72 counters. Subtract 4 counters.
B. Subtract 4 counters from 72 and repeat the processes until the remainder cannot be subtracted from the divisor.
C. Record the number of counters left and the number of times you subtracted.
D. The number of times you subtracted is the quotient is 18

Question 3.
93 ÷ 3 = ______

Answer: 31

Explanation:
A. Begin with 93 counters. Subtract 3 counters.
B. Subtract 3 counters from 93 and repeat the processes until the remainder cannot be subtracted from the divisor.
C. Record the number of counters left and the number of times you subtracted.
D. The number of times you subtracted is the quotient is 31

Question 4.
35 ÷ 4 = ______ r ______

Answer: 8r3

Explanation:
Quotient:
A. Use 35 counters to represent the 35 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 35 ÷ 4
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 8
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 35 ÷ 4, the quotient is 8 and the remainder is 3, or 8 r3.

Question 5.
93 ÷ 10 = ______ r ______

Answer: 9r3

Explanation:
Quotient:
A. Use 93 counters to represent the 93 dominoes. Then draw 10 circles to represent the divisor.
B. Share the counters equally among the 10 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 93 ÷ 10
D. Number of circles are equally filled with 10 counters, therefore, the quotient is 9
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 93 ÷ 10, the quotient is 9 and the remainder is 3, or 9 r3.

Question 6.
86 ÷ 9 = ______ r ______

Answer: 9r5

Explanation:
Quotient:
A. Use 86 counters to represent the 86 dominoes. Then draw 9 circles to represent the divisor.
B. Share the counters equally among the 9 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 86 ÷ 9
D. Number of circles are equally filled with 9 counters, therefore, the quotient is 9
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 5
For 86 ÷ 9, the quotient is 9 and the remainder is 5, or 9 r5.

Draw a number line to divide.

Question 7.
70 ÷ 5 = ______

Answer: 14

Explanation:
A. Draw a number line with 5 as each interval.
B. Draw up to 70 and count the intervals, it gives the quotient.
C. The quotient is 14

Problem Solving

Question 8.
Gretchen has 48 small shells. She uses 2 shells to make one pair of earrings. How many pairs of earrings can she make?
______ pairs

Answer: 24 pairs

Explanation:
Total number of small shells= 48
Number of shells used to make one pair of earrings = 2
Number of pair of earrings made = 48 ÷ 2 =24

Question 9.
James wants to purchase a telescope for $54. If he saves $3 per week, in how many weeks will he have saved enough to purchase the telescope?
______ weeks

Answer: $18

Explanation:
Cost of the telescope=$54
Amount saved each week = $3
Number of weeks he has to save the money to purchase the telescope = $54 ÷ $3 = $18

Common Core – Divide by 1-Digit Numbers – Page No. 82

Lesson Check

Question 1.
Randall collects postcards that his friends send him when they travel. He can put 6 cards on one scrapbook page. How many pages does Randall need to fit 42 postcards?
Options:
a. 3
b. 4
c. 6
d. 7

Answer: 7

Explanation:
Total number of postcards Randall has = 42 postcards
Number of postcards on one scrapbook page = 6 cards
Number of pages needed to fit the postcards = 42 ÷ 6=7
The correct answer is option d.

Question 2.
Ari stocks shelves at a grocery store. He puts 35 cans of juice on each shelf. The shelf has 4 equal rows and another row with only 3 cans. How many cans are in each of the equal rows?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:
Total number of cans of juice on each shelf = 35
Number of rows = 4
Number of cans on the other shelf = 3
Number of cans placed on the first shelf = 35 – 3 = 32
Number of juice cans in the first row = 32 ÷ 4 = 8 cans
The correct answer is option c.

Spiral Review

Question 3.
Fiona sorted her CDs into separate bins. She placed 4 CDs in each bin. If she has 160 CDs, how many bins did she fill?
Options:
a. 4
b. 16
c. 40
d. 156

Answer: 40

Explanation:
Total number of CD’s in Fiona has = 160 CD’s
Number of CD’s placed in each bin = 4
Number of bins required to place the CD’s = 160 ÷ 4 = 40
The correct answer is option c.

Question 4.
Eamon is arranging 39 books on 3 shelves. If he puts the same number of books on each shelf, how many books will there be on each shelf?
Options:
a. 11
b. 12
c. 13
d. 14

Answer: 13

Explanation:
Total number of books Eamon has = 39 books
Number of shelves = 3
Number of books in each shelf = 39 ÷ 3 = 13
The correct answer is option c.

Question 5.
A newborn boa constrictor measures 18 inches long. An adult boa constrictor measures 9 times the length of the newborn plus 2 inches. How long is the adult?
Options:
a. 142 inches
b. 162 inches
c. 164 inches
d. 172 inches

Answer: 164 inches

Explanation:
Length of newborn boa constrictor = 18 inches
Length of an adult boa constrictor = 9 x Length of newborn boa constrictor = 9 x 18 = 162
Total length of an adult boa constrictor = 162 + 2 = 164 inches
The correct answer is option c.

Question 6.
Madison has 6 rolls of coins. Each roll has 20 coins. How many coins does Madison have in all?
Options:
a. 110
b. 120
c. 125
d. 130

Answer: 120

Explanation:
Number of rolls of coins = 6
Number of coins in each roll = 20
Total number of coins Madison has = 20 x 6 = 120
The correct answer is option b.

Common Core – Divide by 1-Digit Numbers – Page No. 83

Divide Using Partial Quotients

Divide. Use partial quotients.

Question 1.
8)\(\overline { 184 } \)
-80 ← 10 × 8 10
——-
104
-80 ← 10 × 8 +10
-24
-24 ← 3 × 8  +3
——-              ———
0                      23

Question 2.
6)\(\overline { 258 } \)
______

Answer: 43

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 40 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 6.
STEP 2
Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 40 x 6 = 240 : 258 – 240 = 18
3 x 6 = 18 : 18 – 18 = 0
Therefore the quotient is 43 ( 40 + 3)

Question 3.
5)\(\overline { 630 } \)
______

Answer: 126

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 5.
STEP 2
Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 5 = 500 : 630 – 500 = 130
5 x 20 = 100 : 130 – 100 = 30 : 5 x 6 = 30 : 30 – 30 = 0
Therefore the quotient is 126 ( 100 + 20 + 6)

Divide. Use rectangular models to record the partial quotients.

