Vijaya Sree

Hello Kids! Here is Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers in pdf. Without wasting any time just refer to the Ch 2 Answer Key of Go Math Grade 4 and gain proper knowledge about the concept. Go Math Grade 4 Answer Key provided here will increase your Mathematical skills and support parents to understand the concept and educate their children effectively. So, get into these online chapter 2 Multiply by 1-Digit Numbers Go Math 4th Grade Solutions Key & get a good grip on the concepts.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers

There are various lessons & concepts included in the Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers such as Multiplication Comparisons, Multiply Tens, Hundreds, and Thousands, Estimate Products, Multiply Using the Distributive Property, and so on. So, move ahead and click on the respective topic to grasp the concept and then solve the sums easily. All these solutions will make you understand the concepts clearly and make you strong on basic fundamentals on your own.

Lesson: 1 – Multiplication Comparisons

Common Core – Multiply by 1-Digit Numbers – Page No. 23
Common Core – Multiply by 1-Digit Numbers – Page No. 24

Lesson: 2 – Comparison Problems

Common Core – Multiply by 1-Digit Numbers – Page No. 25
Common Core – Multiply by 1-Digit Numbers – Page No. 26

Lesson: 3 – Multiply Tens, Hundreds, and Thousands

Common Core – Multiply by 1-Digit Numbers – Page No. 27
Common Core – Multiply by 1-Digit Numbers – Page No. 28

Lesson: 4 – Estimate Products

Common Core – Multiply by 1-Digit Numbers – Page No. 29
Common Core – Multiply by 1-Digit Numbers – Page No. 30

Lesson: 5 – Multiply Using the Distributive Property

Common Core – Multiply by 1-Digit Numbers – Page No. 31
Common Core – Multiply by 1-Digit Numbers – Page No. 32

Lesson: 6 – Multiply Using Expanded Form

Common Core – Multiply by 1-Digit Numbers – Page No. 33
Common Core – Multiply by 1-Digit Numbers – Page No. 34

Lesson: 7 – Multiply Using Partial Products

Common Core – Multiply by 1-Digit Numbers – Page No. 35
Common Core – Multiply by 1-Digit Numbers – Page No. 36

Lesson: 8 – Multiply Using Mental Math

Common Core – Multiply by 1-Digit Numbers – Page No. 37
Common Core – Multiply by 1-Digit Numbers – Page No. 38

Lesson: 9 – Problem Solving Multistep Multiplication Problems

Common Core – Multiply by 1-Digit Numbers – Page No. 39
Common Core – Multiply by 1-Digit Numbers – Page No. 40

Lesson: 10 – Multiply 2-Digit Numbers with Regrouping

Common Core – Multiply by 1-Digit Numbers – Page No. 41
Common Core – Multiply by 1-Digit Numbers – Page No. 42

Lesson: 11 – Multiply 3-Digit and 4-Digit Numbers with Regrouping

Common Core – Multiply by 1-Digit Numbers – Page No. 43
Common Core – Multiply by 1-Digit Numbers – Page No. 44

Lesson: 12 – Solve Multistep Problems Using Equations

Common Core – Multiply by 1-Digit Numbers – Page No. 45
Common Core – Multiply by 1-Digit Numbers – Page No. 46

Lesson: 13 

Common Core – Multiply by 1-Digit Numbers – Page No. 47
Common Core – Multiply by 1-Digit Numbers – Page No. 48

Common Core – Multiply by 1-Digit Numbers – Page No. 23

Multiplication Comparisons

Write a comparison sentence.

Question 1.
6 × 3 = 18
6 times as many as 3 is 18.

Question 2.
63 = 7 × 9
_____ is _____ times as many as _____.

Answer: 63 is 7 times as many as 9.

Explanation:

Question 3.
5 × 4 = 20
_____ times as many as _____ is _____.

Answer: 5 times as many as 4 is 20.

Explanation:

Question 4.
48 = 8 × 6
_____ is _____ times as many as _____.

Answer: 48 is 6 times as many as 8.

Explanation:

Write an equation.

Question 5.
2 times as many as 8 is 16.
_____ × _____ = _____

Answer: 2 × 8 = 16

Explanation:

Question 6.
42 is 6 times as many as 7.
_____ = _____ × _____

Answer: 42 = 6 × 7

Explanation:

Question 7.
3 times as many as 5 is 15.
_____ × _____ = _____

Answer: 3 × 5 = 15

Explanation:

Question 8.
36 is 9 times as many as 4.
_____ = _____ × _____

Answer: 36 = 9 × 4

Explanation:

Question 9.
72 is 8 times as many as 9.
_____ = _____ × _____

Answer: 72 = 8 × 9

Explanation:

Question 10.
5 times as many as 6 is 30.
_____ × _____ = _____

Answer: 5 × 6 = 30

Explanation:

Problem Solving

Question 11.
Alan is 14 years old. This is twice as old as his brother James is. How old is James?
_____ years old

Answer: 7 years old.

Explanation:
Alan’s age is 14 years old and his brother is James is twice younger than Alan, So James’s age is 14÷2= 7.

Question 12.
There are 27 campers. This is nine times as many as the number of counselors. How many counselors are there?
_____ counselors

Answer: 3 counselors.

Explanation: 27 campers= 9× no.of counselors,
So no.of counselors are 27÷9= 3.

Common Core – Multiply by 1-Digit Numbers – Page No. 24

Lesson Check

Question 1.
Which equation best represents the comparison sentence?
24 is 4 times as many as 6.
Options:
a. 24 × 4 = 6
b. 24 = 4 × 6
c. 24 = 4 + 6
d. 4 + 6 = 24

Answer: 24 = 4 × 6

Explanation:

The correct answer is option b.

Question 2.
Which comparison sentence best represents the equation?
5 × 9 = 45
Options:
a. 5 more than 9 is 45.
b. 9 is 5 times as many as 45.
c. 5 is 9 times as many as 45.
d. 45 is 5 times as many as 9.

Answer: 45 is 5 times as many as 9.

Explanation:

The correct answer is option d.

Spiral Review

Question 3.
Which of the following statements correctly compares the numbers?
Options:
a. 273,915 > 274,951
b. 134,605 < 143,605
c. 529,058 > 530,037
d. 452,731 > 452,819

Answer: 134,605 < 143,605

Explanation:
134,605 is lesser compared to 143,605.
The correct answer is option b.

Question 4.
What is the standard form for
200,000 + 80,000 + 700 + 6?
Options:
a. 2,876
b. 28,706
c. 208,706
d. 280,706

Answer: 280,706

Explanation:
200,000+80,000+700+6= 280,706.
The correct answer is option d.

Question 5.
Sean and Leah are playing a computer game. Sean scored 72,491 points. Leah scored 19,326 points more than Sean. How many points did Leah score?
Options:
a. 53,615
b. 91,717
c. 91,815
d. 91,817

Answer: 91,817

Explanation:
Sean’s score is 72,491 and Leah’s score is 19,326 more than Sean’s score. So Sean score is 72,491+19,326 = 91,817.
The correct answer is option d.

Question 6.
A baseball stadium has 38,496 seats. Rounded to the nearest thousand, how many seats is this?
Options:
a. 38,000
b. 38,500
c. 39,000
d. 40,000

Answer: 38,000

Explanation:
Round off to the nearest thousand is 38,000.
The correct answer is option a.

Common Core – Multiply by 1-Digit Numbers – Page No. 25

Comparison Problems

Draw a model. Write an equation and solve.

Question 1.
Stacey made a necklace using 4 times as many blue beads as red beads. She used a total of 40 beads. How many blue beads did Stacey use?

Question 2.
At the zoo, there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there?
______ monkeys

Answer: 18 monkeys

Explanation:

Therefore there are 18 monkeys.

Question 3.
Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?
______ inches

Answer: 49 inches

Explanation:

Therefore Fred’s frog jumps 49 inches.

Question 4.
Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?
______ markers

Answer: 15 markers

Explanation:

Therefore Sheila has 15 markers.

Problem Solving

Question 5.
Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did Rafael count?
______ white cars

Answer: 36 white cars

Explanation:
Let yellow cars be X, As white cars are 9 times as many as yellow cars, So white cars be 9X. Therefore 9X+X=40, X=4. So no.of white cars are 9×4= 36.
Therefore Rafael count 36 white cars.

Question 6.
Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many more points did she score in the second game?
______ more points

Answer: 30 more points

Explanation:
Let the first game points are X and second game points be 6X. Sue’s total score is 35 points in two games so 6X+X= 35 then X is 5.
Therefore the second game score is 6 × 5= 30.

Common Core – Multiply by 1-Digit Numbers – Page No. 26

Lesson Check

Question 1.
Sari has 3 times as many pencil erasers as Sam. Together, they have 28 erasers. How many erasers does Sari have?
Options:
a. 7
b. 14
c. 18
d. 21

Answer: 21

Explanation:
Let the X be pencil erasers of Sam and Sari erasers be 3X. As Sari and Sam together have 28 erasers.
So 3X+X= 28. And X is 7. Then Sari has 3×7= 21.
The correct answer is option d.

Question 2.
In Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies?
Options:
a. 5
b. 12
c. 15
d. 18

Answer: 18

Explanation:

Let Guppies be X and Goldfishes be 6X.
And the total fishes are 21, So X+6X= 21 then X= 3.
So Goldfishes are 6×3= 18.
The correct answer is option d.

Spiral Review

Question 3.
Barbara has 9 stuffed animals. Trish has 3 times as many stuffed animals as Barbara. How many stuffed animals does Trish have?
Options:
a. 3
b. 12
c. 24
d. 27

Answer: 27

Explanation:
Barbara has 9 stuffed animals and Trish has 3 times as Barbara, So 9×3= 27.
The correct answer is option d.

Question 4.
There are 104 students in the fourth grade at Allison’s school. One day, 15 fourth-graders were absent. How many fourth-graders were at school that day?
Options:
a. 89
b. 91
c. 99
d. 119

Answer: 89

Explanation:
Total students in fourth grade are 104, as 15 students were absent 104-15= 89.
The correct answer is option a.

Question 5.
Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks. What is the correct order of the boys from the least to the greatest number of rocks owned?
Options:
a. Jose, Albert, Joshua
b. Jose, Joshua, Albert
c. Albert, Jose, Joshua
d. Joshua, Albert, Jose

Answer: Jose, Albert, Joshua

Explanation:

Given,
Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks.
As 98<107<112. So Jose, Albert, Joshua.
The correct answer is option a.

Question 6.
Alicia has 32 stickers. This is 4 times as many stickers as Benita has. How many stickers does Benita have?
Options:
a. 6
b. 8
c. 9
d. 28

Answer: 8

Explanation:
Given,
Alicia has 32 stickers. This is 4 times as many stickers as Benita has.
Let Benita stickers be S and Alicia has 32 stickers, So 4×S= 32. Therefore Benita stickers are 8.

Common Core – Multiply by 1-Digit Numbers – Page No. 27

Multiply Tens, Hundreds, and Thousands

Find the product.

Question 1.
4 × 7,000 = 28,000
Think: 4 × 7 = 28
So, 4 × 7,000 = 28,000

Question 2.
9 × 60 = ______

Answer: 540

Explanation: 9×6= 54.

Question 3.
8 × 200 = ______

Answer: 1600

Explanation: 8×2=16

Question 4.
5 × 6,000 = ______

Answer: 30,000

Explanation: 5×6=30.

Question 5.
7 × 800 = ______

Answer: 5600

Explanation: 7×8= 56.

Question 6.
8 × 90 = ______

Answer: 720

Explanation: 8×9=72.

Question 7.
6 × 3,000 = ______

Answer: 18,000

Explanation: 6×3= 18.

Question 8.
3 × 8,000 = ______

Answer: 24,000

Explanation: 3×8= 24.

Question 9.
5 × 500 = ______

Answer: 2500

Explanation: 5×5= 25.

Question 10.
9 × 4,000 = ______

Answer: 36,000

Explanation: 9×4= 36.

Question 11.
7 × 7,000 = ______

Answer: 49,000

Explanation: 7×7= 49.

Question 12.
3 × 40 = ______

Answer: 120

Explanation: 3×4= 12.

Question 13.
4 × 5,000 = ______

Answer: 20,000

Explanation: 4×5= 20.

Question 14.
2 × 9,000 = ______

Answer: 18,000

Explanation: 2×9= 18.

Problem Solving

Question 15.
A bank teller has 7 rolls of coins. Each roll has 40 coins. How many coins does the bank teller have?
______ coins

Answer: 280 coins

Explanation:
The bank teller has 7 rolls of coins.
As each roll has 40 coins, So total coins are 7×40= 280
Thus the bank teller has 280 coins.

Question 16.
Theo buys 5 packages of paper. There are 500 sheets of paper in each package. How many sheets of paper does Theo buy?
______ sheets.

Answer: 2,500

Explanation:
Total no.of sheets of papers in each package are 500, And Theo buys 5 packages of papers.
So total sheets of paper Theo bought are 500×5= 2,500.

Common Core – Multiply by 1-Digit Numbers – Page No. 28

Lesson Check

Question 1.
A plane is traveling at a speed of 400 miles per hour. How far will the plane travel in 5 hours?
Options:
a. 200 miles
b. 2,000 miles
c. 20,000 miles
d. 200,000 miles

Answer: 2,000 miles

Explanation:
The speed of the plane is 400 miles per hour.
In 5 hours plane can travel 400×5= 2,000 miles.
Thus the correct answer is option b.

Question 2.
One week, a clothing factory made 2,000 shirts in each of 6 different colors. How many shirts did the factory make in all?
Options:
a. 2,000
b. 12,000
c. 120,000
d. 200,000

Answer: 12,000

Explanation:
The shirts made in one week are 2000 in 6 different colors.
So total shirts made in all are 2000×6= 12,000.
Thus the correct answer is option b.

Spiral Review

Question 3.
Which comparison sentence best represents the equation?
6 × 7 = 42
Options:
a. 7 is 6 times as many as 42.
b. 6 is 7 times as many as 42.
c. 42 is 6 times as many as 7.
d. more than 7 is 42.

Answer: 42 is 6 times as many as 7.

Explanation:
By comparing 42= 6×7 represents the equation.
Thus the correct answer is option c.

Question 4.
The population of Middleton is six thousand, fifty-four people. Which of the following shows this number written in standard form?
Options:
a. 654
b. 6,054
c. 6,504
d. 6,540

Answer: 6,054

Explanation:
The standard form is Six thousand fifty-four is equal to 6,054.
Thus the correct answer is option b.

Question 5.
In an election for mayor, 85,034 people voted for Carl Green and 67,952 people voted for Maria Lewis. By how many votes did Carl Green win the election?
Options:
a. 17,082
b. 17,182
c. 22,922
d. 152,986

Answer: 17,082

Explanation:
Total votes Carl Green has got are 85,034and Maria Lewis got are 67,952. By 85,034-67,952= 17,082 votes Carl Green won the election.
Thus the correct answer is option a.

Question 6.
Meredith picked 4 times as many green peppers as red peppers. If she picked a total of 20 peppers, how many green peppers did she pick?
Options:
a. 4
b. 5
c. 16
d. 24

Answer: 16

Explanation:
Meredith picked 4 times as many green peppers as red peppers.
Let the red peppers be X and green peppers be 4X, And the total she picked is 20 peppers. So X+4X=20
Then X=4. Green peppers she picked are 4×4= 16.
Thus the correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 29

Estimate Products

Estimate the product by rounding.

Question 1.
4 × 472
4 × 472
↓
4 × 500 = 2,000

Question 2.
2 × 6,254
Estimate: _______

Answer: 12,000

Explanation:
The nearest rounding off for 6,254 is 6,000.
So 2×6,000= 12,000.

Question 3.
9 × 54
Estimate: _______

Answer: 450

Explanation:
The nearest rounding off for 54 is 50. So 9×50= 450.

Question 4.
5 × 5,503
Estimate: _______

Answer: 30,000

Explanation:
The nearest rounding off for 5,503 is 6,000.
So 5×6,000= 30,000.

Question 5.
3 × 832
Estimate: _______

Answer: 2,400

Explanation:
The nearest rounding off for 832 is 800.
So 3×800= 2,400.

Question 6.
6 × 98
Estimate: _______

Answer: 600

Explanation:
The nearest rounding off for 98 is 100. So 6×100= 600.

Question 7.
8 × 3,250
Estimate: _______

Answer: 24,000

Explanation:
The nearest rounding off for 3,250 is 3,000.
So 8×3,000= 24,000.

Question 8.
7 × 777
Estimate: _______

Answer: 5,600

Explanation:
The nearest rounding off for 777 is 800.
So 7×800= 5,600.

Find two numbers the exact answer is between.

Question 9.
3 × 567
_____ and _____

Answer: 1500 and 1800

Explanation:
The rounding off for 567 is 500 and 600.
So 3×500= 1500 and 3×600= 1800.

Question 10.
6 × 7,381
_____ and _____

Answer: 42,000 and 48,000

Explanation:
The rounding off for 7,381 is 7,000 and 8,000.
So 6×7000= 42,000 and 6×8000= 48,000.

Question 11.
4 × 94
_____ and _____

Answer: 360 and 400

Explanation:
The rounding off for 94 is 90 and 100.
So 4×90= 360 and 4×100= 400.

Question 12.
8 × 684
_____ and _____

Answer: 3600 and 4200

Explanation:
The rounding off for 684 is 600 and 700.
So 6×600= 3600 and 6×700= 4200.

Problem Solving

Question 13.
Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable? Explain.
_____

Answer: Yes

Explanation:
As the round-off for 365 can be 300 or 400.
So 8×300= 2,400 and 8×400= 3,200.
The estimated answer can be between 2,400 to 3,200.
So the answer is Yes.

Question 14.
Most Americans throw away about 1,365 pounds of trash each year. Is it reasonable to estimate that Americans throw away over 10,000 pounds of trash in 5 years? Explain.
_____

Answer: No

Explanation:
As the round-off for 1,365 can be 1000 or 2000.
So 5×1000= 5,000 and 5×2000= 10,000.
The estimated answer can be between 5,000 to 10,000.

Common Core – Multiply by 1-Digit Numbers – Page No. 30

Lesson Check

Question 1.
A theater has 4,650 seats. If the theater sells all the tickets for each of its 5 shows, about how many tickets will the theater sell in all?
Options:
a. 2,500
b. 10,000
c. 25,000
d. 30,000

Answer: 25,000

Explanation:
A theater has 4,650 seats.
As the nearest round off for 4,650 is 5,000.
So 5,000×5= 25,000.
The correct answer is option c.

Question 2.
Washington Elementary has 4,358 students. Jefferson High School has 3 times as many students as Washington Elementary. About how many students does Jefferson High School have?
Options:
a. 16,000
b. 12,000
c. 10,000
d. 1,200

Answer: 12,000

Explanation:
Given,
Washington Elementary has 4,358 students.
Jefferson High School has 3 times as many students as Washington Elementary.
As the nearest round off for 4,358 is 4,000.
So 4,000×3= 12,000.
The correct answer is option b.

Spiral Review

Question 3.
Diego has 4 times as many autographed baseballs as Melanie has. Diego has 24 autographed baseballs. How many autographed baseballs does Melanie have?
Options:
a. 28
b. 20
c. 8
d. 6

Answer: 6

Explanation:
Let the Melanie baseballs be S.
As Diego has 4 times as many as Melanie and Diego has a total of 24 baseballs.
So 4×S= 24, Then S= 24÷4 which is 6.
The correct answer is option d.

Question 4.
Mr. Turkowski bought 4 boxes of envelopes at the office supply store. Each box has 500 envelopes. How many envelopes did Mr. Turkowski buy?
Options:
a. 200
b. 504
c. 2,000
d. 20,000

Answer: 2,000

Explanation:
Turkowski has 4 boxes of envelopes and each box contains 500 envelopes.
So total envelopes did Turkowski bought are 4×500= 2,000.
The correct answer is option c.