Question 4.
246 ÷ 3 = ____

Answer: 82

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 80 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 80 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 80 x 3 = 240 : 246 – 240 = 6
3 x 2 = 6 : 6 – 6 = 0
Therefore the quotient is 82 ( 80 + 2)
The rectangle models are given below :

Question 5.
126 ÷ 2 = ____

Answer: 63

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 60 times the divisor.
Continue subtracting until the remaining number is less than the multiple,2.
STEP 2
Subtract smaller multiples, such as 60 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 60 x 2 = 120 : 126 – 120 = 6
2 x 3 = 6 : 6 – 6 = 0
Therefore the quotient is 63 ( 60 +3)
The rectangle models are given below :

Question 6.
605 ÷ 5 = ____

Answer: 121

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 5.
STEP 2
Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 5 = 500 : 605 – 500 = 105
5 x 20 = 100 : 105 – 100 = 5 : 5 x 1 = 5 : 5 – 5 = 0
Therefore the quotient is 121 ( 100 + 20 + 1)
The rectangle models are given below :

Divide. Use either way to record the partial quotients.

Question 7.
492 ÷ 3 = ____

Answer: 164

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 50 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 3 = 300 : 492 – 300 = 192
50 x 3 = 150 : 192 – 150 = 42 : 3 x 14 = 42 : 42 – 42 = 0
Therefore the quotient is 164 ( 100 + 50 + 14)

Question 8.
224 ÷ 7 = ____

Answer: 32

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 30 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 7.
STEP 2
Subtract smaller multiples, such as 30 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 30 x 7 = 210 : 224 – 210 = 14
7 x 2 = 14 : 14 – 14 = 0
Therefore the quotient is 32 ( 30 + 2)

Question 9.
692 ÷ 4 = ____

Answer: 173

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 4 = 400 : 692 – 400 = 392
4 x 50 = 200 : 392 – 200 = 192 : 4 x 48 = 192 : 192 – 192 = 0
Therefore the quotient is 198 ( 100 + 50 + 48)

Problem Solving

Question 10.
Allison took 112 photos on vacation. She wants to put them in a photo album that holds 4 photos on each page. How many pages can she fill?
____ pages

Answer: 28 pages

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 20 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 20 x 4 = 80 : 112 – 80 = 32
4 x 8 = 32 : 32 – 32 = 0
Therefore the quotient is 28 ( 20 + 8)

Question 11.
Hector saved $726 in 6 months. He saved the same amount each month. How much did Hector save each month?
$ ____

Answer: $121

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 6.
STEP 2
Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 6 = 600 : 726 – 600 = 126
6 x 20 = 120 : 126 – 120 = 6 : 6 x 1 = 6 : 6 – 6 = 0
Therefore the quotient is 121 ( 100 + 20 +1)

Common Core – Divide by 1-Digit Numbers – Page No. 84

Lesson Check

Question 1.
Annaka used partial quotients to divide 145 ÷ 5. Which shows a possible sum of partial quotients?
Options:
a. 50 + 50 + 45
b. 100 + 40 + 5
c. 10 + 10 + 9
d. 10 + 4 + 5

Answer: 10 + 10 + 9

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 10 x 5 = 50 : 145 – 50 = 95
5 x 10 = 50 : 95 – 50 = 45 : 5 x 9 = 45 : 45 – 45 = 0
Therefore the quotient is 29 ( 10 + 10 +9)

Question 2.
Mel used partial quotients to find the quotient 378 ÷ 3. Which might show the partial quotients that Mel found?
Options:
a. 100, 10, 10, 9
b. 100, 10, 10, 6
c. 100, 30, 30, 6
d. 300, 70, 8

Answer: 100, 10, 10, 6

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 3 = 300 : 378 – 300 = 78
10 x 3 =30 : 78 – 30 = 48 : 3 x 16 = 48 : 48 – 48 = 0
Therefore the quotient is 126 ( 100 + 10 +10 + 6)

Spiral Review

Question 3.
What are the partial products of 42 × 5?
Options:
a. 9 and 7
b. 20 and 10
c. 200 and 7
d. 200 and 10

Answer: 200 and 10

Explanation:
STEP1
42 x 5
Start by multiplying the digit five with the units digit 2 = 5 x 2 =10
Multiply the digit 5 with 4 in the tens place = 4 x 5 = 20
Since 4 is in the tens place when we multiply 4 and 5 we must place it in the hundreds place by assuming the units digit to be zero.
Therefore, the partial product of 42 x 5 = 200

Question 4.
Mr. Watson buys 4 gallons of paint that cost $34 per gallon. How much does Mr. Watson spend on paint?
Options:
a. $38
b. $126
c. $136
d. $1,216

Answer: $136

Explanation:
Cost of each gallon of paint = $34
Number of gallons = 4
The total cost of the gallons = $ 34 x 4 = $136

Question 5.
Use the area model to find the product 28 × 32.

Options:
a. 840
b. 856
c. 880
d. 896

Answer: 896

Explanation:
The whole rectangle is divided into four small rectangles the areas of these rectangles are:

Area of yellow rectangle= 30 x 20=600
Area of green rectangle= 2 x 20 = 40
Area of pink rectangle= 8 x 30= 240
Area of blue rectangle= 2 x 8= 16
Product of 32 and 28 = Area of yellow rectangle + Area of green rectangle + Area of pink rectangle + Area of the blue rectangle = 600+40+240+16 = 896

Question 6.
An adult male lion eats about 108 pounds of meat per week. About how much meat does an adult male lion eat in one day?
Options:
a. about 14 pounds
b. about 15 pounds
c. about 16 pounds
d. about 17 pounds

Answer: about 15 pounds

Explanation:
Mass of meat an adult lion eats in one week = 108
Number of days in a week = 7
Mass of meat ate by the lion in one day = 108 ÷ 7 = 15.4 pounds = about 15 pounds

Common Core – Divide by 1-Digit Numbers – Page No. 85

Model Division with Regrouping

Divide. Use base-ten blocks.

Question 1.
63 ÷ 4 = 15 r3

Explanation:
A. draw 4 circles to represent the divisor. Then use base-ten blocks to model 63. Show 63 as 6 tens and 3 ones.
B. Share the tens equally among the 4 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups.
D. There are 1 ten(s) and 5 one(s) in each group. So, the quotient is 15.
E. After grouping, there are 3 blocks that weren’t grouped. So, the remainder is 3

Question 2.
83 ÷ 3
_____ R _____

Answer: 27 r 2

Explanation:
A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 83. Show 83 as 8 tens and 3 ones.
B. Share the tens equally among the 3 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups.
D. There are 2 ten(s) and 7 one(s) in each group. So, the quotient is 27.
E. After grouping, there are 2 blocks that weren’t grouped. So, the remainder is 2

Divide. Draw quick pictures. Record the steps.

Question 3.
85 ÷ 5
_____

Answer: 17

Explanation:
A. Draw 5 circles to represent the divisor. Then use base-ten blocks to model 85. Show 85 as 8 tens and 5 ones.
B. Share the tens equally among the 5 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 5 groups.
D. There are 1 ten(s) and 7 one(s) in each group. So, the quotient is 17.

Question 4.
97 ÷ 4
_____ R _____

Answer: 24 r 1

Explanation:
A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 97. Show 97 as 9 tens and 7 ones.
B. Share the tens equally among the 4 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups.
D. There are 2 ten(s) and 4 one(s) in each group. So, the quotient is 24.
E. After grouping, there is 1 block that wasn’t grouped. So, the remainder is 1.

Problem Solving

Question 5.
Tamara sold 92 cold drinks during her 2-hour shift at a festival food stand. If she sold the same number of drinks each hour, how many cold drinks did she sell each hour?
_____ cold drinks

Answer: 46 cold drinks

Explanation:
Total number of cold drinks Tamara sold = 92
The time in which she sold the drinks = 2 hours
Number of drinks she sold in each hour = 92 ÷ 2 = 46

Question 6.
In 3 days Donald earned $42 running errands. He earned the same amount each day. How much did Donald earn from running errands each day?
$ _____

Answer: $14

Explanation:
Total amount earned by Donald = $42
Number of days = 3
Amount earned on each day = $42 ÷ 3 = $14

Common Core – Divide by 1-Digit Numbers – Page No. 86

Lesson Check

Question 1.
Gail bought 80 buttons to put on the shirts she makes. She uses 5 buttons for each shirt. How many shirts can Gail make with the buttons she bought?
Options:
a. 14
b. 16
c. 17
d. 18

Answer: 16

Explanation:
Total number of buttons = 80
Number of buttons used for each shirt = 5
Number of shirts she can make = 80 ÷ 5 =16
The correct answer is option b.

Question 2.
Marty counted how many breaths he took in 3 minutes. In that time, he took 51 breaths. He took the same number of breaths each minute. How many breaths did Marty take in one minute?
Options:
a. 15
b. 16
c. 17
d. 19

Answer: 17

Explanation:
Total number of breaths Marty counted = 51
Time in which the breath was counted = 3 minutes
Number of breaths in one minute = 51 ÷ 3 = 17
The correct answer is option c.

Spiral Review

Question 3.
Kate is solving brain teasers. She solved 6 brain teasers in 72 minutes. How long did she spend on each brain teaser?
Options:
a. 12 minutes
b. 14 minutes
c. 18 minutes
d. 22 minutes

Answer: 12 minutes

Explanation:
Number of brain teasers solved = 6
Number of minutes spent on brain teasers = 72 minutes
Number of minutes spent on each problem = 72 ÷ 6 =12 minutes
The correct answer is option a.

Question 4.
Jenny works at a package delivery store. She puts mailing stickers on packages. Each package needs 5 stickers. How many stickers will Jenny use if she is mailing 105 packages?
Options:
a. 725
b. 625
c. 525
d. 21

Answer: 525

Explanation:
Number of packages = 105
Number of stickers on each package = 5
Total number of stickers on the packages = 105 x 5 = 525
The correct answer is option c.

Question 5.
The Puzzle Company packs standardized puzzles into boxes that hold 8 puzzles. How many boxes would it take to pack up 192 standard-sized puzzles?
Options:
a. 12
b. 16
c. 22
d. 24

Answer: 24

Explanation:
Total number of puzzles = 192
Number of puzzles in each box = 8
Number of boxes used = 192 ÷ 8 = 24 boxes
The correct answer is option d.

Question 6.
Mt. Whitney in California is 14,494 feet tall. Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney. How tall is Mt. McKinley?
Options:
a. 21,310 feet
b. 20,320 feet
c. 20,230 feet
d. 19,310 feet

Answer: 20,320 feet

Explanation:
Height of Mt. Whitney in California = 14,494 feet
The height of Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney.
Therefore the height of Mt. McKinley in Alaska = 14,494 feet + 5,826 feet = 20,320 feet
The correct answer is option b.

Common Core – Divide by 1-Digit Numbers – Page No. 87

Place the First Digit

Divide.

Question 1.
62
3)\(\overline { 186 } \)
-18
——–
06
-6
——–
0

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 186. 180 hundred can be shared among 3 groups
without regrouping.
Now there is 18 tens and 6 ones to share among 3 groups.
The first digit of the quotient will be in the tens place.
STEP 2 Divide the tens.
Divide. 180 ÷ 3
Multiply. 3 × 60 = 180
Subtract. 186 − 180 = 6 ones
STEP 3 Divide the ones.
Now there are 6 ones to share among 3 groups.
Divide. 6 ones ÷ 3
Multiply. 2×3 ones
Subtract. 6 ones − 2 ones =0 one
So, the quotient is 62 (60 + 2) and the remainder is 0

Question 2.
4)\(\overline { 298 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the hundreds in 298. 280 hundred can be shared among 4 groups
without regrouping.
Now there are 28 tens and 18 ones to share among 4 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 280 ÷ 4
Multiply. 4 × 70 = 280
Subtract. 280 − 280 = 0 ones
STEP 3 Divide the ones.
Now there are 18 ones to share among 4 groups.
Divide. 18 ones ÷ 4
Multiply. 4×4 ones
Subtract. 18 ones − 16 ones = 2 ones
So, the quotient is 74 (70 + 4) and the remainder is 2.

Question 3.
3)\(\overline { 461 } \)
_____ R _____

Answer: 153

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 461. 450 hundred can be shared among 3 groups
without regrouping.
Now there is 45 tens and 11 ones to share among 3 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 450 ÷ 3
Multiply. 3 × 150 = 450
Subtract. 450 − 450 = 0 ones
STEP 3 Divide the ones.
Now there are 11 ones to share among 3 groups.
Divide. 11 ones ÷ 3
Multiply. 3×3 ones
Subtract. 11 ones − 9 ones = 2 ones
So, the quotient is 153 (150 + 3) and the remainder is 2

Question 4.
9)\(\overline { 315 } \)
_____ R _____

Answer: 35

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 315. 310 hundred can be shared among 9 groups
without regrouping.
Now there is 31 tens and 5 ones to share among 9 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide.310 ÷ 9
Multiply. 9 × 30 = 270
Subtract. 310 − 270 = 40 ones
STEP 3 Divide the ones.
Now there are 40 + 5 = 45 ones to share among 9 groups.
Divide. 45 ones ÷ 9
Multiply. 5×9 ones
Subtract. 45 ones − 45 ones = 0 ones
So, the quotient is 35 (30 + 5) and the remainder is 0

Question 5.
2)\(\overline { 766 } \)
_____ R _____

Answer: 383

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 766. 760 hundred can be shared among 2 groups
without regrouping.
Now there is 76 tens and 6 ones to share among 2 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 760 ÷ 2
Multiply. 2 × 380 = 760
Subtract. 760 − 760 = 0 ones
STEP 3 Divide the ones.
Now there are 6 ones to share among 2 groups.
Divide. 6 ones ÷ 2
Multiply. 2×3 ones
Subtract. 6 ones − 6 ones = 0 ones
So, the quotient is 383 (380 + 3) and the remainder is 0