Question 5.
Pennsylvania has a land area of 44,816 square miles. Which of the following shows the land area of Pennsylvania rounded to the nearest hundred?
Options:
a. 44,000 square miles
b. 44,800 square miles
c. 44,900 square miles
d. 45,000 square miles

Answer: 44,800 square miles

Explanation:
As the nearest round off for 44,816 is 44,800.
The correct answer is option b.

Question 6.
The table shows the types of DVDs customers rented from Sunshine Movie Rentals last year.

Options:
How many comedy and action movies were rented in all last year?
a. 13,620
b. 13,000
c. 12,260
d. 10,752

Answer: 12,260

Explanation:
Comedy and action movies that are rented in last year are 6,720+5,540= 12,260.
The correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 31

Multiply Using the Distributive Property

Model the product on the grid. Record the product.

Question 1.
4 × 19 = 76

4 × 10 = 40 and 4 × 9 = 36
40 + 36 = 76

Question 2.

5 × 13 = _____

Answer: 65

Explanation:
5×10= 50 and 5×3= 15
50+15= 65.

Find the product.

Question 3.

4 × 14 = _____

Answer: 56

Explanation:
4×10= 40 and 4×4= 16
40+16= 56.

Question 4.

3 × 17 = _____

Answer: 51

Explanation:
3×10=30 and 3×7= 21
30+21= 51

Question 5.

6 × 15 = _____

Answer: 90

Explanation:
6×10= 60 and 6×5= 30
60+30= 90

Problem Solving

Question 6.
Michael arranged his pennies in the following display.

How many pennies does Michael have in all?
_____ pennies

Answer: 91

Explanation: As there are 7 columns and 13 rows, So 13×7= 91.

Question 7.
A farmer has an apple orchard with the trees arranged as shown below.

If the farmer wants to pick one apple from each tree, how many apples will he pick?
_____ apples

Answer: 70 apples

Explanation:
As there are 5 columns and 14 rows, So 5×14= 70.

Common Core – Multiply by 1-Digit Numbers – Page No. 32

Lesson Check

Question 1.
The model shows how Maya planted flowers in her garden.

How many flowers did Maya plant?
Options:
a. 15
b. 18
c. 30
d. 45

Answer: 45

Explanation:
As 3×10= 30 and 3×5= 15
30+15= 45.
The correct answer is option d.

Question 2.
The model below represents the expression 5 × 18.

How many tens will there be in the final product?
Options:
a. 5
b. 6
c. 8
d. 9

Answer: 9

Explanation:
As 5×18 is 90 and 90÷10= 9.
So the answer is 9.
The correct answer is option d.

Spiral Review

Question 3.
Center City has a population of twenty one thousand, seventy people. Which of the following shows the population written in standard form?
Options:
a. 21,007
b. 21,070
c. 21,077
d. 21,700

Answer: 21,070

Explanation:
Center City has a population of twenty one thousand, seventy people.
Twenty-one thousand seventy is equal to 21,070.
The correct answer is option b.

Question 4.
Central School collected 12,516 pounds of newspaper to recycle. Eastland School collected 12,615 pounds of newspapers. How many more pounds of newspaper
did Eastland School collect than Central School?
Options:
a. 99 pounds
b. 101 pounds
c. 199 pounds
d. 1,099 pounds

Answer: 99 pounds

Explanation:
Central school has collected 12,516 pounds and Eastland school collected 12,615 pounds. So 12,615-12,516= 99.
The correct answer is option a.

Question 5.
Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?
Options:
a. 20
b. 24
c. 96
d. 100

Answer: 100

Explanation:
Let Football cards be X and baseball cards be 5X. So 5X+X= 120 in which X= 20.
As Allison has 5 times as many baseball cards as football cards.
So 5×20= 100.
The correct answer is option d.

Question 6.
A ruby-throated hummingbird beats its wings about 53 times each second. About how many times does a ruby-throated hummingbird beat its wings in 5 seconds?
Options:
a. 25
b. 58
c. 250
d. 300

Answer: 250

Explanation:
As the nearest round-off for 53 is 50, So 50×5= 250.
The correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 33

Multiply Using Expanded Form

Record the product. Use expanded form to help.

Question 1.
7 × 14 = 98
7 × 14 = 7 × (10 + 4)
= (7 × 10) + (7 × 4)
= 70 + 28
= 98

Question 2.
8 × 43 = ______

Answer: 344

Explanation:
8×(40+3)
= (8×40)+(8×3)
= 320+24
= 344.

Question 3.
6 × 532 = ______

Answer: 3192

Explanation:
6×(500+30+2)
= (6×500)+(6×30)+(6×2)
= 3000+180+12
= 3,192.

Question 4.
5 × 923 = ______

Answer: 4,615

Explanation:
5×923= 5×(900+20+3)
=(5×900)+(5×20)+(5×3)
=4500+100+15
=4,615.

Question 5.
4 × 2,371 = ______

Answer: 9,484

Explanation:
4×2,371= 4×(2000+300+70+1)
= (4×2,000)+(4×300)+(4×70)+(4×1)
=8000+1200+280+4
=9,484

Question 6.
7 × 1,829 = ______

Answer: 12,803

Explanation:
7×1,829= 7×(1,000+800+20+9)
=(7×1,000)+( 7×800)+( 7×20)+( 7×9)
=7,000+5600+140+63
=12,803

Problem Solving

Question 7.
The fourth-grade students at Riverside School are going on a field trip. There are 68 students on each of the 4 buses. How many students are going on the field trip?
______ students

Answer: 272 students

Explanation:
No. of buses are 4 and on each bus, there are 68 students.
So 68 × 4= 272.
Therefore 272 students are going on the field trip.

Question 8.
There are 5,280 feet in one mile. Hannah likes to walk 5 miles each week for exercise. How many feet does Hannah walk each week?
______ feet

Answer: 26,400 feet

Explanation:
There are 5,280 feet in one mile and Hannah walks 5 miles each week.
So 5,280 5= 26,400.
Hannah walk 26,400 feet each week.

Common Core – Multiply by 1-Digit Numbers – Page No. 34

Lesson Check

Question 1.
Which expression shows how to multiply 7 × 256 by using expanded form and the Distributive Property?
Options:
a. (7 × 2) + (7 × 5) + (7 × 6)
b. (7 × 200) + (7 × 500) + (7 × 600)
c. (7 × 2) + (7 × 50) + (7 × 600)
d. (7 × 200) + (7 × 50) + (7 × 6)

Answer: (7 × 200) + (7 × 50) + (7 × 6)

Explanation:
By Distributive property of multiplication 7×256=(7×200)+(7×50)+(7×6)
The correct answer is option d.

Question 2.
Sue uses the expression (8 × 3,000) + (8 × 200) + (8 × 9) to help solve a multiplication problem. Which is Sue’s multiplication problem?
Options:
a. 8 × 329
b. 8 × 3,029
c. 8 × 3,209
d. 8 × 3,290

Answer: 8 × 3,029

Explanation:
The expression (8×3,000)+(8×200)+(8×9) is written in the Distributive property of multiplication. So 8×3,029.
The correct answer is option b.

Spiral Review

Question 3.
What is another way to write 9 x 200?
Options:
a. 18 ones
b. 18 tens
c. 18 hundreds
d. 18 thousands

Answer: 18 hundreds

Explanation: 9×200= 1800
The correct answer is option c.

Question 4.
What is the value of the digit 4 in 46,000?
Options:
a. 4 ten thousands
b. 4 thousands
c. 4 hundreds
d. 4 tens

Answer: 4 ten thousand

Explanation:
The place value of 4 in 46,000 is 40,000.
The correct answer is option a.

Question 5.
Chris bought 6 packages of napkins for his restaurant. There were 200 napkins in each package. How many napkins did Chris buy?
Options:
a. 120
b. 1,200
c. 12,000
d. 120,000

Answer: 1,200

Explanation:
Total packages are 6 and each package contains 200 napkins.
So 6 × 200=1,200.
The correct answer is option b.

Question 6.
Which of the following lists the numbers in order from least to greatest?
Options:
a. 8,512; 8,251; 8,125
b. 8,251; 8,125; 8,512
c. 8,125; 8,512; 8,251
d. 8,125; 8,251; 8,512

Answer: 8,125; 8,251; 8,512

Explanation:
8,125>8,251>8,512.
The correct answer is option d.

Common Core – Multiply by 1-Digit Numbers – Page No. 35

Multiply Using Partial Products

Estimate. Then record the product.

Question 1.
Estimate: 1,200
2 4 3
×    6
———
1,200
2 4 0
+ 1 8
———
1,458

Question 2.
6 4 0
×    3
———
Estimate: ________
Product: _______

Answer:

Question 3.
$ 1 4 9
×       5
———
Estimate: $ ________
Product: $ _______

Answer:

Question 4.
7 2 1
×   8
———
Estimate: ________
Product: _______

Answer:

Question 5.
2 9 3
×    4
———
Estimate: ________
Product: _______

Answer:

Question 6.
$ 4 1 6
×       6
———
Estimate: $ ________
Product: $ _______

Answer:

Question 7.
9 6 1
×    2
———
Estimate: ________
Product: _______

Answer:

Question 8.
8 3 7
×    9
———
Estimate: ________
Product: _______

Answer:

Question 9.
6 5 2
×    4
———
Estimate: ________
Product: _______

Answer:

Question 10.
3 0 7
×    3
———
Estimate: ________
Product: _______

Answer:

Question 11.
5 4 3
×     7
———
Estimate: ________
Product: _______

Answer:

Question 12.
$ 8 2 2
×       5
———
Estimate: $ ________
Product: $ _______

Answer:

Problem Solving

Question 13.
A maze at a county fair is made from 275 bales of hay. The maze at the state fair is made from 4 times as many bales of hay. How many bales of hay are used for the maze at the state fair?
______ bales

Answer: 1100 bales

Explanation:
No. of country fair bales are 275 and state fair bales are 4 times as many as country fair bales.
So 275 × 4= 1100 bales.

Question 14.
Pedro gets 8 hours of sleep each night. How many hours does Pedro sleep in a year with 365 days?
______ hours

Answer: 2,920 hours

Explanation:
Given,
Pedro sleeps 8 hours each night and 365 days Pedro sleeps 365 × 8= 2,920 hours.

Common Core – Multiply by 1-Digit Numbers – Page No. 36

Lesson Check

Question 1.
A passenger jet flies at an average speed of 548 miles per hour. At that speed, how many miles does the plane travel in 4 hours?
Options:
a. 2,092 miles
b. 2,112 miles
c. 2,192 miles
d. 2,480 miles

Answer: 2,192 miles

Explanation:
The average speed of a passenger jet is 548 miles per hour.
And the plane travels in 4 hours is 548 × 4= 2,192 miles.
The correct answer is option c.

Question 2.
Use the model to find 3 × 157.

Options:
a. 300,171
b. 300,157
c. 471
d. 451

Answer: 471

Explanation:
By distributive property of multiplication 3 x 157= 3 x(100+50+7)
= (3 x100)+(3×50)+(3×7)
= 300+150+21
= 471
The correct answer is option c.

Spiral Review

Question 3.
The school fun fair made $1,768 on games and $978 on food sales. How much money did the fun fair make on games and food sales?
Options
a. $2,636
b. $2,646
c. $2,736
d. $2,746

Answer: $2746

Explanation:
Money made on games is $1,768 and on food, sale is $978.
So total money make on games and food sales are 1768+978= 2746.
The correct answer is option d.

Question 4.
Use the table below.

Which of the following lists the states from least to greatest population?
Options:
a. Alaska, North Dakota, Vermont
b. Vermont, Alaska, North Dakota
c. North Dakota, Vermont, Alaska
d. Vermont, North Dakota, Alaska

Answer: Vermont, North Dakota, Alaska

Explanation:
Vermont has 621,760, North Dakota has 646,844 and Alaska has 698,473.
So Vermont, North Dakota, Alaska.
The correct answer is option d.

Question 5.
A National Park covers 218,375 acres. What is this number written in expanded form?
Options:
a. 200,000 + 10,000 + 8,000 + 300 + 70 + 5
b. 20,000 + 1,000 + 800 + 30 + 75
c. 218 + 375
d. 218 thousand, 375

Answer: 200,000 + 10,000 + 8,000 + 300 + 70 + 5

Explanation:
218,375 is expanded as 200,000 + 10,000 + 8,000 + 300 + 70 + 5
The correct answer is option a.

Question 6.
Last year a business had profits of $8,000. This year its profits are 5 times as great. What are this year’s profits?
Options:
a. $4,000
b. $40,000
c. $44,000
d. $400,000

Answer: $40,000

Explanation:
Last year’s profit of $8,000 and this year 5 times more.
So this year profit is 8000 × 5= 40,000.
The correct answer is option b.

Common Core – Multiply by 1-Digit Numbers – Page No. 37

Multiply Using Mental Math

Find the product. Tell which strategy you used.

Question 1.
6 × 297
Think: 297 = 300 – 3
6 × 297 = 6 × (300 – 3)
= (6 × 300) – (6 × 3)
= 1,800 – 18
= 1,782;
use subtraction

Question 2.
8 × 25 × 23 = _____

Answer: 4,600, Associative property.

Explanation:
8×25×23=(8×25)× 23
=(200) ×23
4,600

Question 3.
8 × 604 = _____

Answer: 4,832, Use Addition.

Explanation:
604= 600+4
8×604= 8×(600+4)
=(8×600)+(8×4)
=4800+32
=4832.

Question 4.
50 × 28 = _____

Answer: 1400, Halving and doubling.

Explanation:
50×28= (25×28)+(50×14)
=700+700
=1400

Question 5.
9 × 199 = _____

Answer: 1,791

Explanation:
By Distributive property 9 × 199= 9 ×(100+90+9)
=(9×100)+(9×90)+(9×9)
=900+810+81
= 1791

Question 6.
20 × 72 × 5 = _____

Answer: 7,200.

Explanation:
The associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same.
20 × 72 × 5= (20×72) ×5
=1440×5
=7,200.

Question 7.
32 × 25 = _____

Answer: 800

Explanation:
Multiplication.
32×25= 800.

Problem Solving

Question 8.
Section J in an arena has 20 rows. Each row has 15 seats. All tickets cost $18 each. If all the seats are sold, how much money will the arena collect for Section J?
$ _____

Answer: $5400

Explanation:
Total rows in the arena are 20 rows and each row has 15 seats.
So total seats are 20×15= 300 seats.
And each ticket cost is $18, So the total ticket price is 300×15= 5400.

Question 9.
At a high-school gym, the bleachers are divided into 6 equal sections. Each section can seat 395 people. How many people can be seated in the gym?
_____ people

Answer: 2,370 people.

Explanation:
Total sections are 6 and each section contains 395 people.
So the total members can be seated in the gym are 395 × 6= 2,370 people.

Common Core – Multiply by 1-Digit Numbers – Page No. 38

Lesson Check

Question 1.
Pencils come in cartons of 24 boxes. A school bought 50 cartons of pencils for the start of school. Each box of pencils cost $2. How much did the school spend
on pencils?
Options:
a. $240
b. $1,200
c. $2,400
d. $4,800

Answer: $2,400

Explanation:
Given,
Total boxes of pencils are 24 and a school bought 50 cartons of pencils.
So the total no. of boxes are 24×50=1200 and each box of pencils cost $2.
So 1200×2= 2400 school has spent.
Thus the correct answer is option c.

Question 2.
The school also bought 195 packages of markers. There are 6 markers in a package. How many markers did the school buy?
Options:
a. 1,170
b. 1,195
c. 1,200
d. 1,230

Answer: 1,170

Explanation:
The school also bought 195 packages of markers. There are 6 markers in a package.
Multiply the number of packages with the number of markers in the package.
So total markers are 195×6= 1170.
Thus the correct answer is option a.

Spiral Review

Question 3.
Alex has 175 baseball cards. Rodney has 3 times as many baseball cards as Alex. How many fewer cards does Alex have than Rodney?
Options:
a. 700
b. 525
c. 450
d. 350

Answer: 350

Explanation:
Alex has 175 baseball cards and Rodney has 3 times as many as Alex.
So the total no. of cards Rodney has is 175×3= 525. And Alex has 525-175= 350 fewer cards than Rodney.
Thus the correct answer is option d.

Question 4.
A theater seats 1,860 people. The last 6 shows have been sold out. Which is the best estimate of the total number of people attending the last 6 shows?
Options:
a. fewer than 6,000
b. about 6,000
c. fewer than 12,000
d. more than 20,000

Answer: fewer than 12,000

Explanation:
Given,
A theater seats 1,860 people.
The last 6 shows have been sold out.
No. of seats in a theater are 1,860 people and the last 6 shows have been sold out.
So 1,860×6= 11,160 which are fewer than 12,000.
Thus the correct answer is option c.

Question 5.
At one basketball game, there were 1,207 people watching. At the next game, there were 958 people. How many people in all were at the two games?
Options:
a. 2,155
b. 2,165
c. 2,265
d. 10,787

Answer: 2,165

Explanation:
There are 1207 people are watching a basketball game and in the next game, 958 people are there.
So the total no. of people is 1,207+958= 2165.
Thus the correct answer is option b.

Question 6.
Bill bought 4 jigsaw puzzles. Each puzzle has 500 pieces. How many pieces are in all the puzzles altogether?
Options:
a. 200
b. 900
c. 2,000
d. 20,000

Answer: 2,000

Explanation:
Given,
Bill bought 4 jigsaw puzzle and each puzzle has 500 pieces.
So altogether pieces are 500×4= 2000.
Thus the correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 39

Problem Solving Multistep Multiplication Problems

Solve each problem.

Question 1.
A community park has 6 tables with a chessboard painted on top. Each board has 8 rows of 8 squares. When a game is set up, 4 rows of 8 squares on each board are covered with chess pieces. If a game is set up on each table, how many total squares are NOT covered by chess pieces?

4 × 8 = 32
32 × 6 = 192 squares

Question 2.
Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of Jonah’s friends pick the same amount as Jonah, how many apples do Jonah and his friends pick in all? Draw a diagram to solve the problem.
_____ apples

Answer: 375 apples

Explanation:
As Jonah fills 5 baskets which hold 15 apples, So Jonah picked 15×5= 75 apples.
And 4 of his friends pick the same amount of apples, which means 75×4=300.
So total apples Jonah and his friends picked up are 300+75= 375 apples.

Question 3.
There are 6 rows of 16 chairs set up for the third-grade play. In the first 4 rows, 2 chairs on each end are reserved for teachers. The rest of the chairs are for students. How many chairs are there for students?
_____ chairs

Answer: 80 chairs

Explanation:
As there are 6 rows of 16 chairs which means 16×6= 96 total chairs.
And the first 4 rows 2 chairs on each end are reserved for teachers, which means 4×4= 16 chairs are reserved for teachers.
So 96-16= 80 chairs are left for the students.
Therefore there are 80 chairs for students.

Common Core – Multiply by 1-Digit Numbers – Page No. 40

Lesson Check

Question 1.
At a tree farm, there are 9 rows of 36 spruce trees. In each row, 14 of the spruce trees are blue spruce. How many spruce trees are NOT blue spruce?
Options:
a. 126
b. 198
c. 310
d. 324

Answer: 198

Explanation:
There are 9 rows of 36 spruce trees which means 9×36= 324 spruce trees.
And in that, each row has 14 blue spruce trees which mean 14×9= 126.
So 324-126= 198 spruce trees are not blue.
Thus the correct answer is option b.

Question 2.
Ron is tiling a countertop. He needs to place 54 square tiles in each of 8 rows to cover the counter. He wants to randomly place 8 groups of 4 blue tiles each and have the rest of the tiles be white. How many white tiles will Ron need?
Options:
a. 464
b. 432
c. 400
d. 32

Answer: 400

Explanation:
Ron places 54 square tiles in each of 8 rows which means 54×8=432 tiles.
And he randomly places 8 groups of 4 blue tiles which means 8×4= 32 blue tiles are placed.
So no. of white tiles are 432 – 32= 400.
Thus the correct answer is option c.