Question 6.
4)\(\overline { 604 } \)
_____ R _____

Answer: 151

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 604. 600 hundred can be shared among 4 groups
without regrouping.
Now there is 60 tens and 4 ones to share among 4 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 600 ÷ 4
Multiply. 4 × 150 = 600
Subtract. 600 − 600 = 0 ones
STEP 3 Divide the ones.
Now there are 4 ones to share among 4 groups.
Divide. 4 ones ÷ 4
Multiply. 4×1 ones
Subtract. 4 ones − 4 ones = 0 ones
So, the quotient is 151 (150 + 1) and the remainder is 0

Question 7.
6)\(\overline { 796 } \)
_____ R _____

Answer: 132

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 796. 790 hundred can be shared among 6 groups
without regrouping.
Now there is 79 tens and 6 ones to share among 6 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 790 ÷ 6
Multiply. 6 × 131 = 786
Subtract. 790 − 786 = 4 ones
STEP 3 Divide the ones.
Now there are 4 + 6 = 10 ones to share among 6 groups.
Divide. 10 ones ÷ 6
Multiply. 6×1 ones
Subtract. 10 ones − 6 ones = 4 ones
So, the quotient is 132 (131 + 1) and the remainder is 4.

Question 8.
5)\(\overline { 449 } \)
_____ R _____

Answer: 89

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 449. 440 hundred can be shared among 5 groups
without regrouping.
Now there is 44 tens and 9 ones to share among 5 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 440 ÷ 5
Multiply. 5 × 88 = 440
Subtract. 440 − 440 = 0 ones
STEP 3 Divide the ones.
Now there are 9 ones to share among 5 groups.
Divide. 9 ones ÷ 5
Multiply. 5×1 ones
Subtract. 9 ones − 5 ones = 4 ones
So, the quotient is 89 (88 + 1) and the remainder is 4

Question 9.
6)\(\overline { 756 } \)
_____ R _____

Answer: 126

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 756. 750 hundred can be shared among 6 groups
without regrouping.
Now there is 75 tens and 6 ones to share among 6 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 750 ÷ 6
Multiply. 6 × 125 = 750
Subtract. 750 − 750 = 0 ones
STEP 3 Divide the ones.
Now there are 6 ones to share among 6 groups.
Divide. 6 ones ÷ 6
Multiply. 6×1 ones
Subtract. 6 ones − 6 ones = 0 ones
So, the quotient is 126 (125 + 1) and the remainder is 0

Question 10.
7)\(\overline { 521 } \)
_____ R _____

Answer: 74

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 521. 520 hundred can be shared among 7 groups
without regrouping.
Now there is 52 tens and 1 one to share among 7 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 520 ÷ 7
Multiply. 7 × 74 = 518
Subtract. 520 − 518 = 2 ones
STEP 3 Divide the ones.
Now there are 2 + 1 = 3 ones to share among 7 groups.
Divide. 3 ones ÷ 7 (not possible)
So, the quotient is 74 and the remainder is 3

Question 11.
5)\(\overline { 675 } \)
_____ R _____

Answer: 135

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 675. 670 hundred can be shared among 5 groups
without regrouping.
Now there is 67 tens and 5 ones to share among 5 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 670 ÷ 5
Multiply. 5 × 134 = 670
Subtract. 670 − 670 = 0 ones
STEP 3 Divide the ones.
Now there are 5 ones to share among 5 groups.
Divide. 5 ones ÷ 5
Multiply. 5×1 ones
Subtract. 5 ones − 5 ones = 0 ones
So, the quotient is 135 (134 + 1) and the remainder is 0.

Question 12.
8)\(\overline { 933 } \)
_____ R _____

Answer: 116

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 933. 930 hundred can be shared among 8 groups
without regrouping.
Now there is 93 tens and 3 ones to share among 8 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 930 ÷ 8
Multiply. 8 × 116 = 928
Subtract. 930 − 928 = 2 ones
STEP 3 Divide the ones.
Now there are 2 + 3 = 5 ones to share among 8 groups.
Divide. 5 ones ÷ 8 (not possible)
So, the quotient is 116 (100 + 3) and the remainder is 5.

Problem Solving

Question 13.
There are 132 projects in the science fair. If 8 projects can fit in a row, how many full rows of projects can be made? How many projects are in the row that is not full?
_____ full rows
_____ projects in the non-full row

Answer: 16 full rows and 4 projects in the non-full row

Explanation:
Total number of projects = 132
Number of projects placed in full row = 8
Number of rows having full projects =Quotient of 132 ÷ 8 = 16
Number of projects in the non-full row = Remainder of 132 ÷ 8 = 4

Question 14.
There are 798 calories in six 10-ounce bottles of apple juice. How many calories are there in one 10-ounce bottle of apple juice?
_____ R _____ calories in one 10-ounce bottles of juice

Answer: 133 calories

Explanation:
Number of calories in 6 bottles of apple juice = 798
Number of calories in each bottle = 798 ÷6 = 133 calories

Common Core – Divide by 1-Digit Numbers – Page No. 88

Lesson Check

Question 1.
To divide 572 ÷ 4, Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quotient?
Options:
a. ones
b. tens
c. hundreds
d. thousands

Answer: hundreds

Explanation:
The quotient of 572÷ 4 is 143
STEP 1 Use place value to place the first digit. Look at the hundreds in 572. 560 hundred can be shared among 4 groups
without regrouping.
Now there is 1 ten to share among 4 groups.
The first digit of the quotient will be in the hundreds place.

Question 2.
Onetta biked 325 miles in 5 days. If she biked the same number of miles each day, how far did she bike each day?
Options:
a. 1,625 miles
b. 320 miles
c. 65 miles
d. 61 miles

Answer: 65 miles

Explanation:
Total number of miles biked = 325 miles
Number of days biked = 5
Number of miles biked on each day = Quotient of 325 ÷ 5 = 65

Spiral Review

Question 3.
Mort makes beaded necklaces that he sells for $32 each. About how much will Mort make if he sells 36 necklaces at the local art fair?
Options:
a. $120
b. $900
c. $1,200
d. $1,600

Answer: $1,200

Explanation:
Cost of each beaded necklace = $32
Number of necklaces = 36
The total cost of the necklaces = $32 x 36 = $1,200 (approx)

Question 4.
Which is the best estimate of 54 × 68?
Options:
a. 4,200
b. 3,500
c. 3,000
d. 350

Answer: 3,500

Explanation:

Taking the terms nearest to the 54 x 68 as 54 x 65 = 3510 = 3500 (approx)

Question 5.
Ms. Eisner pays $888 for 6 nights in a hotel. How much does Ms. Eisner pay per night?
Options:
a. $5,328
b. $882
c. $148
d. $114

Answer: $148

Explanation:
Total pays of Ms Eisner in a hotel = $888
Number of nights = 6
Amount Ms Eisner pay per night = $888 ÷ 6 = $148

Question 6.
Which division problem does the model show?

Options:
a. 42 ÷ 3
b. 44 ÷3
c. 51 ÷ 3
d. 54 ÷ 3

Answer: 54 ÷ 3

Explanation:
Number of counters in each model = 18
Number of models = 3
Total number of counters = 18 x 3 = 54
Therefore the model displays = 54 ÷ 3

Common Core – Divide by 1-Digit Numbers – Page No. 89

Divide by 1-Digit Numbers

Divide and check.

Question 1.
318
\(\overline { 2)636 } \) 318
-6     × 2
———  ———
03 636
-2
———
16
-16
———
0

Question 2.
4)\(\overline { 631 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 3.
8)\(\overline { 906 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 4.
6)\(\overline { 6,739 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the thousands in 6,739. 6 thousand can be shared among 6 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Question 5.
4)\(\overline { 2,328 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the thousands in 2,328. 2 thousand can be shared among 4 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Question 6.
5)\(\overline { 7,549 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the thousands in 7,549. 7 thousand can be shared among 5 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Problem Solving

Use the table for 7 and 8.

Question 7.
The Briggs rented a car for 5 weeks. What was the cost of their rental car per week?
$ _____

Answer: $197

Explanation:
Cost of the car of Briggs = $985
Number of weeks = 5
Cost of rent per week = $985 ÷ 5 =$ 197

Question 8.
The Lees rented a car for 4 weeks. The Santos rented a car for 2 weeks. Whose weekly rental cost was lower? Explain.
The rental cost of _________

Answer: Weekly rental cost was lower for Lees compared to Santos

Explanation:
Cost of the car of Lees = $632
Number of weeks = 4
Cost of rent per week = $632 ÷ 4 =$ 158

Cost of the car of Santos = $328
Number of weeks = 2
Cost of rent per week = $328 ÷ 2 =$ 164
Therefore weekly rental cost was lower for Lees compared to Santos.

Common Core – Divide by 1-Digit Numbers – Page No. 90

Lesson Check

Question 1.
Which expression can be used to check
the quotient 646 ÷ 3?
Options:
a. (251 × 3) + 1
b. (215 × 3) + 2
c. (215 × 3) + 1
d. 646 × 3

Answer: (215 × 3) + 1

Explanation:
Multiply 215 x 3 = 645
Then add 1 to 645
Then the dividend is 645 + 1 = 646
Thus the correct answer is option c.

Question 2.
There are 8 volunteers at the telethon. The goal for the evening is to raise $952. If each volunteer raises the same amount, what is the minimum amount each needs to raise to meet the goal?
Options:
a. $7,616
b. $944
c. $119
d. $106

Answer: $7,616

Explanation:
Number of volunteers = 8
Amount raised by each volunteer = $952
Total amount raised = $952 x 8 = $7,616

Thus the correct answer is option a.

Spiral Review

Question 3.
Which product is shown by the model?

Options:
a. 5 × 15 = 75
b. 5 × 16 = 80
c. 5 × 17 = 75
d. 5 × 17 = 85

Answer: 5 × 17 = 85

Explanation:
By counting the number of counters we can give the expression.
Number of counters in one row = 17
Number of rows = 5
Therefore the expression = 5 × 17 = 85
Thus the correct answer is option d.

Question 4.
The computer lab at a high school ordered 26 packages of CDs. There were 50 CDs in each package. How many CDs did the computer lab order?
Options:
a. 1,330
b. 1,300
c. 1,030
d. 130

Answer: 1,300

Explanation:
Number of packages = 26
Number of CDs in each pack = 50
Total number of CDs the computer lab ordered = 26 x 50 = 1,300
Thus the correct answer is option b.

Question 5.
Which of the following division problems has a quotient with the first digit in the hundreds place?
Options:
a. 892 ÷ 9
b. 644 ÷ 8
c. 429 ÷ 5
d. 306 ÷ 2

Answer: 306 ÷ 2

Explanation:
Use place value to place the first digit. Look at the hundreds in 306. 300 hundred can be shared among 2 groups
without regrouping.
Now there is 30 tens and 6 ones to share among 2 groups.
The first digit of the quotient will be in the hundreds place.
Thus the correct answer is option d.

Question 6.
Sharon has 64 ounces of juice. She is going to use the juice to fill as many 6-ounce glasses as possible. She will drink the leftover juice. How much juice will Sharon drink?
Options:
a. 4 ounces
b. 6 ounces
c. 10 ounces
d. 12 ounces

Answer: 4 ounces

Explanation:
The total quantity of juice = 64 ounces
Quantity of juice she filled = 6 ounces
Quantity of juice she drank = Remainder of 64 ÷ 6 = 4

Thus the correct answer is option a.

Common Core – Divide by 1-Digit Numbers – Page No. 91

Problem Solving Multistep Division Problems

Solve. Draw a diagram to help you.

Question 1.
There are 3 trays of eggs. Each tray holds 30 eggs. How many people can be served if each person eats 2 eggs?

Think: What do I need to find? How can I draw a diagram to help?
45 people can be served

Question 2.
There are 8 pencils in a package. How many packages will be needed for 28 children if each child gets 4 pencils?
______ packages

Answer: 14 packages

Explanation:
Number of pencils in each package = 8

Number of children = 28

Number of pencils each child needs = 4
Total number of pencils = 28 x 4 =112
Number of packages = 112 ÷ 8 = 14

Question 3.
There are 3 boxes of tangerines. Each box has 93 tangerines. The tangerines will be divided equally among 9 classrooms. How many tangerines will each classroom get?
______ tangerines

Answer: 31

Explanation:
Number of boxes = 3
Number of tangerines in each box = 93
Total number of tangerines = 93 x 3 = 279

Number of classrooms = 9
Number of tangerines in each classroom = 279 ÷ 9 = 31

Question 4.
Misty has 84 photos from her vacation and 48 photos from a class outing. She wants to put all the photos in an album with 4 photos on each page. How many pages does she need?
______ pages

Answer: 33 pages

Explanation:
Number of photos from her vacation = 84

Number of photos from her class outing = 48

Total number of photos = 84 + 48 = 132
Number of photos in each page = 4
Number of pages required = 132 ÷ 4 = 33

Common Core – Divide by 1-Digit Numbers – Page No. 93

Lessons 4.1, 4.5

Estimate the quotient.

Question 1.
67 ÷ 4
about ______

Answer: About 17

Explanation:
The number close to 67 is 70.
Divide 70 by 4 is 17.5
Thus the estimated quotient of 67 ÷ 4 is 17.