Question 3.
Juan reads a book with 368 pages. Savannah reads a book with 172 fewer pages than Juan’s book. How many pages are in the book Savannah reads?
Options:
a. 196
b. 216
c. 296
d. 540

Answer: 196

Explanation:
Given,
Juan reads a book with 368 pages and Savannah reads a book with 172 fewer pages than Juan’s which means 368-172= 196 pages are in Savannah’s read.
Thus the correct answer is option a.

Question 4.
Hailey has bottles that hold 678 pennies each. About how many pennies does she have if she has 6 bottles filled with pennies?
Options:
a. 3,600
b. 3,900
c. 4,200
d. 6,000

Answer: 4,200

Explanation:
Given,
Hailey has bottles that hold 678 pennies each.
Let’s round off 678 to 700 and Hailey has bottles that hold 700 pennies each and if she has 6 bottles filled with pennies which means 700×6= 4200.
Thus the correct answer is option c.

Question 5.
Terrence plants a garden that has 8 rows of flowers, with 28 flowers in each row. How many flowers did Terrence plant?
Options:
a. 1,664
b. 224
c. 164
d. 36

Answer: 224

Explanation:
As the garden has 8 rows of flowers with 28 flowers in each row.
So no. of flowers is 28×8= 224.
Thus the correct answer is option b.

Question 6.
Kevin has 5 fish in his fish tank. Jasmine has 4 times as many fish as Kevin has. How many fish does Jasmine have?
Options:
a. 15
b. 20
c. 25
d. 30

Answer: 20

Explanation:
Given that,
Kevin has 5 fishes and Jasmine has 4 times as many as Kevin which means 5×4= 20 fishes Jasmine has.
Thus the correct answer is option b.

Common Core – Multiply by 1-Digit Numbers – Page No. 41

Multiply 2-Digit Numbers with Regrouping

Estimate. Then record the product.

Question 1.
Estimate: 150

Question 2.
3 2
× 8
———-
Estimate: _________
Product: __________

Answer:
Estimate: 240
Product: 256

Explanation:
The number close to 32 is 30 and 30×8=240.
3 2
× 8
256
Thus the product is 256.

Question 3.
$ 5 5
×   2
———-
Estimate: $ _________
Product: $ __________

Answer:
Estimate: $120
Product: $110

Explanation:
Round off 55 to 60 and 60×2= 120.
$ 5 5
×   2
$110
Thus the product is $110.

Question 4.
6 1
× 8
———-
Estimate: _________
Product: __________

Answer:
Estimate: 480
Product: 488

Explanation:
Round off 61 to 60 and 60×8= 480.
6 1
× 8
488
Thus the product is 488.

Question 5.
3 7
× 9
———-
Estimate: _________
Product: __________

Answer:
Estimate: 360
Product: 333

Explanation:
Round off 37 to 40 and 40×6= 360.
3 7
× 9
333
Thus the product is 333.

Question 6.
$ 1 8
×    7
———-
Estimate: $ _________
Product: $ __________

Answer:
Estimate: $140
Product: $126

Explanation:
Round off 18 to 20 and 20×7= 140.
$ 1 8
×    7
$126
Thus the product is $126.

Question 7.
8 3
× 5
———-
Estimate: _________
Product: __________

Answer:
Estimate: 400
Product: 415

Explanation:
Round off 83 to 80 and 80×5= 400.
8 3
× 5
415
Thus the product is 415.

Question 8.
9 5
× 8
———-
Estimate: _________
Product: __________

Answer:

Estimate: 800
Product: 760

Explanation:
Round off 95 to 100 and 100×8= 800.
9 5
× 8
760
Thus the product is 760.

Question 9.
9 4
× 9
———-
Estimate: _________
Product: __________

Answer:
Estimate: 810
Product: 846

Explanation:
Round off 94 to 90 and 90×9= 810.
9 4
× 9
846
Thus the product is 846.

Question 10.
5 7
× 6
———-
Estimate: _________
Product: __________

Answer:
Estimate: 360
Product: 342

Explanation:
Round off 57 to 60 and 60×6= 360.
5 7
× 6
342
Thus the product is 342.

Question 11.
7 2
× 3
———-
Estimate: _________
Product: __________

Answer:
Estimate: 210
Product: 216

Explanation: Round off 72 to 70 and 70×3= 210.
7 2
× 3
216
Thus the product is 216.

Question 12.
$ 7 9
× 8
———-
Estimate: $ _________
Product: $ __________

Answer:
Estimate: $640
Product: $632

Explanation: Round off 79 to 80 and 80×8= 640.
$ 7 9
× 8
$632
Thus the product is $632.

Problem Solving

Question 13.
Sharon is 54 inches tall. A tree in her backyard is 5 times as tall as she is. The floor of her treehouse is at a height that is twice as tall as she is. What is the difference, in inches, between the top of the tree and the floor of the treehouse?
_______ inches

Answer: 162 inches

Explanation:
Given,
Sharon is 54 inches tall and a tree in her backyard is 5 times as tall as she is which means 54×5= 270.
And her treehouse is twice as tall as she is which means 54×2= 108 inches.
So the difference between the top of the tree and the floor of the treehouse is 270-108= 162 inches.

Question 14.
Mr. Diaz’s class is taking a field trip to the science museum. There are 23 students in the class, and a student admission ticket is $8. How much will the student
tickets cost?
$ _______

Answer: $184

Explanation:
Given,
Mr. Diaz’s class is taking a field trip to the science museum.
There are 23 students in the class, and a student admission ticket is $8.
Total no. of students are 23 and tickets cost is $8, So 23×8= $184.

Common Core – Multiply by 1-Digit Numbers – Page No. 42

Lesson Check

Question 1.
A ferryboat makes four trips to an island each day. The ferry can hold 88 people. If the ferry is full on each trip, how many passengers are carried by the ferry
each day?
Options:
a. 176
b. 322
c. 332
d. 352

Answer: 352

Explanation:
Total trips made by the ferryboat each day are 4 and it can hold 88 people.
So 88×4= 352 passengers are carried by ferryboat each day.
Thus the correct answer is option d.

Question 2.
Julian counted the number of times he drove across the Seven Mile Bridge while vacationing in the Florida Keys. He crossed the bridge 34 times. How many miles in all did Julian drive crossing the bridge?
Options:
a. 328 miles
b. 248 miles
c. 238 miles
d. 218 miles

Answer: 238 miles

Explanation:
Given,
No. of times Julian drive across the bridge is 7 miles and he crossed the bridge 34 times.
So 34×7= 238 miles Julian drive crossing the bridge.
Thus the correct answer is option c.

Spiral Review

Question 3.
Sebastian wrote the population of his city as 300,000 + 40,000 + 60 + 7. Which of the following shows the population of Sebastian’s city written in standard form?
Options:
a. 346,700
b. 340,670
c. 340,607
d. 340,067

Answer: 340,067

Explanation:
300,000+40,000+60+7= 340,067.
Thus the correct answer is option d.

Question 4.
A plane flew 2,190 kilometers from Chicago to Flagstaff. Another plane flew 2,910 kilometers from Chicago to Oakland. How much farther did the plane that flew to Oakland fly than the plane that flew to Flagstaff?
Options:
a. 720 kilometers
b. 820 kilometers
c. 5,000 kilometers
d. 5,100 kilometers

Answer: 720 kilometers

Explanation:
Given,
A plane flew from Chicago to Flagstaff is 2,190 km and another plane flew from Chicago to Oakland is 2,910.
So 2910-2190= 720 km.
Thus the correct answer is option a.

Question 5.
Tori buys 27 packages of miniature racing cars. Each package contains 5 cars. About how many miniature racing cars does Tori buy?
Options:
a. 15
b. 32
c. 100
d. 150

Answer: 150

Explanation:
Given,
Tori buys 27 packages of miniature racing cars.
Each package contains 5 cars.
Let’s round off 27 packages to 30 and each package contains 5 cars, which means 30×5=150.
Thus the correct answer is option d.

Question 6.
Which of the following equations represents the Distributive Property?
Options:
a. 3 × 4 = 4 × 3
b. 9 × 0 = 0
c. 5 × (3 + 4) = (5 × 3) + (5 × 4)
d. 6 × (3 × 2) = (6 × 3) × 2

Answer: 5 × (3 + 4) = (5 × 3) + (5 × 4)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.

Common Core – Multiply by 1-Digit Numbers – Page No. 43

Multiply 3-Digit and 4-Digit Numbers with Regrouping

Estimate. Then find the product.

Question 1.
Estimate: 4,000

Question 2.
5,339
×     6
———-
Estimate: ________
Product: _________

Answer:
Estimate: 30,000
Product: 32,034

Explanation:
Round off 5,339 to 5000 then 5000×6= 30,000.
5,339
×     6
32,034
Thus the product is 32,034.

Question 3.
$ 8 7 9
×       8
———-
Estimate: $ ________
Product: $ _________

Answer:
Estimate: $7,200.
Product: $7,032.

Explanation: Round off 879 to 900 then 900×8= 7,200.
$ 8 7 9
×       8
$7,032
Thus the product is $7,032

Question 4.
3,182
×    5
———-
Estimate: ________
Product: _________

Answer:
Estimate: 15,000
Product: 15,910

Explanation: Round off 3,182 to 3000 then 3000×5= 15,000.
3,182
×    5
15,910
Thus the product is 15,910.

Question 5.
4,616
×     3
———-
Estimate: ________
Product: _________

Answer:
Estimate: 15,000
Product: 13,848

Explanation: Round off 4,616 to 5,000 then 5000×3= 15,000.
4,616
×     3
13,848
Thus the product is 13,848.

Question 6.
2,854
× 9
———-
Estimate: $ ________
Product: $ _________

Answer:
Estimate: 27,000
Product: 25,686

Explanation: Round off 2,854 to 3000 then 3000×9= 27,000.
2,854
×      9
25,686
Thus the product is 25,686.

Question 7.
7,500
× 2
———-
Estimate: ________
Product: _________

Answer:
Estimate: 16,000
Product: 15,000

Explanation: Round off 7,500 to 8000 then 8000×2= 16,000.
7,500
×       2
15,000
Thus the product is 15,000.

Question 8.
9 4 2
×    7
———-
Estimate: ________
Product: _________

Answer:
Estimate: 6,300
Product: 6,594

Explanation: Round off 942 to 900 then 900×7= 6,300.
9 4 2
×    7
6,594
Thus the product is 6,594.

Question 9.
1,752
×     6
———-
Estimate: ________
Product: _________

Answer:
Estimate: 12,000.
Product: 10,512.

Explanation: Round off 1,752 to 2000 then 2000×6= 12,000.
1,752
×     6
10,512
Thus the product is 10,512.

Question 10.
5 5 0
×    9
———-
Estimate: ________
Product: _________

Answer:
Estimate: 5,400
Product: 4,950

Explanation: Round off 550 to 600 then 600×9= 5,400.
5 5 0
×    9
4,950
Thus the product is 4,950.

Question 11.
6,839
×     4
———-
Estimate: ________
Product: _________

Answer:
Estimate: 28,000
Product: 27,356

Explanation: Round off 6,839 to 7000 then 7000×4= 28,000.
6,839
×     4
27,356
Thus the product is 27,356.

Question 12.
$ 9,614
×        3
———-
Estimate: $ ________
Product: $ _________

Answer:
Estimate: 60,000.
Product: 57,684.

Explanation: Round off 9,614 to 10,000 then 10,000×6= 60,000.
$ 9,614
×      3
57,684
Thus the product is 57,684.

Problem Solving

Question 13.
Lafayette County has a population of 7,022 people. Columbia County’s population is 8 times as great as Lafayette County’s population. What is the population of Columbia County?
_____ people

Answer: 56,176 people

Explanation:
Lafayette County has a population of 7,022 people and Columbia County’s population is 8 times Lafayette County which means 7,022×8= 56,176.
Therefore the population of Columbia County is 56,176.

Question 14.
A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all?
_____ pounds

Answer: 54,750 pounds.

Explanation:
As the seafood company sold 9,125 pounds of fishes last month and 6 seafood companies also sold the same amount which means 9,125×6= 54,750 pounds.

Common Core – Multiply by 1-Digit Numbers – Page No. 44

Lesson Check

Question 1.
By recycling 1 ton of paper, 6,953 gallons of water are saved. How many gallons of water are saved by recycling 4 tons of paper?
Options:
a. 24,602 gallons
b. 27,612 gallons
c. 27,812 gallons
d. 28,000 gallons

Answer: 27,812 gallons

Explanation:
Given that,
By recycling 1 ton of paper, 6,953 gallons of water are saved.
So 4 tons of paper can save 6,953×4= 27,812.
The correct answer is option c.

Question 2.
Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps. How many steps does he take walking to and from school each day?
Options:
a. 2,000
b. 2,266
c. 2,276
d. 22,616

Answer: 2,276

Explanation:
Given, Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps.
As Esteban counted 1,138 steps to school and from school, it will be 1,138+1,138=2,276 steps
The correct answer is option c.

Spiral Review

Question 3.
A website has 13,406 people registered. What is the word form of this number?
Options:
a. thirty thousand, four hundred six
b. thirteen thousand, four hundred sixty
c. thirteen thousand, four hundred six
d. thirteen thousand, six hundred six

Answer: thirteen thousand, four hundred six

Explanation:
13,406 in words are thirteen thousand four hundred six.
The correct answer is option c.

Question 4.
In one year, the McAlister family drove their car 15,680 miles. To the nearest thousand, how many miles did they drive their car that year?
Options:
a. 15,000 miles
b. 15,700 miles
c. 16,000 miles
d. 20,000 miles

Answer: 16,000 miles

Explanation: 15,680 nearest thousand is 16,000.
The correct answer is option c.

Question 5.
Connor scored 14,370 points in a game. Amy scored 1,089 fewer points than Connor. How many points did Amy score?
Options:
a. 12,281
b. 13,281
c. 15,359
d. 15,459

Answer: 13,281

Explanation:
Connor scored 14,370 points and Amy scored 1,089 fewer points.
So Amy score is 14,370-1089= 13,281.
The correct answer is option b.

Question 6.
Lea buys 6 model cars that each cost $15. She also buys 4 bottles of paint that each cost $11. How much does Lea spend in all on model cars and paint?
Options:
a. $134
b. $90
c. $44
d. $36

Answer: $134

Explanation: Lea buys 6 model cars that each cost $15.
So the total cost for cars is $15×6= $90.
And 4 bottles of paint that each cost $11.
So the total cost of the paints is $11×4= $44. Then
$90+$44= $134.
The correct answer is option a.

Common Core – Multiply by 1-Digit Numbers – Page No. 45

Solve Multistep Problems Using Equations

Find the value of n.

Question 1.
4 × 27 + 5 × 34 – 94 = n
108 + 5 × 34 – 94 = n
108 + 170 – 94 = n
278 – 94 = n
184 = n

Question 2.
7 × 38 + 3 × 45 – 56 = n
_____ = n

Answer: 345

Explanation:
7 × 38 + 3 × 45 – 56 = n
n = 266 + 135 – 56
n = 401 – 56
n = 345

Question 3.
6 × 21 + 7 × 29 – 83 = n
_____ = n

Answer: 246

Explanation:
6 × 21 + 7 × 29 – 83 = n
n = 126 + 203 – 83
n = 329 – 83
n = 246

Question 4.
9 × 19 + 2 × 57 – 75 = n
_____ = n

Answer: 210

Explanation:
9 × 19 + 2 × 57 – 75 = n
n = 171 + 114 – 75
n = 285 – 75
n = 210.

Question 5.
5 × 62 + 6 × 33 – 68 = n
_____ = n

Answer: 440

Explanation:
5 × 62 + 6 × 33 – 68= n
n = 310 + 198 – 68
n = 508 – 68
n = 440

Question 6.
8 × 19 + 4 × 49 – 39 = n
_____ = n

Answer: 309

Explanation:
8 × 19 + 4 × 49 – 39 = n
n =152 + 196 – 39
n = 348 – 39
n = 309

Problem Solving

Question 7.
A bakery has 4 trays with 16 muffins on each tray. The bakery has 3 trays of cupcakes with 24 cupcakes on each tray. If 15 cupcakes are sold, how many muffins and cupcakes are left?
_____ muffins and cupcakes

Answer: 121 muffins and cupcakes.

Explanation:
Given,
A bakery has 4 trays with 16 muffins on each tray.
The bakery has 3 trays of cupcakes with 24 cupcakes on each tray.
4 × 16 + 3 × 24 – 15 = n
64 + 3 × 24 – 15 = n
64 + 72 – 15 = n
136 – 15 = n
121 = n
Thus 121 muffins and cupcakes are left.

Question 8.
Katy bought 5 packages of stickers with 25 stickers in each package. She also bought 3 boxes of markers with 12 markers in each box. If she receives 8 stickers from a friend, how many stickers and markers does Katy have now?
_____ stickers and markers

Answer: 69 stickers and markers

Explanation:
Given,
Katy bought 5 packages of stickers with 25 stickers in each package.
She also bought 3 boxes of markers with 12 markers in each box.
5 × 25 + 3 × 12 + 8 = n
125 + 3 × 12 + 8 = n
125 + 36 + 8 = n
169 = n
Thus Katy have 69 stickers and markers.

Common Core – Multiply by 1-Digit Numbers – Page No. 46

Lesson Check

Question 1.
What is the value of n?
9 × 23 + 3 × 39 – 28 = n
Options:
a. 240
b. 296
c. 2,310
d. 8,162

Answer: 296

Explanation:
Given the expression,
9 × 23 + 3 × 39 – 28 = n
n = 207 + 117 – 28
n = 324 – 28
n = 296
Thus the correct answer is option b.

Question 2.
Which expression has a value of 199?
Options:
a. 4 × 28 + 6 × 17 – 15
b. 4 × 17 + 6 × 28 – 38
c. 4 × 38 + 6 × 15 – 28
d. 4 × 15 + 6 × 38 – 88

Answer: 4 × 28 + 6 × 17 – 15

Explanation:
Given the expression,
4 × 28 + 6 × 17 – 15 = n
n = 112 + 102 – 15
n = 214 – 15
n = 199.
Thus the correct answer is option a.

Spiral Review

Question 3.
Which expression shows how you can multiply 9 × 475 using expanded form and the Distributive Property?
Options:
a. (9 × 4) + (9 × 7) + (9 × 5)
b. (9 × 4) + (9 × 70) + (9 × 700)
c. (9 × 400) + (9 × 70) + (9 × 5)
d. (9 × 400) + (9 × 700) + (9 × 500)

Answer: (9 × 400) + (9 × 70) + (9 × 5)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.
9 × 475= (9×400)+(9×70)+(9×5)
Thus the correct answer is option c.

Question 4.
Which equation best represents the comparison sentence?
32 is 8 times as many as 4
Options:
a. 32 = 8 × 4
b. 32 × 8 = 4
c. 32 = 8 + 4
d. 8 + 4 = 32

Answer: 32 = 8 × 4

Explanation:
The equation for the sentence 32 is 8 times as many as 4 is 32 = 8 × 4.
Thus the correct answer is option a.

Question 5.
Between which pair of numbers is the exact product of 379 and 8?
Options:
a. between 2,400 and 2,500
b. between 2,400 and 2,800
c. between 2,400 and 3,000
d. between 2,400 and 3,200

Answer: between 2,400 and 3,200

Explanation:
379 × 8 = 3,032
Thus the correct answer is option d.

Question 6.
Which of the following statements shows the halving and doubling strategy to find 28 × 50?
Options:
a. 28 × 50 = 14 × 100
b. 28 × 50 = (14 × 25) × (14 × 25)
c. 28 × 50 = (20 × 50) × (8 × 50)
d. 28 × 50 = 2 × (14 × 25)

Answer: 28 × 50 = 14 × 100

Explanation:
28×50 = 14×100
Thus the correct answer is option a.

Common Core – Multiply by 1-Digit Numbers – Page No. 47

Lesson 2.1

Write a comparison sentence.

Question 1.
27 = 3 × 9
____ is ____ times as many as ____

Answer: 27 is 3 times as many as 9.

Question 2.
7 × 8 = 56
____ times as many as ____ is ____

Answer: 7 times as many as 8 is 56.

Lessons 2.3, 2.5–2.6

Find the product.

Question 3.
2 × 700 = ____

Answer: 1400

Explanation:
2 × 7 = 14
2 × 700 = 1400

Question 4.
6 × 6,000 = ____

Answer: 36000

Explanation:
6 × 6 = 36
6 × 6,000 = 36,000

Question 5.
7 × 13 = ____

Answer: 91

Explanation:
The multiple of 7 and 13 is 91.
7 × 13 = 91

Question 6.
4 × 19 = ____

Answer: 76

Explanation:
The product of 4 and 19 is 76.

Question 7.
5 × 216 = ____

Answer: 1080

Explanation:
The product of 5 and 216 is 1080.

Question 8.
9 × 1,362 = ____

Answer: 12258

Explanation:
The product of 9 and 1,362 is 12,258.

Lessons 2.2, 2.9

Draw a diagram. Write an equation and solve.

Question 9.
Julia saw 5 times as many cars as trucks in a parking lot. If she saw 30 cars and trucks altogether in the parking lot, how many were trucks?
____ trucks

Answer: 5 trucks

Explanation:
Given,
Julia saw 5 times as many cars as trucks in a parking lot.
25 + 5 = 30
25/5 = 5
Thus there are 5 trucks altogether in the parking lot.

Question 10.
Ivan has 6 times as many blue beads as red beads. He has 49 red and blue beads in all. How many blue beads does Ivan have?
____ blue beads

Answer: 42 blue beads

Explanation:
Given that,
Ivan has 6 times as many blue beads as red beads.
He has 49 red and blue beads in all.
Let x be the number of blue beads
y be the number of red beads
We know that,
x + y = 49
x = 49 – y ——> eq. 1
x = 6y ———> eq. 2
Equate equation 1 and 2
49 – y = 6y
6y + y = 49
7y = 49
y = 49/7
y = 7
Now find the value of x
x = 6y
x = 6 × 7 = 42
Therefore the answer is 42 blue beads.

Question 11.
There are 6 rows with 18 chairs in each row. In the center of the chairs, 4 rows of 6 chairs are brown. The rest of the chairs are blue. How many chairs are blue?
____ blue chairs

Answer: 84 blue chairs

Explanation:
Given that,
There are 6 rows with 18 chairs in each row.
In the center of the chairs, 4 rows of 6 chairs are brown. The rest of the chairs are blue.
18 × 6 = 108
4 × 6 = 24
To find the number of chairs that are blue
We have to subtract 24 from 108.
108 – 24 = 84
Thus there are 84 blue chairs.

Common Core – Multiply by 1-Digit Numbers – Page No. 48

Lessons 2.7, 2.10–2.11

Estimate. Then record the product.

Question 1.
3 1 8
×   3
———-
Estimate: _______
Product: _________

Answer:
Estimate: 900
Product: 954

Explanation:
The number close to 318 is 300.
300 × 3 = 900.
The estimated product of 318 and 3 is 900.
3 1 8
×  3
954
The product of 318 and 3 is 954.

Question 2.
$ 5 2 2
×       9
———-
Estimate: _______
Product: _________

Answer:
Estimate: 4500
Product: 4698

Explanation:
The number close to 522 is 500.
500 × 9 = 4500
The estimated product of 522 and 9 is 4500.
$ 5 2 2
×      9
$4698

Question 3.
$ 3 6
×    6
———-
Estimate: _______
Product: _________

Answer:
Estimate: 240
Product: 216

Explanation:
The number close to 36 is 40.
40 × 6 = 240
The estimated product of 40 and 6 is 240.
$ 3 6
×  6
216

Question 4.
5 7
× 8
———-
Estimate: _______
Product: _________

Answer:
Estimate: 480
Product: 456

Explanation:
The number close to 57 is 60.
60 × 8 = 480.
The estimated product of 57 and 8 is 480.
5 7
× 8
456

Question 5.
3,600
×      8
———-
Estimate: _______
Product: _________

Answer:
Estimate: 32,000
Product: 28,800

Explanation:
The number close to 3600 is 4000.
4000 × 8 = 32,000
The estimated product of 3600 and 8 is 32,000.
3,600
×     8
28,800

Question 6.
$ 9,107
× 5
———-
Estimate: _______
Product: _________

Answer:
Estimate: 45,000
Product: 45,535

Explanation:
The number close to 9107 is 9000.
9000 × 5 = 45,000
The estimated product of 9107 and 5 is 45,000.
$ 9,107
×       5
45,535

Lesson 2.8

Find the product. Tell which strategy you used.

Question 7.
(4 × 10) × 10 = ______
Explain:
_________

Answer: 400, Associative property

Explanation:
(4 × 10) × 10 = 4 × 10 × 10
40 × 10 = 400

Question 8.
2 × 898 = ______
Explain:
_________

Answer: 1796, Distributive property

Explanation:
2 × 898 = (2 × 800) + (2 × 90) + (2 × 8)
1600 + 180 + 16 = 1796

Question 9.
______
Explain:
_________

Answer:

Lessons 2.4, 2.12

Question 10.
School pennants cost $18 each. Ms. Lee says she will pay $146 for 7 pennants. Is her answer reasonable? Explain.
______

Answer: No

Explanation:
Given,
School pennants cost $18 each. Ms. Lee says she will pay $146 for 7 pennants.
18 multiplied by 7 is equal to 126 when Ms. Lee is buying the pennants for 146.

Question 11.
Caleb draws 14 dogs on each of 4 posters. He draws 18 cats on each of 6 other posters. If he draws 5 more dogs on each poster with dogs, how many dogs and cats does he draw?
______ dogs and cats

Answer: 184 dogs and cats

Explanation:
Given,
Caleb draws 14 dogs on each of 4 posters. He draws 18 cats on each of 6 other posters.
14 × 4 = 56
18 × 6 = 108
5 × 4 =20
Total = 56 + 108 + 20 = 184
Thus he draw 184 dogs and cats.

Conclusion

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns

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Lesson: 1 – Model Factors

• Common Core – Factors, Multiples, and Patterns – Page No. 97
• Common Core – Factors, Multiples, and Patterns – Page No. 98

Lesson: 2

• Common Core – Factors, Multiples, and Patterns – Page No. 99
• Common Core – Factors, Multiples, and Patterns – Page No. 100

Lesson: 3 – Problem Solving Common Factors

• Common Core – Factors, Multiples, and Patterns – Page No. 101
• Common Core – Factors, Multiples, and Patterns – Page No. 102

Lesson: 4 – Factors and Multiples

• Common Core – Factors, Multiples, and Patterns – Page No. 103
• Common Core – Factors, Multiples, and Patterns – Page No. 104

Lesson: 5 – Prime and Composite Numbers

• Common Core – Factors, Multiples, and Patterns – Page No. 105
• Common Core – Factors, Multiples, and Patterns – Page No. 106

Lesson: 6 – Number Patterns

• Common Core – Factors, Multiples, and Patterns – Page No. 107
• Common Core – Factors, Multiples, and Patterns – Page No. 108

Lesson: 7

• Common Core – Factors, Multiples, and Patterns – Page No. 109
• Common Core – Factors, Multiples, and Patterns – Page No. 110

Common Core – Factors, Multiples, and Patterns – Page No. 97

Model Factors

Use tiles to find all the factors of the product.

Record the arrays on grid paper and write the factors shown.

Question 1.

Question 2.
Write the factors of: 30
Type below:
_________

Answer: The Factors of 30 are: 1,2,3,5,6,10,15,30.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 30 when multiplied together.
1 × 30 =30
2 × 15 = 30
3 × 10 = 30
5 × 6 = 30
6 × 5 = 30
10 × 3 = 30
15 × 2 = 30
30 × 1 = 30
So the factors of 30 are 1,2,3.5,6,10,15,30.

Question 3.
Write the factors of: 45
Type below:
_________

Answer: The Factors of 45 are:1,3,5,9,15,45

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 45 when multiplied together.
1×45=45
3×15=45
5×9=45
9×5=45
15×3=45
45×1=45
So the factors of 45 are: 1,3,5,9,15,45.

Question 4.
Write the factors of: 19
Type below:
_________

Answer: The Factors of 19 are: 1,19

Explanation:
Since 19 is a Prime number that means it is divisible by 1 and itself.
1 × 19 = 19
19 × 1 = 19
So the factors of 19 are 1,19.

Question 5.
Write the factors of: 40
Type below:
_________

Answer:

The Factors of 40 are:1,2,4,5,8,10,20,40.

Explanation:
Factors are the numbers that divide the original number completely.
1×40=40
2×20=40
4×10=40
5×8=40
8×5=40
10×4=40
20×2=40
40×1=40
The Factors of 40 are: 1,2,4,5,8,10,20,40.

Question 6.
Write the factors of: 36
Type below:
_________

Answer: The Factors Of 36 are:1,2,3,4,6,9,12,18,36.

Explanation:
Factors are the numbers which divides the original number completely.
1×36=36
2×18=36
3×12=36
4×9=36
6×6=36
9×4=36
12×3=36
18×3=36
36×1=36.
The factors of 36 are:1,2,3,4,6,9,12,18,36

Question 7.
Write the factors of: 22
Type below:
_________

Answer: The Factors Of 22 are:1,2,11,22.

Explanation:
Factors are the numbers that divide the original number completely.
1×22=22
2×11=22
11×2=22
22×1=22.
The factors of 22 are:1,2,11,22.

Question 8.
Write the factors of: 4
Type below:
_________

Answer: The Factors Of 4 are: 1,2,4.

Explanation:
Factors are the numbers that divide the original number completely.
1×4=4
2×2=4
4×1=4.
The Factors Of 4 are 1,2,4.

Question 9.
Write the factors of: 26
Type below:
_________

Answer: The Factors Of 26 are:1,2,13,26.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 26 when multiplied together.
1×26=26
2×13=26
13×2=26
26×1=26.
So the factors of 26 are:1,2,13,26.

Question 10.
Write the factors of: 49
Type below:
_________

Answer: The Factors Of 49 are: 1,7,49.

Explanation:
Factors are the numbers that divide the original number completely.
1×49=49
7×7=49
49×1=49.
The Factors Of 49 are 1,7,49.

Question 11.
Write the factors of: 32
Type below:
_________

Answer: The Factors Of 32 are:1,2,4,8,16,32.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 32 when multiplied together.
1×32=32
2×16=32
4×8=32
8×4=32
16×2=32
32×1=32.
So the factors of 32 are:1,2,4,8,16,32.

Question 12.
Write the factors of: 23
Type below:
_________

Answer: The Factors Of 23 are: 1,23.

Explanation:
Since 23 is a Prime number that means it is divisible by 1 and itself.
1×23=23
23×1=23.
So the factors of 23 are 1,23.

Question 13.
Brooke has to set up 70 chairs in equal rows for the class talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?
Type below:
_________

Answer: 2,5,7,10,14.

Explanation:
Let the possible no.of rows be X, As there is no room for more than 20 rows so there should not be more than 20 rows.X should be less than or equal to 20 (X<=20).
As Brooke has 70 chairs to set up in equal rows we will find the factors of 70 and in that, we must pick up the numbers which are less than equal to 20.
Therefore the factors of 70 are 2,5,7,10,14.

Question 14.
Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?
_________

Answer: 16

Explanation:
If find factors for 1 to 20 we don’t get exactly 5 factors for any number except 16.
So the answer is 16.
Thus Eduardo might be thinking of the number 16.

Common Core – Factors, Multiples, and Patterns – Page No. 98

Lesson Check

Question 1.
Which of the following lists all the factors of 24?
Options:
a. 1, 4, 6, 24
b. 1, 3, 8, 24
c. 3, 4, 6, 8
d. 1, 2, 3, 4, 6, 8, 12, 24

Answer: 1, 2, 3, 4, 6, 8, 12, 24

Explanation:
Factors are the numbers that divide the original number completely.
Here, we can see the numbers which give the result as 24 when multiplied together.
1×24=24
2×12=24
3×8=24
4×6=24
6×4=4
8×3=24
12×2=24
24×1=24
So the factors of 24 are:1, 2, 3, 4, 6, 8, 12, 24.
Thus the correct answer is option d.

Question 2.
Natalia has 48 tiles. Which of the following shows a factor pair for the number 48?
Options:
a. 4 and 8
b. 6 and 8
c. 2 and 12
d. 3 and 24

Answer: 6 and 8

Explanation:
Given that, Natalia has 48 tiles.
We have to find the factor pair of the number 48.
6 and 8 are factor pairs for 48 because 6×8=48.
Thus the correct answer is option b.

Spiral Review

Question 3.
The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days?
Options:
a. 210 pounds
b. 2,100 pounds
c. 14,000 pounds
d. 21,000 pounds

Answer: 21,000 pounds

Explanation:
Given that, The Pumpkin Patch is open every day.
Let’s round off 2750 pounds to 3000 pounds. In one day 3000 pounds pumpkins were sold out, and in
7 days?? —- 3000×7= 21,000 pounds.
It sold 21,000 pounds in 7 days.
Thus the correct answer is option d.

Question 4.
What is the remainder in the division problem modeled below?

Options:
a. 2
b. 3
c. 5
d. 17

Answer: 2

Explanation:
We can see in the above figure 3 circles with 5 sub circles inside it and a pair of sub circles.
Here total sub circles are (3×5)+2=17.
If we divide 17 with 3 then we will get a reminder as 2.
So the answer is 2.
Thus the correct answer is option a.

Question 5.
Which number sentence is represented by the following array?

Options:
a. 4 × 5 = 20
b. 4 × 4 = 16
c. 5 × 2 = 10
d. 5 × 5 = 25

Answer: 4 × 5 = 20

Explanation:
By seeing the above figure we can say that there are 4 rows and 5 columns.
As we can see 4 rows and 5 squares.
Multiply the number of rows with the number of columns.
So 4 × 5 = 20.
Thus the correct answer is option a.

Question 6.
Channing jogs 10 miles a week. How many miles will she jog in 52 weeks?
Options:
a. 30 miles
b. 120 miles
c. 200 miles
d. 520 miles

Answer: 520 miles

Explanation:
No.of weeks = 52. So 1 week = 10 miles,
then 52 weeks =?????
52 × 10 = 520 miles.
Thus the correct answer is option d.

Common Core – Factors, Multiples, and Patterns – Page No. 99

Is 6 a factor of the number? Write yes or no.

Question 1.

Question 2.
56
_____

Answer: No

Explanation:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56 .
56 is not divisible by 6.
So the answer is No.

Question 3.
42
_____

Answer: Yes

Explanation:
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
Since 42 is divisible by 6.
So the answer is yes.

Question 4.
66
_____

Answer: Yes

Explanation:
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
66 is divisible by 6.
So the answer is yes.

Is 5 a factor of the number? Write yes or no.

Question 5.
38
_____

Answer: No

Explanation:
If the end is 0 or 5 then the number is divisible by 5.
The factors of 38 are 1, 2, 19, 38.
As the number is 38 the answer is No.

Question 6.
45
_____

Answer: Yes

Explanation:
45 is divisible by 5.
The factors of 45 are 1,3,5,9,15,45.
So the answer is Yes.

Question 7.
60
_____

Answer: Yes

Explanation:
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
60 is a factor of 5 because 60 is divisible by 5.

Question 8.
39
_____

Answer: No

Explanation:
The factors of 39 are 1,3,13,39.
As 39 is not divisible by 5.
So the answer is No.

List all the factor pairs

Question 9.
Factors of 12
_____ × _____ = 12; ( _____ , _____ )
_____ × _____ = 12; ( _____ , _____ )
_____ × _____ = 12; ( _____ , _____ )

Answer:
1 × 12 = 12; ( 1 , 12 )
2 × 6 = 12; ( 2, 6 )
3 × 4 = 12; ( 3 , 4 )

Question 10.
Factors of 25
_____ × _____ = 25; ( _____ , _____ )
_____ × _____ = 25; ( _____ , _____ )

Answer:
1 ×25 = 25; ( 1 , 25 )
5 × 5 = 25; ( 5 , 5 )

Question 11.
List all the factor pairs for 48.
Type below:
_________

Answer:
Factor pairs of 48 are (1,48),(2,24),(3,16),(4,12),(6,8),(12,2),(6,3),(24,2),(48,1).

Explanation:
Factor pairs are the pairs when we multiplied both numbers will get the result. Here factor pairs for 48 are
1×48=48 (1,48)
2×24=48 (2,24)
3×16=48 (3,16)
4×12=48 (4,12)
6×8 =48 (6,8)

Problem Solving

Question 12.
Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six storage containers and not have any left over?
_____

Answer: No

Explanation:
Given that,
Bryson buys a bag of 64 plastic miniature dinosaurs.
64 is not divisible by 6, So he cannot distribute them equally into six storage containers.

Question 13.
Lori wants to distribute 35 peaches equally into baskets. She will use more than 1 but fewer than 10 baskets. How many baskets does Lori need?
Type below:
_________

Answer: 5 or 7.

Explanation:
First, we need to know the factors of 35.
The factors of 35 are 1,5,7,35. As Lori uses more than 1 but fewer than 10, the answer is 5 or 7. Lori can distribute 35 peaches equally in 5 or 7 baskets.

Common Core – Factors, Multiples, and Patterns – Page No. 100

Lesson Check

Question 1.
Which of the following numbers has 9 as a factor?
Options:
a. 28
b. 30
c. 39
d. 45

Answer: 45

Explanation:
45 is divisible 9.
So the answer is 45.
Thus the correct answer is option d.

Question 2.
Which of the following numbers does NOT have 5 as a factor?
Options:
a. 15
b. 28
c. 30
d. 45

Answer: 28

Explanation:
28 is not divisible by 5.
So 28 is not a factor of 5.
Thus the correct answer is option b.

Spiral Review

Question 3.
Which of the following shows a strategy to use to find 4 × 275?
Options:
a. (4 × 300) + (4 × 25)
b. (4 × 300) – (4 × 25)
c. (4 × 275) – 100
d. (4 × 200) + 75

Answer: (4 × 300) – (4 × 25)

Explanation:
First, we must replace 300-25 in the place of 275 then it becomes 4×(300-25), Now we must use the distributive property of multiplication then (4×300)-(4×25).
So the answer is b.

Question 4.
Jack broke apart 5 × 216 as (5 × 200) + (5 × 16) to multiply mentally. What strategy did Jack use?
Options:
a. the Commutative Property
b. the Associative Property
c. halving and doubling
d. the Distributive Property

Answer: the Distributive Property

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. This is the strategy Jack used.
Thus the correct answer is option d.

Question 5.
Jordan has $55. She earns $67 by doing chores. How much money does Jordan have now?
Options:
a. $122
b. $130
c. $112
d. $12

Answer: $122

Explanation:
Jordan has $55, she earns by doing chores is $67.
So the total money is $55+$67=$122.
Thus the correct answer is option a.

Question 6.
Trina has 72 collector’s stamps. She puts 43 of the stamps into a stamp book. How many stamps are left?
Options:
a. 29
b. 31
c. 39
d. 115

Answer: 29

Explanation:
Given,
Trina has 72 collector’s stamps.
She puts 43 of the stamps into a stamp book.
Stamps left are 72-43=29.
Thus the correct answer is option a.

Common Core – Factors, Multiples, and Patterns – Page No. 101

Problem Solving Common Factors

Solve each problem.

Question 1.
Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag?

Question 2.
Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?
Type below:
_________

Answer: 1,2,3,4,6 or 12 items Simon puts on each wreath.