Question 2.
72 ÷ 5
about ______

Answer: About 14

Explanation:
The number close to 72 is 70.
Divide 70 by 5 is 14.
Thus the estimated quotient of 72 ÷ 5 is 14.

Question 3.

213 ÷ 3
about ______

Answer: About 70

Explanation:
The number close to 213 is 210.
Divide 210 by 3 is 70.
Thus the estimated quotient of 213 ÷ 3 is 70.

Question 4.
484 ÷ 6
about ______

Answer: About 80

Explanation:
The number close to 484 is 480.
Divide 480 by 6 is 80.
Thus the estimated quotient of 484 ÷ 6 is 80.

Question 5.
446 ÷ 7
about ______

Answer: About 60

Explanation:
The number close to 446 is 440.
Divide 440 by 7 is 60.
Thus the estimated quotient of 446 ÷ 7 is 60.

Question 6.
1,246 ÷ 4
about ______

Answer: About 300

Explanation:
The number close to 1246 is 1200.
Divide 1200 by 4 is 300.
Thus the estimated quotient of 1,246 ÷ 4 is 300.

Question 7.
708 ÷ 9
about ______

Answer: About 80

Explanation:
The number close to 708 is 700.
Divide 700 by 9 is 80 (approx).
Thus the estimated quotient of 708 ÷ 9 is 80.

Question 8.
2,657 ÷ 3
about ______

Answer: About 900

Explanation:
The number close to 2,657 is 2700.
Divide 2700 by 3 is 900.
Thus the estimated quotient of 2,657 ÷ 3 is 900.

Lesson 4.2

Use counters or quick pictures to find the quotient and remainder.

Question 9.
44 ÷ 5
______ R ______

Answer: 8R4

Explanation:
Quotient:
A. Use 44 counters to represent the 44 dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 44 ÷ 5
D. Number of circles equally filled is8, therefore, the quotient is 8.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 44 ÷ 5, the quotient is 8 and the remainder is 4, or 8R4.

Question 10.
8)\(\overline { 21 } \)
______ R ______

Answer: 2R5

Explanation:
Quotient:
A. Use 21 counters to represent the 21 dominoes. Then draw 8 circles to represent the divisor.
B. Share the counters equally among the 8 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 21 ÷ 8
D. Number of circles equally filled is 2, therefore, the quotient is 2.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 5
For 21 ÷ 8, the quotient is 2 and the remainder is 5, or 2R5.

Question 11.
4)\(\overline { 75 } \)
______ R ______

Answer: 18R3

Explanation:
Quotient:
A. Use 75 counters to represent the 75 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 75 ÷ 4
D. Number of circles equally filled is 18, therefore, the quotient is 18.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 21 ÷ 8, the quotient is 18 and the remainder is 3, or 18R3.

Question 12.
76 ÷ 6
______ R ______

Answer: 12R4

Explanation:
Quotient:
A. Use 76 counters to represent the 76 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 6 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 76 ÷ 6
D. Number of circles equally filled is 12, therefore, the quotient is 12.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 76 ÷ 6, the quotient is 12 and the remainder is 4, or 12R4.

Lesson 4.3

Interpret the remainder to solve.

Question 13.
Kelly divides 29 markers equally among 7 friends. If Kelly keeps the leftover markers, how many markers will she keep?
______ marker(s)

Answer: 1 marker

Explanation:
Given,
Kelly divides 29 markers equally among 7 friends.
1 because 4 markers for each friend (4 × 7) would be 28 and the last one would be leftover because it’s not enough for everyone.

Question 14.
Dave has a board that is 29 inches long. He cuts the board into 4 equal pieces. How long will each piece be?
______ inches

Answer: 7 inches

Explanation:
Dave has a board that is 29 inches long and want to cut it into 4 pieces.
You are asked the length of each piece.
To solve the question, you need to divide the total length of the board by the number of pieces Dave wants to make.
Then, the length of each piece would be: 29 inches/4= 7.25 inches

Question 15.
Eight students can ride in each van. How many vans are needed for 29 students?
______ vans

Answer: 4 vans

Explanation:
Given,
Eight students can ride in each van.
29/8 = 3.625 = 4(approx)
Therefore 4 vans are needed for 29 students.

Question 16.
Mac has 40 ounces of juice. He pours 6 ounces in each glass. How many glasses can he fill?
______ glasses

Answer: 6 glasses

Explanation:
Given,
Mac has 40 ounces of juice. He pours 6 ounces in each glass.
Divide 40 by 6
40/6 = 6.66 ≈ 6
Thus Mac can fill 6 glasses.

Lesson 4.4

Use basic facts and place value to find the quotient.

Question 17.
120 ÷ 4 = ______

Answer: 30

Explanation:
STEP 1 Identify the basic fact. 120 ÷ 4
STEP 2 Use place value. 120 = 12 tens
STEP 3 Divide. 12 tens ÷ 4 = 3 tens
120 ÷ 4 = 30

Question 18.
280 ÷ 7 = ______

Answer: 40

Explanation:
STEP 1 Identify the basic fact. 280 ÷ 7
STEP 2 Use place value. 280 = 28 tens
STEP 3 Divide. 28 tens ÷ 7 = 4 tens
280 ÷ 7 = 40

Question 19.
3,000 ÷ 5 = ______

Answer: 600

Explanation:
STEP 1 Identify the basic fact. 3000 ÷ 5
STEP 2 Use place value. 3000 = 300 tens
STEP 3 Divide. 300 tens ÷ 5 = 60 tens
3,000 ÷ 5 = 60 tens

Question 20.
4,800 ÷ 6 = ______

Answer: 800

Explanation:
STEP 1 Identify the basic fact. 4,800 ÷ 6
STEP 2 Use place value. 4800 = 480 tens
STEP 3 Divide. 480 tens ÷ 6 = 80 tens
4,800 ÷ 6 = 800

Question 21.
5,600 ÷ 8 = ______

Answer: 700

Explanation:
STEP 1 Identify the basic fact. 5,600 ÷ 8
STEP 2 Use place value. 5600 = 560 tens
STEP 3 Divide. 560 tens ÷ 8 = 70 tens
5,600 ÷ 8 = 700

Question 22.
6,300 ÷ 9 = ______

Answer: 700

Explanation:
STEP 1 Identify the basic fact. 6,300 ÷ 9
STEP 2 Use place value. 6300 = 630 tens
STEP 3 Divide. 630 tens ÷ 9 = 70 tens
6,300 ÷ 9 = 700

Common Core – Divide by 1-Digit Numbers – Page No. 94

Lessons 4.6–4.7

Choose a method and divide.