Explanation:
Given that,
Simon is making wreaths to sell.
He has 60 bows, 36 silk roses, and 48 silk carnations.
He wants to put the same number of items on each wreath.
First we will find the common factors of 36,48,60
factors of 36 are: 1,2,3,4,6,9,12,18,36.
factors of 48 are: 1,2,3,4,6,8,12,16,24,48
factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30,60.
The common factors of 36,48,60 are 1,2,3,4,6,12.
So Simon can put 1,2,3,4,6 or 12 items on each wreath.

Question 3.
Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes them into groups with the same number of items in each group. All the items in a group will be the same type. How many items can he put in each group?
Type below:
_________

Answer: Justin can put 1 or 5 items in each group.

Explanation:
Given,
Justin has 20 pencils, 25 erasers, and 40 paper clips.
He organizes them into groups with the same number of items in each group.
We will find common factors of 20,25,40.
factors of 20 are: 1,2,4,5,10,20.
factors of 25 are: 1,5,25.
factors of 40 are: 1,2,4,5,8,10,20,40
So common factors are 1 and 5.
Therefore, Justin can put 1 or 5 items in each group.

Question 4.
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water. The volunteers will put the items into boxes. Each box will have the same number of food items and all the items in the box will be the same type. How many items can they put in each box?
Type below:
_________

Answer: 1,2,5, or 10.

Explanation:
Given,
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water.
The volunteers will put the items into boxes.
1,2,5 or 10 are the common factors of 30,50 and 100.
factors for 30 are: 1,2,3,5,6,10,15,30
factors for 50 are: 1,2,5,10,25,50
factors of 100 are: 1,2,4,5,10,20,25,50,100
So the answer is 1,2,5,10.

Question 5.
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team?
Type below:
_________

Answer: 3

Explanation:
Given,
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy.
Lets find the common factors of 12,15,18
factors of 12 are: 1,2,3,4,6,12
factors of 15 are: 1,3,5,15
factors of 18 are: 1,2,3,6,9,18
3 is the common factor for 12,15,18
Therefore 3 students can be on each team.

Common Core – Factors, Multiples, and Patterns – Page No. 102

Lesson Check

Question 1.
What are all the common factors of 24, 64, and 88?
Options:
a. 1 and 4
b. 1, 4, and 8
c. 1, 4, 8, and 12
d. 1, 4, 8, and 44

Answer: 1, 4, and 8

Explanation:
factors of 24 are: 1,2,3,4,8,12,24
factors of 64 are: 1,2,4,8,16,32,64
factors of 88 are: 1,2,4,8,11,22,44,88
Thus the correct answer is option b.

Question 2.
Which number is NOT a common factor of 15, 45, and 90?
Options:
a. 3
b. 5
c. 10
d. 15

Answer: 10

Explanation:
As 15 and 45 are not divisible by 10.
Thus the correct answer is option c.

Spiral Review

Question 3.
Dan puts $11 of his allowance in his savings account every week. How much money will he have after 15 weeks?
Options:
a. $165
b. $132
c. $110
d. $26

Answer: $165

Explanation:
Dan puts $11 in his savings account every week.
So after 15 weeks, it will be 15×11=165.
The total money he will have after 15 weeks is $165.
Thus the correct answer is option a.

Question 4.
James is reading a book that is 1,400 pages. He will read the same number of pages each day. If he reads the book in 7 days, how many pages will he read each day?
Options:
a. 20
b. 50
c. 140
d. 200

Answer: 200

Explanation:
Given,
James is reading a book that is 1,400 pages.
He will read the same number of pages each day.
Total no.of.pages is 1400, no.of pages James read each day is 1400÷7= 200
Thus the correct answer is option d.

Question 5.
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks. Which is the best estimate of the number of hours she volunteered each week?
Options:
a. 10 hours
b. 20 hours
c. 120 hours
d. 714 hours

Answer: 20 hours

Explanation:
Given,
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks.
Total hours Emma volunteered is 119 hours over 6 weeks.
To find:
how much she volunteered each week is
119÷6= 19.833 i.e 20 hours.
We must round off to the nearest one i.e 20 hours.
Thus the correct answer is option b.

Question 6.
Which strategy can be used to multiply 6 × 198 mentally?
Options:
a. 6 × 198 = (6 × 19) + (6 × 8)
b. 6 × 198 = (6 × 200) + (6 × 2)
c. 6 × 198 = (6 × 200) – (6 × 2)
d. 6 × 198 = (6 + 200) × (6 + 2)

Answer: 6 × 198 = (6 × 200) – (6 × 2)

Explanation:
By Distributive property of multiplication 6×198 can be written as (6 × 200) – (6 × 2).
Thus the correct answer is option c.

Common Core – Factors, Multiples, and Patterns – Page No. 103

Factors and Multiples

Is the number a multiple of 8? Write yes or no.

Question 1.

Question 2.
8
_____

Answer: Yes

Explanation: Since 8×1=8, it is a multiple of 8

Question 3.
20
_____

Answer: No

Explanation: 20 is not a multiple of 8

Question 4.
40
_____

Answer: Yes

Explanation: 8×5=40, So 40 is multiple of 8

List the next nine multiples of each number. Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 7:
Common multiples:
Type below:
__________

Answer:

Multiples of 4: 4,8,12,16,20,24,28,32,36,40.
Multiples of 7: 7,14,21,28,35,42,49,56,63,70.
Common Multiples: 28,

Question 6.
Multiples of 3:
Multiples of 9:
Common multiples:
Type below:
__________

Answer: 9,18,45,54,63, etc.

Explanation:
Multiples of 3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63.
Multiples of 9: 9,18,27,36,45,54,63,72,81,90.
Common multiples: 9,18,45,54,63, etc.

Question 7.
Multiples of 6:
Multiples of 8:
Common multiples:
Type below:
__________

Answer: 24,48,72.

Explanation:
Multiples of 6: 6,12,18,24,30,36,42,48,54,60,66,72,78.
Multiples of 8: 8,16,24,32,40,48,56,64,72,80.
Common multiples: 24,48,72.

Tell whether 24 is a factor or multiple of the number. Write factor, multiple, or neither.

Question 8.
6
__________

Answer: Multiple

Explanation: 6×4=24

Question 9.
36
__________

Answer: Neither

Explanation: 36 is not a factor or multiple of 24.

Question 10.
48
__________

Answer: Factor

Explanation: 24×2= 48, So 48 is a factor of 24

Problem Solving

Question 11.
Ken paid $12 for two magazines. The cost of each magazine was a multiple of $3. What are the possible prices of the magazines?
Type below:
__________

Answer: $3+$9=$12.

Explanation:
As each magazine cost was multiple of $3.
The possible price for 2 magazines are $3+$9=$12, which is a multiple of 3

Question 12.
Jodie bought some shirts for $6 each. Marge bought some shirts for $8 each. The girls spent the same amount of money on shirts. What is the least amount they could have spent?
$ _____

Answer: $24

Explanation:
Given,
Jodie bought some shirts for $6 each.
Marge bought some shirts for $8 each.
The girls spent the same amount of money on shirts.
So multiples of 6 are: 6,12,18,24,30,36,42 and
multiples of 8 are: 8,16,24,32,40. The least amount they could spend is 24. As 24 is the least common multiple.

Common Core – Factors, Multiples, and Patterns – Page No. 104

Lesson Check

Question 1.
Which list shows numbers that are all multiples of 4?
Options:
a. 2, 4, 6, 8
b. 3, 7, 11, 15, 19
c. 4, 14, 24, 34
d. 4, 8, 12, 16

Answer: 4, 8, 12, 16

Explanation:
Multiples of 4 are 4,8,12,16.
Thus the correct answer is option d.

Question 2.
Which of the following numbers is a common multiple of 5 and 9?
Options:
a. 9
b. 14
c. 36
d. 45

Answer: 45

Explanation:
The common multiple of 5 and 9 is
5×9= 45
Thus the correct answer is option d.

Spiral Review

Question 3.
Jenny has 50 square tiles. She arranges the tiles into a rectangular array of 4 rows. How many tiles will be left over?
Options:
a. 0
b. 1
c. 2
d. 4

Answer: 2

Explanation:
As Jenny arranges in 4 rows, each row contains 12 tiles.
So 12×4= 48.
The tiles left are 50 – 48 = 2.
Thus the correct answer is option c.

Question 4.
Jerome added two numbers. The sum was 83. One of the numbers was 45. What was the other number?
Options:
a. 38
b. 48
c. 42
d. 128

Answer: 38

Explanation:
The sum of the two numbers is 83, in that one number is 45.
To find another number we will do subtraction,
i.e 83 – 45 = 38.
Thus the correct answer is option a.

Question 5.
There are 18 rows of seats in the auditorium. There are 24 seats in each row. How many seats are in the auditorium in all?
Options:
a. 42
b. 108
c. 412
d. 432

Answer: 432

Explanation:
Given,
There are 18 rows of seats in the auditorium.
There are 24 seats in each row.
No.of rows= 18, each row has 24 seats.
So total no.of seats are 18×24= 432.
Thus the correct answer is option d.

Question 6.
The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735?
Options:
a. 7
b. 700
c. 735
d. 7,000

Answer: 700

Explanation:
Given,
The population of Riverdale is 6,735.
In 6,735 the 7 is in the Hundreds Place.
So the answer is 7.
Thus the correct answer is option b.

Common Core – Factors, Multiples, and Patterns – Page No. 105

Prime and Composite Numbers

Tell whether the number is prime or composite

Question 1.

Question 2.
68
_________

Answer: Composite number.

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 68 are: 1,2,4,17,34,69.

Question 3.
52
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 52 are: 1,2,4,13,26,52.

Question 4.
63
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 63 are: 1,2,3,7,9,21,63.

Question 5.
75
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 75 are: 1,3,5,15,25,75

Question 6.
31
_________

Answer: Prime number

Explanation:
31 is a prime number that means it is divisible by 1 and itself.

Question 7.
77
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 77 are 1,7,11,77.

Question 8.
59
_________

Answer: Prime number

Explanation:
59 is a prime number that means it is divisible by 1 and itself.

Question 9.
87
_________

Answer: Composite Number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 87 are: 1,3,29,87.

Question 10.
72
_________

Answer: Composite Number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Question 11.
49
_________

Answer: Composite Number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 49 are 1,7,49.

Question 12.
73
_________

Answer: Prime number

Explanation:
A Prime number is a number that is divisible 1 and itself.

Problem Solving

Question 13.
Kai wrote the number 85 on the board. Is 85 prime or composite?
_________

Answer: Composite number

Explanation: The number which has more than two factors is called composite numbers.
Factors of 85 are 1,5,17,85

Question 14.
Lisa says that 43 is a 2-digit odd number that is composite. Is she correct?
_____

Answer: No

Explanation:
43 is a prime number.
A Prime number is a number that is divisible 1 and itself.

Common Core – Factors, Multiples, and Patterns – Page No. 106

Lesson Check

Question 1.
The number 5 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Answer: Prime number

Explanation:
A Prime number is a number that is divisible 1 and itself.
Thus the correct answer is option a.

Question 2.
The number 1 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Answer: neither prime nor composite

Explanation:
A Prime number is a number that is divisible 1 and itself. So prime number should have two divisors but 1 has only one divisor. The number which has more than two factors is called composite numbers. So 1 doesn’t have more than two factors. So 1 is neither Prime nor Composite.
Thus the correct answer is option d.

Spiral Review

Question 3.
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
Options:
a. 134 calories
b. 150 calories
c. 154 calories
d. 231 calories

Answer: 154 calories

Explanation:
Total no.of calories are 924, which serves 6 people.
To find each serving we will perform division
924 ÷ 6 = 154 calories.
Thus the correct answer is option c.

Question 4.
A store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts. What is the fewest boxes the clerk will need to pack all the shirts?
Options:
a. 9
b. 8
c. 7
d. 6

Answer: 8

Explanation:
As the box holds only 6 shirts, 42 shirts are packed in 7 boxes, and the remaining 3 shirts will be packed in another box.
So the total number of boxes is 8.
Thus the correct answer is option b.

Question 5.
Which number rounds to 200,000?
Options:
a. 289,005
b. 251,659
c. 152,909
d. 149,889

Answer: 152,909

Explanation:
152,909 is nearest to 200,000.
Thus the correct answer is option c.

Question 6.
What is the word form of the number 602,107?
Options:
a. six hundred twenty thousand,seventeen
b. six hundred two thousand, one hundred seven
c. six hundred twenty-one thousand, seventeen
d. six hundred two thousand, one hundred seventy

Answer: six hundred two thousand, one hundred seven

Explanation:
Convert the number 602,107 into the word form.
The word form of 602,107 is six hundred two thousand, one hundred seven
Thus the correct answer is option b.

Common Core – Factors, Multiples, and Patterns – Page No. 107

Number Patterns

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 1.
Rule: Add 8. First-term: 5

Question 2.
Rule: Subtract 7. First-term: 95
Type below:
_________

Answer: 95,88,81,74,67,60,53,46,39,32,25,118,11.

Explanation: 95
95-7= 88
88-7= 81
81-7= 74
74-7= 67
67-7= 60
60-7= 53
53-7= 46
46-7= 39
39-7= 32
32-7= 25
25-7= 18
18-7= 11

Question 3.
Rule: Add 15, subtract 10. First-term: 4
Type below:
_________

Answer: 4,19,9,24,14,29,19,34,24,39,29,44,34.

Explanation: 4
4+15= 19
19-10= 9
9+15= 24
24-10= 14
14+15= 29
29-10= 19
19+15= 34
34-10= 24
24+15= 39
39-10=29
29+15=44
44-10=34

Question 4.
Rule: Add 1, multiply by 2. First-term: 2
Type below:
_________

Answer: 2,4,5,10,11,22,23,46,47,94,95,190.

Explanation: 2
2+1= 2
2×2= 4
4+1= 5
5×2= 10
10+1= 11
11×2= 22
22+1= 23
23×2= 46
46+1= 47
47×2= 94
94+1= 95
95×2= 190.

Problem Solving

Question 5.
Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is the rule for the pattern?
Type below:
_________

Answer: The serial numbers of first 8 white beads are = 1, 5, 9, 13, 17, 21, 25, 29

Explanation:
Since there are 3 blue beads after each white beads.
Hence we can design the progression in the following way looking at the sequence:
W,B,B,B,W,B,B,B,W…….
Hence the required formula for white beads serial number is,
N = (X-1)(A+1) + L
Where, A = number of blue beads after each white beads = 3
L = initial position at which the first white bead is placed = 1
X = number of white bead
Putting the values in the above formula our equation becomes,
N = 4(X-1) + 1
Hence we can find out the serial numbers as follows:
N₁ = 4 x 0 + 1 = 1
N₂ = 4×1 + 1 = 5
N₃ = 4×2 + 1 = 9
and so on upto
N₈ = 4 x 7 + 1 = 29

Question 6.
An artist is arranging tiles in rows to decorate a wall. Each new row has 2 fewer tiles than the row below it. If the first row has 23 tiles, how many tiles will be in the seventh row?
_____ tiles

Answer: 11 tiles

Explanation:
Given that,
An artist is arranging tiles in rows to decorate a wall.
Each new row has 2 fewer tiles than the row below it.
23
23-2= 21
21-2= 19
19-2= 17
17-2= 15
15-2= 13
13-2= 11

Common Core – Factors, Multiples, and Patterns – Page No. 108

Lesson Check

Question 1.
The rule for a pattern is add 6. The first term is 5. Which of the following numbers is a term in the pattern?
Options:
a. 6
b. 12
c. 17
d. 22

Answer: 17

Explanation:
Given that,
The rule for a pattern is add 6. The first term is 5.
5+6= 11
11+6= 17
Thus the correct answer is option c.

Question 2.
What are the next two terms in the pattern 3, 6, 5, 10, 9, 18, 17, . . .?
Options:
a. 16, 15
b. 30, 31
c. 33, 34
d. 34, 33

Answer: 34, 33

Explanation: 3
3×2= 6
6-1= 5
5×2= 10
10-1= 9
9×2= 18
18-1= 17
17×2= 34
34-1= 33
Thus the correct answer is option d.

Spiral Review

Question 3.
To win a game, Roger needs to score 2,000 points. So far, he has scored 837 points. How many more points does Roger need to score?
Options:
a. 1,163 points
b. 1,173 points
c. 1,237 points
d. 2,837 points

Answer: 1,163 points

Explanation:
Roger has scored 837 points, He needs to score 2000 points to win, So to know how much more points do Roger needs we need to subtract i.e 2,000-837= 1,163.
Thus the correct answer is option a.

Question 4.
Sue wants to use mental math to find 7 × 53. Which expression could she use?
Options:
a. (7 × 5) + 3
b. (7 × 5) + (7 × 3)
c. (7× 50) + 3
d. (7 × 50) + (7 × 3)

Answer: (7 × 50) + (7 × 3)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.
Thus the correct answer is option d.

Question 5.
Pat listed numbers that all have 15 as a multiple. Which of the following could be Pat’s list?
Options:
a. 1, 3, 5, 15
b. 1, 5, 10, 15
c. 1, 15, 30, 45
d. 15, 115, 215

Answer: 1, 3, 5, 15

Explanation:
Given,
Pat listed numbers that all have 15 as a multiple.
1×15= 15
3×5= 15
5×3= 15
15×1= 15
Thus the correct answer is option a.

Question 6.
Which is a true statement about 7 and 14?
Options:
a. 7 is a multiple of 14.
b. 14 is a factor of 7.
c. 14 is a common multiple of 7 and 14.
d. 21 is a common multiple of 7 and 14.

Answer: 14 is a common multiple of 7 and 14.

Explanation:
7×2=14
14×1=14
Thus the correct answer is option c.

Common Core – Factors, Multiples, and Patterns – Page No. 109

Use tiles to find all the factors of the product. Record the arrays on grid paper and write the factors shown.

Question 1.
Write the factors of: 17
Type below:
_________

Answer: The factors of 17 are: 1, 17

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 17 when multiplied together.
1 × 17 = 17
17 × 1 = 17
So the factors of 17 are: 1, 17.

Question 2.
Write the factors of: 42
Type below:
_________

Answer: The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 42 when multiplied together.
1 × 42 = 42
2 × 21= 42
3 × 14 = 42
6 × 7 = 42
7 × 6 = 42
14 × 3 = 42
21 × 2 = 42
42 × 1 = 42
So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

Question 3.
Write the factors of: 28
Type below:
_________

Answer: The factors of 28 are: 1, 2, 4, 7, 14, 28.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 28 when multiplied together.
1 × 28 = 28
2 × 14 = 28
4 × 7 = 28
7 × 4 = 28
14 × 2 = 28
28 × 1 = 28
So the factors of 28 are:1, 2, 4, 7, 14, 28.

Question 4.
Write the factors of: 50
Type below:
_________

Answer: The factors of 50 are 1, 2, 5, 10, 25, and 50.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 50 when multiplied together.
1 × 50 = 50
2 × 25 = 50
5 × 10 = 50
10 × 5 = 50
25 × 2 = 50
50 × 1 = 50
The factors of 50 are 1, 2, 5, 10, 25, and 50.

Is 5 a factor of the number? Write yes or no.

Question 5.
35
_____

Answer: Yes

Explanation:
The factors of 35 are 1, 5, 7, 35. So, the answer is yes.

Question 6.
56
_____

Answer: No

Explanation:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. So, the answer is no.

Question 7.
51
_____

Answer: No

Explanation:
The factors of 51 are 1, 3, 17, 51. So, the answer is no.

Question 8.
40
_____

Answer: Yes

Explanation:
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. So, the answer is yes.

List all the factor pairs.