Question 1.
68 ÷ 4 = ______

Answer: 17

Explanation:
The number close to 68 is 70.
Divide 70 by 4 is 17 (approx).
Thus the estimated quotient of 68 ÷ 4 is 17.

Question 2.
48 ÷ 3 = ______

Answer: 16

Explanation:
The number close to 48 is 50.
Divide 50 by 3 is 16  (approx).
Thus the estimated quotient of 48 ÷ 3 is 16.

Question 3.
108 ÷ 9 = ______

Answer: 12

Explanation:
The number close to 108 is 100.
Divide 100 by 9 is 12 (approx).
Thus the estimated quotient of 108 ÷ 9 is 12.

Question 4.
74 ÷ 2 = ______

Answer: 37

Explanation:
The number close to 74 is 70.
Divide 70 by 2 is 37 (approx).
Thus the estimated quotient of 74 ÷ 2 is 37.

Question 5.
122 ÷ 5 = ______ R ______

Answer: 24R2

Explanation:
Quotient:
A. Use 122 counters to represent the 122 dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 122 ÷ 5
D. Number of circles equally filled are 24, therefore, the quotient is 24.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 122 ÷ 5, the quotient is 24 and the remainder is 2, or 24R2.

Question 6.
165 ÷ 6 = ______ R ______

Answer: 27R3

Explanation:
Quotient:
A. Use 165 counters to represent the 165 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 6 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 165 ÷ 6.
D. Number of circles equally filled are 27, therefore, the quotient is 27.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 165 ÷ 6, the quotient is 27 and the remainder is 3, or 27R3.

Lessons 4.8–4.9

Divide.

Question 7.
4)\(\overline { 848 } \)
______

Answer: 212

Question 8.
7)\(\overline { 287 } \)
______

Answer: 41

Question 9.
5)\(\overline { 405 } \)
______

Answer: 81

Question 10.
3)\(\overline { 696 } \)
______

Answer: 232

Question 11.
96 ÷ 6 = ______

Answer: 16

Question 12.
76 ÷ 5 = ______ R ______

Answer: 15R1

Question 13.
58 ÷ 4 = ______ R ______

Answer: 14R2

Question 14.
85 ÷ 2 = ______ R ______

Answer: 42R1

Lessons 4.10–4.11

Divide and check.

Question 15.
4)\(\overline { 896 } \)
______

Answer: 224

Explanation:
224
× 4
896

Question 16.
5)\(\overline { 833 } \)
______ R ______

Answer: 166r3

Explanation:
166
× 5
830
+ 3
833

Question 17.
6)\(\overline { 527 } \)
______ R ______

Answer: 87r5

Explanation:
87
×6
522
+ 5
527

Question 18.
3)\(\overline { 935 } \)
______ R ______

Answer: 311r2

Explanation:
311
× 3
933
+ 2
935

Question 19.
3)\(\overline { 1,976 } \)
______ R ______

Answer: 658R2

Explanation:
658
× 3
1974
+    2
1976

Question 20.
6)\(\overline { 1,042 } \)
______ R ______

Answer: 173r4

Explanation:
173
×   6
1038
+   4
1042

Lesson 4.12

Solve. Draw a diagram to help you.

Question 21.
Ellis has 2 dozen white baseballs and 4 dozen yellow baseballs. He needs to divide them into cartons that hold 6 each. How many cartons can he fill?
______ cartons

Answer: 6 cartons

Explanation:
Given,
Ellis has 2 dozen white baseballs and 4 dozen yellow baseballs.
He needs to divide them into cartons that hold 6 each.
6 2 Dozens and 4 Dozens are 12+24 = 36/6 = 6
Therefore he can fill 6 cartons.

Question 22.
A family of 2 adults and 3 children went out to dinner. The total bill was $42. Each child’s dinner cost $4. How much did each adult’s dinner cost?
$ ______

Answer: $15

Explanation:
Each child’s dinner – $4
3 child’s dinner – $4 x 3 = $12
$42 – 12 = $30
$30 divided by 2 = $15
Thus each adult’s dinner cost is $15.

Conclusion:

Find more questions for practice from here, Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers and develop your mathematical skills. Drop your queries and feedback by posting the comment below and we’ll update if anything requires as well as we’ll answer your doubts Asap.

If you looking to practice Go Math 3rd Grade Textbook Questions then take the help of the Go Math Grade 3 Answer Key Chapter 6 Understand Division Extra Practice. You need to have strong fundamentals in Maths in order to become a pro in the Subject. You can easily understand the basics of the division with the Go Math Grade 3 Answer Key Chapter 6 Understand Division Extra Practice. Solve as Many Questions as possible from the Extra Practice and Clear the Final Exams with better grades.

3rd Grade Go Math Answer Key Ch 6 Understand Division Extra Practice

Repeated subtraction, Equal groups, Number line, related multiplication, and division facts are all the topics covered in the 3rd Grade Go Math Answer Key Ch 6. Before you begin your preparation firstly know the syllabus i.e. concepts in Chapter 6 Understand Division and prepare accordingly. Check out the Step by Step Solutions provided for 3rd Grade Go Math Answer Key Chapter 6 Understand Division Extra Practice and learn the concepts efficiently.

Common Core – Page No. 123000

Lessons 6.1–6.3 Make equal groups.

Complete the table.

	Counters	Number of Equal Groups	Number in Each Group
1.	18	9	________
2.	24	________	8
3.	12	6	________
4.	35	7	________
5.	32	________	4
6.	25	________	5

Answer:

	Counters	Number of Equal Groups	Number in Each Group
1.	18	9	2
2.	24	3	8
3.	12	6	2
4.	35	7	5
5.	32	8	4
6.	25	5	5

Explanation:

1. Number of counters = 18
Number of equal groups = 9
Number in each group = x
x × 9 = 18
x= 18/9 = 2
Therefore number in each group = 2

2. Number of counters = 24
Number in each group = 8
Number of equal groups = x
x × 8 = 24
x = 24/8 = 3
Thus the number of equal groups = 3

3. Number of counters = 12
Number of equal groups = 6
Number in each group = x
x × 6 = 12
x = 12/6 = 2
So, the number in each group = 2

4. Number of counters = 35
Number of equal groups = 7
Number in each group = x
x × 7 = 35
x = 35/7 = 5
x = 5
Therefore number in each group = 5

5. Number of counters = 32
Number of equal groups = x
Number in each group = 8
x × 8 = 32
x = 32/8 = 4
Thus the number of equal groups = 4

6. Number of counters = 25
Number of equal groups = x
Number in each group = 5
x × 5 = 25
x = 25/5 = 5
So, the number of equal groups = 5

Lesson 6.4

Write a division equation for the picture.

Question 1.