Question 9.
Factors of 16
_____ × _____ = 16; ( _____ , _____ )
_____ × _____ = 16; ( _____ , _____ )
_____ × _____ = 16; ( _____ , _____ )

Answer: The factor pairs of 16 are (1, 16), (2, 8), (4, 4)
1× 16 = 16; ( 1, 16)
2× 8 = 16; ( 2, 8)
4× 4 = 16; ( 4, 4)

Question 10.
Factors of 49
_____ × _____ = 49; ( _____ , _____ )
_____ × _____ = 49; ( _____ , _____ )

Answer: The factors in pairs of number 49 are (1, 49) and (7, 7).
1× 49= 49; ( 1, 49)
7× 7= 49; ( 7, 7)

Question 11.
Hana is putting the fruit she bought into bowls. She bought 8 melons, 12 pears, and 24 apples. She puts the same number of pieces of fruit in each bowl and puts only one type of fruit in each bowl. How many pieces can Hana put in each bowl?
Type below:
_________

Answer:
If she wants the same number of pieces of each kind of fruit in each bowl (same number of melons, the same number of pears, and the same number of apples in each bowl), then she can put 11 pieces in each of the 4 bowls.

Explanation:
To answer this, we find the greatest common factor (GCF) of all 3 numbers. To do this, we find the prime factorization of 8, 12 and 24:
8 = 4 × 2
4 = 2 × 2
8 = 2 × 2× 2
12 = 4 × 3
4 = 2 × 2
12 = 2 × 2 × 3
24 = 4 × 6
4 = 2 × 2
6 = 2 × 3
24 = 2 × 2 × 2 × 3
The GCF is made of all of the common factors. The factors common to all 3 numbers are 2 and 2; 2(2) = 4 for the GCF.
This means we can use 4 bowls.
She has a total of 8+12+24 = 44 pieces of fruit; 44/4 = 11. She would have 11 pieces of fruit in each bowl.

Question 12.
A store owner is arranging clothing on racks. She has 30 sweaters, 45 shirts, and 15 pairs of jeans. She wants to put the same number of items on each rack, with only one type of item on each. How many items can she put on a rack?
Type below:
_________

Answer:
I think what the teacher wants is 15 which is the greatest common factor of all three numbers and the factors of 15 are 1 x 15 and 3 x 5 so she can put one of each, or she can put 3 of each, or she can put 5 of each, or she can put 15 of each.

Common Core – Factors, Multiples, and Patterns – Page No. 110

Is the number a multiple of 9? Write yes or no.

Question 1.
24
_____

Answer: No

Explanation:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. So the answer is no.

Question 2.
18
_____

Answer: Yes

Explanation:
The factors of 18 are 1, 2, 3, 6, 9, 18. So, the answer is yes.

Question 3.
27
_____

Answer: Yes

Explanation:
The factors of 27 are 1, 3, 9, 27. So, the answer is yes.

Question 4.
42
_____

Answer: No

Explanation:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. So the answer is no.

List the next nine multiples of each number.

Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 5:
Common multiples:
Type below:
_________

Answer: 20, 40.

Explanation:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Common multiples: 20, 40.

Question 6.
Multiples of 3:
Multiples of 6:
Common multiples:
Type below:
_________

Answer: 6, 12, 18, 24, 30.

Explanation:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
Common multiples: 6, 12, 18, 24, 30.

Tell whether the number is prime or composite.

Question 7.
39
_____

Answer: Composite

Explanation: The number which has more than two factors is called composite numbers.
The factors of 39 are 1, 13, 39.
Thus 39 is the composite number.

Question 8.
29
_____

Answer: Prime

Explanation: A Prime number is a number that is divisible 1 and itself.
The factors of 29 are 1, 29.
So, 29 is the prime number.

Question 9.
51
_____

Answer: Composite

Explanation: The number which has more than two factors is called composite numbers.
The factors of 51 are 1, 3, 17, 51.
Therefore 51 is the composite number.

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 10.
Rule: Add 6. First term: 10
Type below:
_________

Answer: 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82.

Explanation: 10
10 + 6 = 16
16 + 6 = 22
22 + 6 = 28
28 + 6 = 34
34 + 6 = 40
40 + 6 = 46
46 + 6 = 52
52 + 6 = 58
58 + 6 = 64
64 + 6 = 70
70 + 6 = 76
76 + 6 = 82

Question 11.
Rule: Add 3, subtract 2. First term: 7
Type below:
_________

Answer: 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13.

Explanation: 7
7 + 3 = 10
10 – 2 = 8
8 + 3 = 11
11 – 2 = 9
9 + 3 = 12
12 – 2 = 10
10 + 3 = 13
13 – 2 = 11
11 + 3 = 14
14 – 2 = 12
12 + 3 = 15
15 – 2 = 13

Conclusion:

Go Math Grade 4 Chapter 5 Answer Key holds Factors, Multiples, and Patterns. Prepare well by using the provided Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns pdf. For better knowledge and information please check out the chapterwise Grade 4 Go Math Answer Key very well.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 1 Place Value, Addition, and Subtraction to One Million Pdf Download is available on this page for an efficient practice session. Provided solutions are very easy to understand and simple to learn the concept of Chapter 1 Place Value, Addition, and Subtraction to One Million. Enhance your kid’s logical and analytical thinking by answering every practice question covered in the HMH Go Math Grade 4 Answer Key Homework Practice FL Chapter 1 Place Value, Addition, and Subtraction to One Million.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 1 Place Value, Addition, and Subtraction to One Million

Here, we have designed a new path for students to solve each and every chapter question & improve their problem-solving skills. It is nothing but the HMH Go Math Grade 4 Answer Key of Chapter 1. The topics of ch 1 Place Value, Addition, and Subtraction to One Million are Model Place Value Relationships, Compare and Order Numbers, Round Numbers, Add and subtract Whole Numbers, etc. Now, you’ll find all topics Go Math Grade 4 Answer Key Homework Practice FL Chapter 1 for better preparation.

Lesson: 1 – Model Place Value Relationships

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 3
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 4

Lesson: 2 – Read and Write Numbers

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 5
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 6

Lesson: 3 – Compare and Order Numbers

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 7
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 8

Lesson: 4 – Round Numbers 

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 9
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 10

Lesson: 5 – Rename Numbers

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 11
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 12

Lesson: 6 – Add Whole Numbers

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 13
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 14

Lesson: 7 – Subtract Whole Numbers

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 15
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 16

Lesson: 8 – Problem Solving Comparison Problems with Addition and Subtraction

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 17
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 18

Lesson: 9 

• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 19
• Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 20

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 3

Model Place Value Relationships

Find the value of the underlined digit.

Question 1.
6,035
30

Question 2.
43,782
________

Answer: 700

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 7 in 43,782 is 700.

Question 3.
506,087
________

Answer: 7

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 7 in 506,087 is 7.

Question 4.
49,254
________

Answer: 9000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 9 in 49,254 is 9000.

Question 5.
136,422
________

Answer: 30,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 136,422 is 30,000.

Question 6.
673,512
________

Answer: 500

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 5 in 673,512 is 500.

Question 7.
814,295
________

Answer: 800,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 8 in 814,295 is 800,000.

Question 8.
736,144
________

Answer: 6,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 6 in 736,144 is 6,000.

Compare the values of the underlined digits.

Question 9.
6,300 and 530
The value of 3 in _____ is _____ times the value of 3 in _____.

Answer: The value of 3 in 6,300 is 10 times the value of 3 in 530.

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 6,300 is 300. And the place value of the digit 3 in 530 is 30. As each hundred is 10 times as many as 10, so 3 hundreds are ten times as many as 3 tens. So, the value of 3 in 6,300 is 10 times the value of 3 in 530.

Question 10.
2,783 and 7,283
The value of 2 in _____ is _____ times the value of 2 in _____.

Answer: The value of 2 in 2783 is 10 times the value of 2 in 7283.

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 2 in 2,783 is 2000. And the place value of the digit 2 in 7,283 is 200. As each hundred is 10 times as many as 10, so 2 thousands are ten times as many as 2 hundred. So, the value of 2 in 2783 is 10 times the value of 2 in 7283.

Question 11.
34,258 and 47,163
The value of 4 in _____ is _____ times the value of 4 in _____.

Answer: The value of 4 in 47,163 is 10 times the value of 4 in 34,258.

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 4 in 34,258 is 4,000. And the place value of the digit 4 in 47,163 is 40,000. As each hundred is 10 times as many as 10, so 4 thousands are ten times as many as 4 thousand tens. So, the value of 4 in 47,163 is 10 times the value of 4 in 34,258.

Question 12.
503,497 and 26,475
The value of 7 in _____ is _____ times the value of 7 in _____.

Answer: The value of 7 in 26,475 is 10 times the value of 7 in 5,03,497.

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 7 in 503,497 is 7. And the place value of the digit 7 in 26,475 is 70. As each hundred is 10 times as many as 10, so 7 are ten times as many as 7 tens. So, the value of 7 in 26,475 is 10 times the value of 7 in 5,03,497.

Problem Solving

Use the table for 13–14.

Question 13.
What is the value of the digit 9 in the attendance at the Redskins vs. Titans game?
The value of 9 is _____

Answer: 9,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 9 in 69,143 is 9,000.

Question 14.
The attendance at which game has a 7 in the ten thousands place?
__________

Answer: Ravens vs. Panthers

Explanation:
Each digit of the number holds its own value. The adjacent digits of the number differ from each other by 10 times. Starting from the leftmost digit going to the right, the order of place values starts from ones, tens, hundreds, thousands, and ten thousand. Therefore, the number should contain a digit 7 on the 5th digit from left to right.
Thus the attendance at Ravens vs. Panthers game has a 7 in the ten thousands place.

Question 15.
How does a digit in the ten thousands place compare to a digit in the thousands place?
Type below:
__________

Answer:
A digit in the ten thousand place has a value of 10,000 times the value of the mere digit. While a digit in the thousands place has a value 1,000 times the value of the digit. So to compare you can do 10,000 / 1,000 = 10, which means that a digit in the ten thousand place values ten times what the same digit values are it is the thousand place.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 4

Lesson Check

Question 1.
During one season, a total of 453,193 people attended a baseball team’s games. What is the value of the digit 5 in the number of people?
Options:
a. 500
b. 5,000
c. 50,000
d. 500,000

Answer: 50,000

Explanation:
Given,
During one season, a total of 453,193 people attended a baseball team’s games.
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 5 in 453,193 is 50,000.
Thus the correct answer is option C.

Question 2.
Hal forgot the number of people at the basketball game. He does remember that the number had a 3 in the tens place. Which number could Hal be thinking of?
Options:
a. 7,321
b. 3,172
c. 2,713
d. 1,237

Answer: 1,237

Explanation:
Given,
Hal forgot the number of people at the basketball game.
He does remember that the number had a 3 in the tens place.
a. 7,321 – the value of 3 in 7321 is 300.
b. 3,172 – the value of 3 in 3172 is 3000.
c. 2,713 – the value of 3 in 2713 is 3.
d. 1,237 – the value of 3 in 1237 is 30.
Thus the number 3 in tens place is 1,237.
Therefore, the correct answer is option D.

Spiral Review

Question 3.
Hot dog buns come in packages of 8. For the school picnic, Mr. Spencer bought 30 packages of hot dog buns. How many hot dog buns did he buy?
Options:
a. 24
b. 38
c. 110
d. 240

Answer: 240

Explanation:
Given,
Hot dog buns come in packages of 8.
For the school picnic, Mr. Spencer bought 30 packages of hot dog buns.
8 × 30 = 240 buns
He bought 240 hot dig buns.
Thus the correct answer is option D.

Question 4.
There are 8 students on the minibus. Five of the students are boys. What fraction of the students are boys?
Options:
a. \(\frac{3}{8}\)
b. \(\frac{5}{8}\)
c. \(\frac{5}{5}\)
d. \(\frac{8}{8}\)

Answer: \(\frac{5}{8}\)

Explanation:
There are 8 students on the minibus. Five of the students are boys.
Divide the number of boys by the total number of students on the minibus.
\(\frac{5}{8}\)
Thus the correct answer is option B.

Question 5.
The clock below shows the time when Amber leaves home for school. At what time does Amber leave home?

Options:
a. 2:41
b. 8:02
c. 8:10
d. 8:20

Answer: 8:10

Explanation:
By seeing the above figure we can say that Amber leave home is 8:10.
Thus the correct answer is option C.

Question 6.
Jeremy drew a polygon with four right angles and four sides with the same length.

What kind of polygon did Jeremy draw?
Options:
a. hexagon
b. square
c. trapezoid
d. triangle

Answer: square

Explanation:
A square has two pairs of parallel sides, four right angles, and all four sides are equal.
Thus the correct answer is option B.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 5

Read and Write Numbers

Read and write the number in two other forms.

Question 1.
six hundred ninety-two thousand, four
standard form: 692,004;
expanded form: 600,000 + 90,000 + 2,000 + 4

Question 2.
314,207
Type below:
________

Answer:
Standard form: Three hundred fourteen thousand, two hundred seven.
Explanded form: 300,000 + 10,000 + 4,000 + 200 + 7

Question 3.
600,000 + 80,000 + 10
Type below:
________

Answer:
Standard form: 680,010
Expanded form: Six hundred eighty thousand ten.

Use the number 913,256.

Question 4.
Write the name of the period that has the digits 913.
________

Answer: thousands
Each group of three digits forms a period. The name of the period that has the digits 913 is thousands group.

Question 5.
Write the digit in the ten thousands place.
________

Answer: 1

Question 6.
Write the value of the digit 9.
________

Answer: 9 hundred thousands or 900,000.

Problem Solving

Use the table for 7 and 8.

Question 7.
Which state had a population of eight hundred four thousand, one hundred ninety-four?
________

Answer: South Dakota

Explanation:
The standard form of eight hundred four thousand, one hundred ninety-four is 804,194.
We can see the population 804,194 in the above table in South Dakota.

Question 8.
What is the value of the digit 8 in Alaska’s population?
________

Answer: 8 ten thousands, or 80,000.

Explanation:
The population in Alaska is 686,293.
The value of the digit 8 in Alaska’s population is 80,000.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 6

Lesson Check

Question 1.
Based on a 2008 study, children 6–11 years old spend sixty-nine thousand, one hundred eight minutes a year watching television. What is this number written in
standard form?
Options:
a. 6,918
b. 69,108
c. 69,180
d. 690,108

Answer: 69,108

Explanation:
Given,
Based on a 2008 study, children 6–11 years old spend sixty-nine thousand, one hundred eight minutes a year watching television.
The standard form of sixty-nine thousand, one hundred eight is 69,108.

Question 2.
What is the value of the digit 4 in the number 84,230?
Options:
a. 4
b. 400
c. 4,000
d. 40,000

Answer: 4,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 4 in 84,230 is 4,000.
Thus the correct answer is option C.

Spiral Review

Question 3.
An ant has 6 legs. How many legs do 8 ants have in all?
Options:
a. 14
b. 40
c. 45
d. 48

Answer: 48

Explanation:
Given,
An ant has 6 legs.
To find:
How many legs do 8 ants have in all
6 legs × 8 = 48 legs
Thus the correct answer is option D.

Question 4.
Latricia’s vacation is in 4 weeks. There are 7 days in a week. How many days is it until Latricia’s vacation?
Options:
a. 9 days
b. 11 days
c. 20 days
d. 28 days

Answer: 28 days

Explanation:
Given,
Latricia’s vacation is in 4 weeks.
There are 7 days in a week.
4 × 7 days = 28 days
Thus the correct answer is option D.

Question 5.
Marta collected 363 cans. Diego collected 295 cans. How many cans did Marta and Diego collect in all?
Options:
a. 668
b. 658
c. 568
d. 178

Answer: 658

Explanation:
Marta collected 363 cans. Diego collected 295 cans.
363 cans + 295 cans = 658 cans
Marta and Diego collect 658 cans in all.
Thus the correct answer is option B.

Question 6.
The city Tim lives in has 106,534 people. What is the value of the 6 in 106,534?
Options:
a. 6,000
b. 600
c. 60
d. 6

Answer: 6,000

Explanation:
The city Tim lives in has 106,534 people.
The value of the 6 in 106,534 is 6,000.
Thus the correct answer is option A.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 7

Compare and Order Numbers

Compare. Write < .> or =.

Question 1.
3,273 < 3,279

Question 2.
$1,323 ______ $1,400

Answer: <
The number $1,323 < $1,400 as 323 is less than 400.

Question 3.
52,692 ______ 52,692

Answer: =
The number 52,692 is equal to 52,692.

Question 4.
$413,005 ______ $62,910

Answer: >
The number $413,005 is greater than $62,910.

Question 5.
382,144 ______ 382,144

Answer: =
The number 382,144 is equal to 382,144.

Question 6.
157,932 ______ 200,013

Answer: <
The number 157,932 is less than 200,013.

Question 7.
401,322 ______ 410,322

Answer: <
The number 401,322 is less than 410,322.

Question 8.
989,063 ______ 980,639

Answer: >
The number 989,063 is greater than 980,639.

Question 9.
258,766 ______ 258,596

Answer: >
The number 258,766 is greater than 258,596.

Order from least to greatest.

Question 10.
23,710; 23,751; 23,715
______ < ______ < ______

Answer: 23,710; 23,715; 23,751

Question 11.
52,701; 54,025; 5,206
______ < ______ < ______

Answer: 5,206; 52,701; 54,025
The numbers from least to greatest is 5,206; 52,701; 54,025

Question 12.
465,321; 456,321; 456,231
______ < ______ < ______

Answer: 456,321; 456,231; 456,231
456,321 is less than 456,231 is less than 456,231. The numbers from least to greatest is 456,321; 456,231; 456,231.

Question 13.
$330,820; $329,854; $303,962
______ < ______ < ______

Answer: $303,962; $329,854; $330,820
$303,962 is less than $329,854 is less than $330,820. The numbers from least to greatest is $303,962; $329,854; $330,820.

Problem Solving

Question 14.
An online newspaper had 350,080 visitors in October, 350,489 visitors in November, and 305,939 visitors in December. What is the order of the months from greatest to least number of visitors?
1. ________
2. ________
3. ________

Answer:
1. November
2. October
3. December

Explanation:
Given,
An online newspaper had 350,080 visitors in October, 350,489 visitors in November, and 305,939 visitors in December.
350,489 is greater than 350,080 is greater than 305,939.
Thus the order of the months from greatest to least number of visitors is November, October and December.

Question 15.
The total land area in square miles of each of three states is shown below.
Colorado: 103,718
New Mexico: 121,356
Arizona: 113,635
What is the order of the states from least to greatest total land area?
1. ________
2. ________
3. ________

Answer:
1. Colorado
2. Arizona
3. New Mexico

Explanation:
The total land area in square miles of each of three states is shown below.
Colorado: 103,718
New Mexico: 121,356
Arizona: 113,635
The greatest number is 121,356, 113,635, 103,718
The order of the states from least to greatest total land area is Colorado, Arizona and New Mexico.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 8

Lesson Check

Question 1.
At the yearly fund-raising drive, the nonprofit company’s goal was to raise $55,500 each day. After three days, it had raised $55,053; $56,482; and $55,593. Which amount was less than the daily goal?
Options:
a. $55,500
b. $55,053
c. $55,593
d. $56,482

Answer: $55,053

Explanation:
At the yearly fund-raising drive, the nonprofit company’s goal was to raise $55,500 each day. After three days, it had raised $55,053; $56,482; and $55,593.
$55,053 < $55,593 < $56,482
The amount was less than the daily goal is $55,053.
Thus the correct answer is option B.

Question 2.
Which of the following lists of numbers is in order from greatest to least?
Options:
a. 60,343; 60,433; 63,043
b. 83,673; 86,733; 86,373
c. 90,543; 90,048; 93,405
d. 20,433; 20,343; 20,043

Answer: 20,433; 20,343; 20,043

Explanation:
The lists of numbers is in order from greatest to least is 20,433; 20,343; 20,043
The correct answer is option D.

Spiral Review

Question 3.
Jess is comparing fractions. Which fraction is greater than \(\frac{5}{6}\)?
Options:
a. \(\frac{7}{8}\)
b. \(\frac{4}{5}\)
c. \(\frac{3}{4}\)
d. \(\frac{2}{3}\)

Answer: \(\frac{7}{8}\)

Explanation:
Given,
Jess is comparing fractions.
The fraction is greater than \(\frac{5}{6}\) is \(\frac{7}{8}\)
The correct answer is option A.

Question 4.
What is the perimeter of the rectangle below?

Options:
a. 14 inches
b. 26 inches
c. 28 inches
d. 48 inches

Answer: 28 inches

Explanation:
Given,
l = 6 in
w = 8 in.
Perimeter of the rectangle = l + l + w + w
P = 6 in + 6 in + 8 in + 8 in
P = 28 inches
Thus the perimeter of the rectangle is 28 inches.
The correct answer is option C.

Question 5.
A website had 826,140 hits last month. What is the value of the 8 in 826,140?
Options:
a. 800
b. 8,000
c. 80,000
d. 800,000

Answer: 800,000

Explanation:
A website had 826,140 hits last month.
The value of the 8 in 826,140 is 800,000.
Thus the correct answer is option D.

Question 6.
Which is 680,705 written in expanded form?
Options:
a. 680 + 705
b. 68,000 + 700 + 5
c. 600,000 + 8,000 + 700 + 5
d. 600,000 + 80,000 + 700 + 5

Answer: 600,000 + 80,000 + 700 + 5

Explanation:
The expanded form of 680,705 is 600,000 + 80,000 + 700 + 5
The correct answer is option D.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 9

Round Numbers 

Round to the place value of the underlined digit.

Question 1.

Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.

Question 2.
123,499
_____

Answer: 123,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 3 in 123,499 is 123,000.

Question 3.
552,945
_____

Answer: 600,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 5 in 552,945 is 600,000.

Question 4.
389,422
_____

Answer: 390,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 8 in 389,422 is 390,000.

Question 5.
209,767
_____

Answer: 200,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 2 in 209,767 is 200,000.

Question 6.
191,306
_____

Answer: 191,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 1 in 191,306 is 191,000.

Question 7.
66,098
_____

Answer: 70,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 6 in 66,098 is 70,000.

Question 8.
73,590
_____

Answer: 74,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 3 in 73,590 is 74,000.

Question 9.
149,903
_____

Answer: 100,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 1 in 149,903 is 100,000.

Question 10.
684,303
_____

Answer: 684,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 4 in 684,303 is 684,000.

Question 11.
499,553
_____

Answer: 500,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 9 in 499,553 is 500,000.

Problem Solving

Use the table for 12–13.

Question 12.
Find the height of Mt. Whitney in the table. Round the height to the nearest thousand feet.
_____ feet

Answer: 14,000 feet

Explanation:
The height to the nearest thousand feet for 14,494 is 14,000 feet.

Question 13.
What is the height of Mt. Bona rounded to the nearest ten thousand feet?
_____ feet

Answer: 20,000 feet

Explanation:
The height of Mt. Bona rounded to the nearest ten thousand feet for 16,500 is 20,000 feet.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 10

Lesson Check

Question 1.
Which number is 247,039 rounded to the nearest thousand?
Options:
a. 200,000
b. 250,000
c. 247,000
d. 7,000

Answer: 247,000

Explanation:
Round off the value means making a number simpler but keeping its value close to what it was. The result is less accurate but easy to use. So the number is 247,039 rounded to the nearest thousand is 247,000.
Thus the correct answer is option C.

Question 2.
To the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008. Which might have been the exact population of Vermont in 2008?
Options:
a. 626,013
b. 621,270
c. 614,995
d. 609,964

Answer: 621,270

Explanation:
To the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008.
The exact population of Vermont in 2008 might be 621,270.
Thus the correct answer is option B.

Spiral Review

Question 3.
Which symbol makes the following number sentence true?
$546,322 Ο $540,997
Options:
a. <
b. >
c. =
d. +

Answer: >

Explanation:
$546,322 is greater than $540,997.
Thus the correct answer is option B.

Question 4.
Pittsburgh International Airport had approximately 714,587 passengers in August 2009. Which number is greater than 714,587?
Options:
a. 714,578
b. 704,988
c. 714,601
d. 714,099

Answer: 714,601

Explanation:
Given,
Pittsburgh International Airport had approximately 714,587 passengers in August 2009.
The number greater than 714,587 is 714,601.
Thus the correct answer is option C.

Question 5.
June made a design with 6 equal tiles. One tile is yellow, 2 tiles are blue, and 3 tiles are purple. What fraction of the tiles are yellow or purple?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{2}{6}\)
c. \(\frac{3}{6}\)
d. \(\frac{4}{6}\)

Answer: \(\frac{4}{6}\)

Explanation:
Given,
June made a design with 6 equal tiles. One tile is yellow, 2 tiles are blue, and 3 tiles are purple.
We have to put the total number of tiles in the denominator.
The number of yellow or purple tiles is 3 + 1 = 4 put it in the numerator.
The fraction of the tiles are yellow or purple is \(\frac{4}{6}\).
Thus the correct answer is option D.

Question 6.
The fourth grade collected 40,583 cans and plastic bottles. Which of the following shows that number in word form?
Options:
a. forty thousand, five hundred eighty
b. forty thousand, five hundred eighty-three
c. four thousand, five hundred eighty-three
d. four hundred thousand, five hundred eighty

Answer: forty thousand, five hundred eighty-three

Explanation:
Given,
The fourth grade collected 40,583 cans and plastic bottles.
The expanded form of 40,583 is forty thousand, five hundred eighty-three.
Thus the correct answer is option B.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 11

Rename Numbers

Rename the number. Use the place-value chart to help.

Question 1.
760 hundreds = 76,000

Question 2.
805 tens = ________

THOUSANDS			ONES
Hundreds	Tens	Ones	Hundreds	Tens	Ones
		_________	_________	_________	_________

Answer:

THOUSANDS			ONES
Hundreds	Tens	Ones	Hundreds	Tens	Ones
		8	0	5	0

Question 3.
24 ten thousands = ________

THOUSANDS			ONES
Hundreds	Tens	Ones	Hundreds	Tens	Ones
_________	_________	_________	_________	_________	_________

Answer:

THOUSANDS			ONES
Hundreds	Tens	Ones	Hundreds	Tens	Ones
2	4	0	0	0	0

Rename the number.

Question 4.
720 = ____ tens

Answer: 72

Explanation:
720 can be calculated as 72 × 10 = 72 tens.

Question 5.
4 thousands 7 hundreds = 47 ________

Answer: hundreds

Explanation:
4 thousands 7 hundreds
4700 = 47 × 100 = 47 hundreds

Question 6.
25,600 = ____ hundreds

Answer: 256

Explanation:
25,600 = 256 × 100 = 256 hundreds

Question 7.
204 thousands = ____

Answer: 204,000

Explanation:
204 thousands = 204 × 1000 = 204,000.

Problem Solving

Question 8.
For the fair, the organizers ordered 32 rolls of tickets. Each roll of tickets has 100 tickets. How many tickets were ordered in all?
____ tickets

Answer: 3,200 tickets

Explanation:
Given,
For the fair, the organizers ordered 32 rolls of tickets. Each roll of tickets has 100 tickets.
32 × 100 tickets = 3200 tickets
Therefore 3200 tickets were ordered in all.

Question 9.
An apple orchard sells apples in bags of 10. The orchard sold a total of 2,430 apples one day. How many bags of apples was this?
____ bags

Answer: 243 bags

Explanation:
Given,
An apple orchard sells apples in bags of 10. The orchard sold a total of 2,430 apples one day.
2430/10 = 243 bags
There were 243 bags of apples.

Question 10.
Explain how you can rename 5,400 as hundreds. Include a quick picture or a place-value chart in your explanation.
____ hundreds

Answer: 54

Explanation:
It would be 54 hundreds because:
In 5400 there are 2 zeros
Also in 100, there are 2 zeros
2 zeros equals a hundred
100=1 hundred, because it has a 1 in front of the 2 zeros
5400=54 hundreds, because it has a 54 in front of the 2 zeros

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 12

Lesson Check

Question 1.
A dime has the same value as 10 pennies. Marley brought 290 pennies to the bank. How many dimes did Marley get?
Options:
a. 29
b. 290
c. 2,900
d. 29,000

Answer: 29

Explanation:
Given,
A dime has the same value as 10 pennies. Marley brought 290 pennies to the bank.
To find How many dimes did Marley get we have to divide 290 pennies by 10 pennies.
290/10 = 29
Therefore Marley gets 29 pennies.
Thus the correct answer is option a.

Question 2.
A citrus grower ships grapefruit in boxes of 10. One season, the grower shipped 20,400 boxes of grapefruit. How many grapefruit were shipped?
Options:
a. 204
b. 2,040
c. 20,400
d. 204,000

Answer: 204,000

Explanation:
Given,
A citrus grower ships grapefruit in boxes of 10.
One season, the grower shipped 20,400 boxes of grapefruit.
We need to find How many grapefruit were shipped.
Multiply 20,400 boxes with 10.
20,400 × 10 = 204,000
Therefore 204,000 grapefruit were shipped.
Thus the correct answer is option d.

Spiral Review

Question 3.
There were 2,605 people at the basketball game. A reporter rounded this number to the nearest hundred for a newspaper article. What number did the reporter use?
Options:
a. 2,600
b. 2,610
c. 2,700
d. 3,000

Answer: 2,600

Explanation:
Given,
There were 2,605 people at the basketball game. A reporter rounded this number to the nearest hundred for a newspaper article.
To find:
What number did the reporter use?
The number 2605 nearest to the hundred is 2600.
Thus the correct answer is option a.

Question 4.
To get to Level 3 in a game, a player must score 14,175 points. Ann scores 14,205 points, Ben scores 14,089 points, and Chuck scores 10,463 points. Which score is greater than the Level 3 score?
Options:
a. 14,205
b. 14,175
c. 14,089
d. 10,463

Answer: 14,205

Explanation:
Given,
To get to Level 3 in a game, a player must score 14,175 points. Ann scores 14,205 points, Ben scores 14,089 points, and Chuck scores 10,463 points.
By seeing the above points we can say that 14,205 is greater than level 3.
Thus the correct answer is option a.

Question 5.
Henry counted 350 lockers in his school. Hayley counted 403 lockers in her school. Which statement is true?
Options:
a. The 3 in 350 is 10 times the value of the 3 in 403.
b. The 3 in 350 is 100 times the value of the 3 in 403.
c. The 3 in 403 is 10 times the value of the 3 in 350.
d. The 3 in 403 is 100 times the value of the 3 in 350.

Answer: The 3 in 350 is 100 times the value of the 3 in 403.

Explanation:
Given,
Henry counted 350 lockers in his school. Hayley counted 403 lockers in her school.
The statement “The 3 in 350 is 100 times the value of the 3 in 403” is true.
Thus the correct answer is option b.

Question 6.
There are 4 muffins on each plate. There are 0 plates of lemon muffins. How many lemon muffins are there?
Options:
a. 4
b. 2
c. 1
d. 0

Answer: 0

Explanation:
Given,
There are 4 muffins on each plate. There are 0 plates of lemon muffins.
Multiply the number of muffins with the number of plates.
4 × 0 = 0
There are 0 lemon muffins.
Thus the correct answer is option d.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 13

Add Whole Numbers

Estimate. Then find the sum.

Question 1.
Estimate: 90,000

Question 2.
73,404
+ 27,865
————
Estimate: _______
Sum: _______

Answer:
Estimate: 100,000
Sum: 101,269
Estimate:
The number rounded to 73,404 is 70,000.
The number rounded to 27,865 is 30,000.
70,000
+30,000
100,000
Sum:
73,404
+ 27,865
101,269

Question 3.
404,446
+ 396,755
————
Estimate: _______
Sum: _______

Answer:
Estimate: 800,000
Sum: 800,201
Estimate:
The number rounded to 400,000
The number rounded to 400,000
400,000
+400,000
800,000
Sum:
404,446
+ 396,755
800,201

Question 4.
137,638
+ 52,091
————
Estimate: _______
Sum: _______

Answer:
Estimate: 200,000
Sum: 189,729
Estimate:
The number rounded to 150,000
The number rounded to 50,000
150,000
+50,000
200,000
Sum:
137,638
+ 52,091
189,729

Question 5.
200,629
+ 28,542
————
Estimate: _______
Sum: _______

Answer:
Estimate: 250,000
Sum: 229,171
Estimate:
The number rounded to 200,000
The number rounded to 50,000
200,000
+50,000
250,000
Sum:
200,629
+ 28,542
229,171

Question 6.
212,514
+ 396,705
————
Estimate: _______
Sum: _______

Answer:
Estimate: 600,000
Sum: 609,219
Estimate:
The number rounded to 200,000
The number rounded to 400,000
200,000
+400,000
600,000
Sum:
212,514
+ 396,705
609,219

Question 7.
324,867
+ 6,233
————
Estimate: _______
Sum: _______

Answer:
Estimate: 330,000
Sum: 331,100
Estimate:
The number rounded to 324,000
The number rounded to 6,000
324,000
+ 6,000
330,000
Sum:
324,867
+ 6,233
331,100

Question 8.
462,809
+ 256,738
————
Estimate: _______
Sum: _______

Answer:
Estimate: 800,000
Sum: 719,547
Estimate:
The number rounded to 500,000
The number rounded to 300,000
500,000
+300,000
800,000
Sum:
462,809
+ 256,738
719,547

Question 9.
624,836
+ 282,189
————
Estimate: _______
Sum: _______

Answer:
Estimate: 900,000
Sum: 907,025
Estimate:
The number rounded to 600,000
The number rounded to 300,000
600,000
+300,000
900,000
Sum:
624,836
+ 282,189
907,025

Problem Solving

Use the table for 10–12.

Question 10.
Beth and Cade were on one team. What was their total score?
______

Answer: 407,502

Explanation:
The score of Beth is 251,567
The score of Cade is 155,935
251,567
+155,935
407,502
Thus the total score of Beth and Cade is 407,502.

Question 11.
Dillan and Elaine were on the other team. What was their total score?
______

Answer: 409,928

Explanation:
The score of Dillan is 188,983
The score of Elaine is 220,945
188,983
+220,945
409,928
The total score of Dillan and Elaine is 409,928.

Question 12.
Which team scored the most points?
_________

Answer: Dillan and Elaine
The total score of Dillan and Elaine is 409,928.
The total score of Beth and Cade is 407,502.
409,928
-407,502
002,226
Thus Dillan and Elaine team scored the most points.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 14

Lesson Check

Question 1.
The coastline of the United States is 12,383 miles long. Canada’s coastline is 113,211 miles longer than the coastline of the United States. How long is the coastline of Canada?
Options:
a. 100,828 miles
b. 115,594 miles
c. 125,594 miles
d. 237,041 miles

Answer: 125,594 miles

Explanation:
Given,
The coastline of the United States is 12,383 miles long.
Canada’s coastline is 113,211 miles longer than the coastline of the United States.
113,211
+12,383 
125,594
Therefore, the coastline of Canada is 125,594 miles.
Thus the correct answer is option c.

Question 2.
Germany is the seventh largest European country and is slightly smaller by area than Montana. Germany has a land area of 134,835 square miles and a water area of 3,011 square miles. What is the total area of Germany?
Options:
a. 7,846 square miles
b. 131,824 square miles
c. 137,846 square miles
d. 435,935 square miles

Answer: 137,846 square miles

Explanation:
Given,
Germany is the seventh largest European country and is slightly smaller by area than Montana. Germany has a land area of 134,835 square miles and a water area of 3,011 square miles.
134,835
+ 3,011
137,846
Therefore the total area of Germany is 137,846 square miles.
Thus the correct answer is option c.

Spiral Review

Question 3.
In an election, about 500,000 people voted in all. Which number could be the exact number of people who voted in the election?
Options:
a. 429,455
b. 441,689
c. 533,736
d. 550,198

Answer: 533,736

Explanation:
Given,
In an election, about 500,000 people voted in all.
The number near to 500,000 is 533,736.
Thus the correct answer is option c.

Question 4.
In 2007, Pennsylvania had approximately 121,580 miles of public roads. What is 121,580 rounded to the nearest thousand?
Options:
a. 100,000
b. 120,000
c. 121,000
d. 122,000

Answer: 122,000

Explanation:
Given,
In 2007, Pennsylvania had approximately 121,580 miles of public roads.
121,580 rounded to the nearest thousand is 122,000.
Thus the correct answer is option d.

Question 5.
Which of the following lists of numbers is in order from greatest to least?
Options:
a. 33,093; 33,903; 33,309
b. 42,539; 24,995; 43,539
c. 682,131; 628,000; 682,129
d. 749,340; 740,999; 740,256

Answer: 749,340; 740,999; 740,256

Explanation:
a. 33,093; 33,903; 33,309
33,093 = 33,903 = 33,309
b. 42,539; 24,995; 43,539
42,539 > 24,995 < 43,539
c. 682,131; 628,000; 682,129
682,131 > 628,000 < 682,129
d. 749,340; 740,999; 740,256
749,340 > 740,999 > 740,256
Thus the correct answer is option d.

Question 6.
Which symbol makes the following statement true?
$413,115 $431,511
Options:
a. <
b. >
c. =
d. +

Answer: <

Explanation:
The number $413,115 is less than $431,511
$413,115 < $431,511
Thus the correct answer is option a.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 15

Subtract Whole Numbers

Estimate. Then find the difference.

Question 1.

Question 2.
428,731
– 175,842
————-
Estimate: _______
Difference: _______

Answer:
Estimate: 200,000
Difference: 252,889
Estimate:
The number rounded to 428,731 is 400,000
The number rounded to 175,842 is 200,000
400,000
-200,000
200,000
Difference:
428,731
– 175,842
252,889

Question 3.
920,026
– 535,722
————-
Estimate: _______
Difference: _______

Answer:
Estimate: 400,000
Difference: 384,304
Estimate:
The number rounded to 920,026 is 900,000
The number rounded to 535,722 is 500,000
900,000
-500,000
400,000
Difference:
920,026
– 535,722
384,304

Question 4.
253,495
– 48,617
————-
Estimate: _______
Difference: _______

Answer:
Estimate: 200,000
Difference: 204,878
Estimate:
The number rounded to 253,495 is 250,000
The number rounded to 48,617 is 50,000

Subtract. Add to check.

Question 5.
735,249 – 575,388 = ______
______ + ______ = ______

Answer: 159,861
735,249
-575,388 
159,861
Now check whether the answer is correct or wrong.
159,861
+575,388 
735,249

Question 6.
512,724 – 96,473 = ______
______ + ______ = ______

Answer: 416,251
512,724
-96,473 
416,251
Now check whether the answer is correct or wrong.
416,251
96,473
512,724

Question 7.
600,000 – 145,782 = ______
______ + ______ = ______

Answer: 454,218
600,000
-145,782
454,218
Now check whether the answer is correct or wrong.
454,218
+145,782 
600,000

Problem Solving

Use the table for 8 and 9.

Question 8.
How many more people attended the Magic’s games than attended the Pacers’ games?
______ people

Answer: 133,606

Explanation:
Number of people attended Magic’s games = 715,901
Number of people attended Pacers’ games = 582,295
To find:
How many more people attended the Magic’s games than attended the Pacers’ games
We need to subtract the Number of people attended Pacers’ games from the Number of people attended Magic’s games
715,901
-582,295
133,606

Question 9.
How many fewer people attended the Pacers’ games than attended the Clippers’ games?
______ people

Answer: 87,768

Explanation:
Number of people attended Pacers’ games = 582,295
Number of people attended Clippers’ games = 670,063
To find:
How many fewer people attended the Pacers’ games than attended the Clippers’ games
We need to subtract the number of people attended Pacers’ games from the Number of people attended Clippers’ games
670,063
-582,295
87,768

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 16

Lesson Check

Question 1.
This year, a farm planted 400,000 corn stalks. Last year, the farm planted 275,650 corn stalks. How many more corn stalks did the farm plant this year than last year?
Options:
a. 124,350
b. 125,450
c. 235,450
d. 275,650

Answer: 124,350

Explanation:
Given,
This year, a farm planted 400,000 corn stalks.
Last year, the farm planted 275,650 corn stalks.
400,000
-275,650 
124,350
Thus the correct answer is option a.