Type below:
__________

Answer: 27 ÷ 3 = 9 or 27 ÷ 9 = 3

Explanation:

Total number of counters = 27
Number of equal groups = 3
Number in each group = 9
The division equation is
Number of counters by number of groups = 27 ÷ 3 = 9
or
Number of counters by number in each group = 27 ÷ 9 = 3

Question 2.

Type below:
__________

Answer: 24 ÷ 4 = 6 or 24 ÷ 6 = 4

Explanation:

Total number of counters = 24
Number of equal groups = 4
Number in each group = 6
The division equation is
Number of counters by number of groups = 24 ÷ 4 = 6
or
Number of counters by number in each group = 24 ÷ 6 = 4

Lesson 6.5

Write a division equation.

Question 3.

Type below:
__________

Answer: 3 groups, 15 ÷ 5 = 3

Explanation:

Step 1:

Starts at 15

Step 2:

Count back by 5s as many times as you can.

Step 3:

Count the number of times you jumped back 5.
You jumped back by 15 three times
There are 3 jumps of 5 in 15.

Question 4.

Type below:
__________

Answer: 24 ÷ 6 = 4

Explanation:

Step 1:

Begins at 24

Step 2:

Subtract with 6 until you get 0.

Step 3:

Count the number of times you subtract with 6.

You subtract 4 times
There are 4 groups of 6 with 24
So, 24 ÷ 6 = 4

Common Core – Page No. 124000

Lesson 6.6

Make an array. Then write a division equation.

Question 1.
12 tiles in 4 rows
______ ÷ ______ = ______

Answer: 12 ÷ 4 = 3

Explanation:

■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
Total number of tiles = 12
Number of rows = 4
Number of tiles in each row = x
Divide the number of tiles by number of rows = 12 ÷ 4 = 3

Question 2.
18 tiles in 3 rows
______ ÷ ______ = ______

Answer: 18 ÷ 3 = 6

Explanation:

■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
Total number of tiles = 18
Number of rows = 3
Number of tiles in each row = y
Divide the number of tiles by no. of rows = 18 ÷ 3 = 6

Question 3.
35 tiles in 5 rows
______ ÷ ______ = ______

Answer: 35 ÷ 5 = 7

Explanation:

■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■

Total number of tiles = 35
Number of rows = 5
Number of tiles in each row = p
Divide the number of tiles by number of rows = 35 ÷ 5 = 7

Question 4.
28 tiles in 7 rows
______ ÷ ______ = ______

Answer: 28 ÷ 7 = 4

Explanation:

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Total number of tiles = 28
Number of rows = 7
Number of tiles in each row = x
Divide the number of tiles by number of rows = 28 ÷ 7 = 4

Lesson 6.7

Complete the equations.

Question 5.
8 × ______ = 40 40 ÷ 8 = ______

Answer: 5, 5

Explanation:

Let x be the unknown factor
8 × x = 40
x = 40/8
x = 5
Check whether the related multiplication and division facts are the same or not.
40 ÷ 8 = 5
The related facts of 40 and 8 are 5.

Question 6.
6 × ______ = 36 36 ÷ 6 = ______

Answer: 6, 6

Explanation:

Let y be the unknown factor
6 × y = 36
y = 36/6 = 6
Check if the related multiplication and division facts are the same or not.
36 ÷ 6 = 6
The related facts of 36 and 6 are 6.

Question 7.
3 × ______ = 21 21 ÷ 3 = ______

Answer: 7, 7

Explanation:

Let x be the unknown factor
3 × x = 21
x = 21
Check whether the related facts are the same or not.
21 ÷ 3 = 7
The quotient is 7.

Question 8.
2 × ______ = 18 18 ÷ 2 = ______

Answer: 9, 9

Explanation:

Let b be the unknown factor
2 × b = 18
b = 18/2 = 9
Check the related multiplication and division facts
18 ÷ 2 = 9
The related facts of 18 and 2 are 9.

Lesson 6.8 (pp. 239–243)

Write the related facts for the array.

Question 9.
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■
______ × ______ = ______
______ × ______ = ______
______ ÷ ______ = ______
______ ÷ ______ = ______

Answer:

3 × 5 = 15
5 × 3 = 15
15 ÷ 3 = 5
15 ÷ 5 = 3

Explanation:

Total number of tiles = 15
Number of equal rows = 3
Number of rows in each group = 5
So, the related 5, 3 and 15 is 5× 3 = 15, 3×5 = 15, 15 ÷ 3 = 5 and 15÷ 5 = 3

Question 10.
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
______ × ______ = ______
______ × ______ = ______
______ ÷ ______ = ______
______ ÷ ______ = ______

Answer:

3 × 6 = 18
6 × 3 = 18
18 ÷ 3 = 6
18 ÷ 6 = 3

Explanation:

Total number of tiles = 18
Number of equal rows = 3
Number of rows in each group = 6
So, the related 18, 3 and 6 is 3 × 6 = 18, 6 × 3 = 18, 18 ÷ 3 = 6 and 18 ÷ 6 = 3

Question 11.
■ ■ ■ ■ ■
■ ■ ■ ■ ■
______ × ______ = ______
______ × ______ = ______
______ ÷ ______ = ______
______ ÷ ______ = ______

Answer:

2 × 5 = 10
5 × 2 = 10
10 ÷ 2 = 5
10 ÷ 5 = 2

Explanation:

Total number of tiles = 10
Number of equal rows = 2
Number of rows in each group = 5
So, the related 2, 5 and 10 is 2 × 5 = 10, 5 × 2 = 10, 10 ÷ 2 = 5 and 10 ÷ 5 = 2

Lesson 6.9

Find the quotient.

Question 12.
7 ÷ 1 = ______

Answer: 7

Explanation:

Any number divided by 1 will be the same number. Thus the quotient is 7.

Question 13.
4 ÷ 4 = ______

Answer: 1

Explanation:

The number divided by the same number will be always 1. Thus the quotient is 1.

Question 14.
9 ÷ 1 = ______

Answer: 9

Explanation:

Any number divided by 1 will be always the same number. So, the quotient is 9.

Question 15.
0 ÷ 1 = ______

Answer: 0

Explanation:

0 divided by any number is always 0. So, the quotient is 0.

Question 16.
Anton has 8 flower pots. He plants 1 seed in each pot. How many seeds does Anton use?
______ seeds

Answer: 8 seeds

Explanation:

Anton has 8 flower pots.
He plants 1 seed in each pot.
Number of seeds Anton used = x
x × 1 = 8
x = 8/1
x = 8
Therefore there are 8 seeds in 8 flower pots.

All the Questions in Go Math Grade 3 Answer Key Chapter 6 Understand Division Extra Practice helps the students to be prepared for their exams. For any assistance needed you can always look upto  Go Math Grade 3 Answer Key Chapter 6 Understand Division.  You can get All Lessons Solutions in Chapter 6 Understand Division here.