Question 2.
One machine can make 138,800 small paper clips in one day. Another machine can make 84,250 large paper clips in one day. How many more small paper clips than large paper clips are made by the two machines in one day?
Options:
a. 44,550
b. 54,550
c. 54,650
d. 154,650

Answer: 54,550

Explanation:
Given,
One machine can make 138,800 small paper clips in one day.
Another machine can make 84,250 large paper clips in one day
138,800
-84,250 
54,550
Thus the correct answer is option b.

Spiral Review

Question 3.
In three baseball games over a weekend, 125,429 people came to watch. The next weekend, 86,353 came to watch the games. How many people in all watched
the six baseball games?
Options:
a. 201,782
b. 211,772
c. 211,782
d. 211,882

Answer: 211,782

Explanation:
Given,
In three baseball games over a weekend, 125,429 people came to watch.
The next weekend, 86,353 came to watch the games.
125,429
+86,353 
211,782
Thus the correct answer is option c.

Question 4.
Kevin read the number “two hundred seven thousand, forty-eight” in a book. What is this number in standard form?
Options:
a. 27,048
b. 27,480
c. 207,048
d. 207,480

Answer: 207,048

Explanation:
Given,
Kevin read the number “two hundred seven thousand, forty-eight” in a book.
The standard form of two hundred seven thousand, forty-eight is 207,048.
Thus the correct answer is option c.

Question 5.
A museum had 275,608 visitors last year. What is this number rounded to the nearest thousand?
Options:
a. 275,600
b. 276,000
c. 280,000
d. 300,000

Answer: 276,000

Explanation:
A museum had 275,608 visitors last year.
The number 275,608 rounded to the nearest thousand is 276,000
Thus the correct answer is option b.

Question 6.
At the Millville Theater, a play ran for several weeks. In all, 28,175 people saw the play. What is the value of the digit 8 in 28,175?
Options:
a. 8
b. 800
c. 8,000
d. 80,000

Answer: 8,000

Explanation:
At the Millville Theater, a play ran for several weeks. In all, 28,175 people saw the play.
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 8 in 28,175 is 8000.
Thus the correct answer is option c.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 17

Problem Solving Comparison Problems with Addition and Substraction

Use the information in the table for 1–3.

Question 1.
How many square miles larger is the surface area of Lake Huron than the surface area of Lake Erie?
Think: How can a bar model help represent the problem? What equation can be written?

Question 1.

Question 2.
Which lake has a surface area that is 14,938 square miles greater than the surface area of Lake Ontario? Draw a model and write a number sentence to solve the problem.
_________

Answer:

Explanation:
The surface area of Lake Ontario is 7,340 square miles.
14,938
+7,340
22,278 square miles

Question 3.
Lake Victoria has the largest surface area of all lakes in Africa. Its surface area is 26,828 square miles. How much larger is the surface area of Lake Superior than that of Lake Victoria?
_____ square milles

Answer: 4,872 square miles

Explanation:
The surface area of Lake Victoria is 26,828 square miles.
The surface area of Lake Superior is 31,700 square miles.
31,700
-26,828
04,872
The surface area of Lake Superior is 4,872 square miles larger than Lake Victoria.

Question 4.
At 840,000 square miles, Greenland is the largest island in the world. The second-largest island is New Guinea, at 306,000 square miles. How much larger is Greenland than New Guinea?
_____ square milles

Answer: 534,000 square miles

Explanation:
Given,
At 840,000 square miles, Greenland is the largest island in the world.
The second-largest island is New Guinea, at 306,000 square miles.
840,000
-306,000
534,000
Greenland is 534,000 square miles larger than New Guinea.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 18

Lesson Check

Question 1.
The Mariana Trench in the Pacific Ocean is about 36,201 feet deep. The Puerto Rico Trench in the Atlantic Ocean is about 27,493 feet deep. Based on these data, how many feet deeper is the Mariana Trench than the Puerto Rico Trench?
Options:
a. 8,708 feet
b. 9,718 feet
c. 9,808 feet
d. 63,694 feet

Answer: 8,708 feet

Explanation:
Given,
The Mariana Trench in the Pacific Ocean is about 36,201 feet deep.
The Puerto Rico Trench in the Atlantic Ocean is about 27,493 feet deep.
36,201
-27,493
08,708 feet
Mariana Trench is 8708 feet deeper than the Puerto Rico Trench.
Thus the correct answer is option a.

Question 2.
At 1,932 feet, Crater Lake, Oregon, is the deepest lake in the United States. The world’s deepest lake, Lake Baykal in Russia, is 3,383 feet deeper. How deep is Lake Baykal?
Options:
a. 3,383 feet
b. 4,215 feet
c. 4,315 feet
d. 5,315 feet

Answer: 5,315 feet

Explanation:
At 1,932 feet, Crater Lake, Oregon, is the deepest lake in the United States.
The world’s deepest lake, Lake Baykal in Russia, is 3,383 feet deeper.
3383
+1932
5315
Thus the correct answer is option d.

Spiral Review

Question 3.
Which of the following amounts is greater than $832,458?
Options:
a. $82,845
b. $832,458
c. $823,845
d. $832,485

Answer: $832,485

Explanation:
We have to compare all the options with $832,458
a. $82,845 < $832,458
b. $832,458 = $832,458
c. $823,845 < $832,458
d. $832,485 > $832,458
Thus the correct answer is option d.

Question 4.
A stadium in Pennsylvania seats 107,282 people. A stadium in Arizona seats 71,706 people. Based on these facts, how many more people does the stadium in Pennsylvania seat than the stadium in Arizona?
Options:
a. 35,576
b. 35,586
c. 36,576
d. 178,988

Answer: 35,576

Explanation:
Given,
A stadium in Pennsylvania seats 107,282 people. A stadium in Arizona seats 71,706 people.
107,282
-71,706 
35,576
Thus the correct answer is option a.

Question 5.
Which of the following numbers is 399,713 rounded to the place value of the underlined digit?
Options:
a. 390,000
b. 398,000
c. 399,800
d. 400,000

Answer: 400,000

Explanation:
The number 399,713 rounded to the place value of the underlined digit is 400,000.
Thus the correct answer is option d.

Question 6.
About 400,000 people visited an art museum in December. Which number could be the exact number of people who visited the art museum?
Options:
a. 478,051
b. 452,223
c. 352,483
d. 348,998

Answer: 352,483

Explanation:
About 400,000 people visited an art museum in December.
The number that could be the exact number of people who visited the art museum is 352,483.
Thus the correct answer is option c.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 19

Lesson 1.1

Find the value of the underlined digit.

Question 1.
6,493
____

Answer: 90

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 9 in 6,493 is 90.

Question 2.
16,403
____

Answer: 10,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 1 in 16,403 is 10,000.

Question 3.
725,360
____

Answer: 300

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 725,360 is 300.

Question 4.
952,635
____

Answer: 900,000

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 9 in 952,635 is 900,000.

Compare the values of the underlined digits in 46,395 and 14,906.

Question 5.
The value of 4 in ____ is ____ times the value of 4 in ____.

Answer: The value of 4 in 46,395 is 10 times the value of 4 in 14,906.

Explanation:
Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 4 in 46,395 is 40,000. And the place value of the digit 4 in 14,906 is 4,000. So, the value of 4 in 46,395 is 10 times the value of 4 in 14,906.

Lesson 1.2

Read and write the number in two other forms.

Question 6.
304,001
word form: _______
expanded form: _______

Answer:
word form: three hundred four thousand one
expanded form: 300,000 + 4000 + 1

Explanation:
Convert the number 304,001 into the word form three hundred four thousand one.
The expanded form of 304,001 is 300,000 + 4000 + 1

Question 7.
two hundred eight thousand, five hundred sixty-one
standard form: _______
_______

Answer:
The standard form of two hundred eight thousand, five hundred sixty-one is 208,561.
The expanded form of 208,561 is 200,000 + 8,000 + 500 + 60 + 1

Use the number 751,486.

Question 8.
Write the name of the period that has the digits 486.
_________

Answer: The name of the period that has the digits 486 is Ones.

Question 9.
Write the name of the period that has the digits 751.
_________

Answer: The name of the period that has the digits 751 is thousands.

Question 10.
Write the digit in the thousands place.
The digit in the thousands place: ____

Answer: The digit in the thousands place is 1.

Question 11.
Write the value of the digit 5.
____

Answer: The value of the digit 5 in 751,486 is 50,000.

Lesson 1.3

Compare. Write <, >, or =.

Question 12.
6,930 ____ 7,023

Answer: <

Explanation:
The number 6,930 is less than 7,023
6,930 < 7,023

Question 13.
98,903 ____ 98,930

Answer: <

Explanation:
The number 98,903 is less than 98,930
98,903 < 98,930

Question 14.
549,295 ____ 547,364

Answer: >

Explanation:
The number 549,295 is greater than 547,364
549,295 > 547,364

Order from least to greatest.

Question 15.
$26,940; $25,949; $26,490
Options:
a. $25,949; $26,490; $26,940
b. $26,490; $25,949; $26,940
c. $26,940; $25,949; $26,490

Answer: $25,949; $26,490; $26,940

Explanation:
We have to write the numbers from the least to the greatest.
$25,949 < $26,490 < $26,940
The order from the least to the greatest is $25,949; $26,490; $26,940
Thus the correct answer is option a.

Question 16.
634,943; 639,443; 589,932
Options:
a. 639,443; 589,932; 634,943
b. 634,943; 639,443; 589,932
c. 589,932; 634,943; 639,443

Answer: 589,932; 634,943; 639,443

Explanation:
We have to write the numbers from the least to the greatest.
589,932 < 634,943 < 639,443
The order from the least to the greatest is 589,932; 634,943; 639,443
Thus the correct answer is option c.

Common Core – Place Value, Addition, and Subtraction to One Million – Page No. 20

Lesson 1.4

Round to the place value of the underlined digit.

Question 1.
286,476
____

Answer: 286,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 6 in 286,476 is 286,000.

Question 2.
289,342
____

Answer: 289,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 9 in 289,342 is 289,000.

Question 3.
245,001
____

Answer: 250,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 4 in 245,001 is 250,000.

Question 4.
183,002
____

Answer: 200,000

Explanation:
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.
Change all the digits to the right of the rounding place to zero.
The place value of 1 in 183,002 is 200,000.

Lesson 1.5

Rename the number.

Question 5.
82 thousands = ____

Answer: 82,000

Explanation:
82 thousands = 82 × 1000 = 82,000.

Question 6.
600,000 = ____ ten thousands

Answer: 60

Explanation:
600,000 = 60 × 10000
60 × 10000 = 60 ten thousands

Question 7.
9,200 = ____ hundreds

Answer: 92

Explanation:
9,200 = 92 × 100 = 92 hundreds

Question 8.
8 ten thousands 4 hundreds = ____

Answer: 80,400

Explanation:
8 ten thousands 4 hundreds
8 × 10,000 + 4 × 100 = 80,000 + 400 = 80,400

Lesson 1.6

Estimate. Then find the sum.

Question 9.
94,903
+ 49,995
————
Estimate: ________
Sum: ________

Answer:
Estimate: 140000
Sum: 144898

Explanation:
Estimate:
The number rounded to 94,903 is 90,000
The number rounded to 49,995 is 50,000
90,000
+50,000
140,000
Sum:
94,903
+ 49,995
144,898

Question 10.
420,983
+ 39,932
————
Estimate: ________
Sum: ________

Answer:
Estimate: 460,000
Sum: 460915

Explanation:
Estimate:
The number rounded to 420,983 is 420,000
The number rounded to 39,932 is 40,000
420,000
+40,000
460,000
Sum:
420,983
+39,932
460,915

Question 11.
540,943
+ 382,093
————
Estimate: ________
Sum: ________

Answer:
Estimate: 940,000
Sum: 923036

Explanation:
Estimate:
The number rounded to 540,943 is 540,000
The number rounded to 382,093 is 400,000
540,000
+400,000
940,000
Sum:
540,943
+ 382,093
923,036

Lesson 1.7

Estimate. Then find the difference.

Question 12.
25,953
– 9,745
————
Estimate: ________
Difference: ________

Answer:
Estimate: 15,000
Difference: 16,208

Explanation:
Estimate:
The number rounded to 25,953 is 25,000
The number rounded to 9,745 is 10,000.
25,000
-10,000
15,000
Difference:
25,953
– 9,745
16,208

Question 13.
740,758
– 263,043
————
Estimate: ________
Difference: ________

Answer:
Estimate: 450,000
Difference: 477715

Explanation:
Estimate:
The number rounded to 740,758 is 750,000
The number rounded to 263,043 is 300,000
750,000
-300,000
450,000
Difference:
740,758
– 263,043
477,715

Question 14.
807,632
– 592,339
————
Estimate: ________
Difference: ________

Answer:
Estimate: 200,000
Difference: 215293

Explanation:
Estimate:
The number rounded to 807,632 is 800,000
The number rounded to 592,339 is 600,000
800,000
-600,000
200,000
Difference:
807,632
– 592,339
215293

Lesson 1.8

Question 15.
The attendance for the first game of the football season was 93,584. The attendance for the second game was 104,227. How many more people attended the second game than the first game?
______ people

Answer: 10643 people

Explanation:
Given,
The attendance for the first game of the football season was 93,584.
The attendance for the second game was 104,227.
104,227
-93,584
10,643
Thus, 10,643 more people attended the second game than the first game.

Question 16.
Abby and Lee sold raffle tickets to raise money for a new playground. Abby sold 1,052 tickets. Lee sold 379 more tickets than Abby. How many tickets did Lee sell?
______ tickets

Answer: 1431 tickets

Explanation:
Given,
Abby and Lee sold raffle tickets to raise money for a new playground.
Abby sold 1,052 tickets. Lee sold 379 more tickets than Abby.
1,052
+379 
1431
Therefore, Lee sell 1431 tickets.

Conclusion

All these solutions explained in the Go Math Grade 4 Answer Key Homework Practice FL Chapter 1 Place Value, Addition, and Subtraction to One Million are easy to understand. Check out HMH Go Math Grade 4 Chapter 1 Solution Key to score good grades in the exams. For any queries go through the exercise problems of Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million pdf.

Free PDF Download links of Go Math Grade 4 Answer Key Homework Practice FL Chapter 6 Fraction Equivalence and Comparison are prevailing here for free. Simply refer to them once and make use of the Go Math Grade 4 Chapter 6 Fraction Equivalence and Comparison Answer Key Homework Practice FL to practice all questions covered in the Go Math Grade 4 Chapter 6 Textbook. The biggest goal of preparing these Answer Key Homework Practice FL by our team is to make students understand the concepts and secure well in the exams.

 

Go Math Grade 4 Answer Key Homework Practice FL Chapter 6 Fraction Equivalence and Comparison

Find all step-by-step explanations for every question from these Answer key of grade 4 HMH Go Math Ch 6 Homework Practice FL. Hence, take a look at the list of the toppers recommended HMH Go Math Grade 4 Solution Key for Chapter 6 Fraction Equivalence and Comparison and learn all the basics easily. In Chapter 6 go math HMH grade 4 Solution Key, you will find the topics like Equivalent Fractions, Comparing fractions, pair of fractions as a pair of fractions with a common denominator, and so on.

Lesson: 1 – Equivalent Fractions

• Common Core – Fraction Equivalence and Comparison – Page No. 113
• Common Core – Fraction Equivalence and Comparison – Page No. 114

Lesson: 2

• Common Core – Fraction Equivalence and Comparison – Page No. 115
• Common Core – Fraction Equivalence and Comparison – Page No. 116

Lesson: 3

• Common Core – Fraction Equivalence and Comparison – Page No. 117
• Common Core – Fraction Equivalence and Comparison – Page No. 118

Lesson: 4

• Common Core – Fraction Equivalence and Comparison – Page No. 119
• Common Core – Fraction Equivalence and Comparison – Page No. 120

Lesson: 5

• Common Core – Fraction Equivalence and Comparison – Page No. 121
• Common Core – Fraction Equivalence and Comparison – Page No. 122

Lesson: 6

• Common Core – Fraction Equivalence and Comparison – Page No. 123
• Common Core – Fraction Equivalence and Comparison – Page No. 124

Lesson: 7

• Common Core – Fraction Equivalence and Comparison – Page No. 125
• Common Core – Fraction Equivalence and Comparison – Page No. 126

Lesson: 8

• Common Core – Fraction Equivalence and Comparison – Page No. 127
• Common Core – Fraction Equivalence and Comparison – Page No. 128

Lesson: 9

• Common Core – Fraction Equivalence and Comparison – Page No. 129
• Common Core – Fraction Equivalence and Comparison – Page No. 130

Common Core – Fraction Equivalence and Comparison – Page No. 113

Equivalent Fractions

Use the model to write an equivalent fraction.

Question 1.

\(\frac{4}{6}=\frac{2}{3}\)

Explanation:
The first image has 4 parts shaded out of 6 parts. Divide 8/10 with 2. You will get 2/3. That means 2 parts are shaded out of 3 parts.

Question 2.

\(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer: \(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
The first image has 3 parts shaded out of 4 parts. Multiply 8/10 with 2. You will get 6/8. That means 6 parts are shaded out of 8 parts.

Tell whether the fractions are equivalent. Write = or ≠.

Question 3.
\(\frac{8}{10}\) _____ \(\frac{4}{5}\)

Answer: \(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation:
Multiply the numerator and denominator of 4/5 with 2.
8/10 = (2/2) × (4/5)
= 8/10
So, 8/10 = 4/5.

Question 4.
\(\frac{1}{2}\) _____ \(\frac{7}{12}\)

Answer: \(\frac{1}{2}\) ≠ \(\frac{7}{12}\)

Explanation:
Multiply the numerator and denominator of 1/2 with 6
1/2 = (6/6) x (1/2)
= (6/12)
So, 1/2 ≠ 7/12

Question 5.
\(\frac{3}{4}\) _____ \(\frac{8}{12}\)

Answer: \(\frac{3}{4}\) ≠ \(\frac{8}{12}\)

Explanation:
Multiply the numerator and denominator of 3/4 with 3.
3/4 = (3/3) × (3/4)
= (9/12)
So, 3/4 ≠ 8/12

Question 6.
\(\frac{2}{3}\) _____ \(\frac{4}{6}\)

Answer: \(\frac{2}{3}\) = \(\frac{4}{6}\)

Explanation:
Multiply the numerator and denominator of 2/3 with 2.
2/3 = (2/2) × (2/3)
= 4/6
So, 2/3 = 4/6.

Question 7.
\(\frac{5}{8}\) _____ \(\frac{4}{10}\)

Answer: \(\frac{5}{8}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 5/8 with 2
5 / 8 =(2/2) x (5/ 8)
= (10/16)
So, 5/8 ≠ 4/10

Question 8.
\(\frac{2}{6}\) _____ \(\frac{4}{12}\)

Answer:

Question 9.
\(\frac{20}{100}\) _____ \(\frac{1}{5}\)

Answer: \(\frac{20}{100}\) = \(\frac{1}{5}\)

Explanation:
Cross Multiply the 20/100 with 20/20
20/100 = (20/20) x (20/100)
= (1/5)
So, 20/100 = 1/5.

Question 10.
\(\frac{5}{8}\) _____ \(\frac{9}{10}\)

Answer: \(\frac{5}{8}\) ≠ \(\frac{9}{10}\)

Explanation:
Multiply the numerator and denominator of 5/8 with 2
5/8 = (2/2) x (5/8)
= 10/16
So, 5/8 ≠ 9/10

Question 11.
Jamal finished \(\frac{5}{6}\) of his homework. Margaret finished \(\frac{3}{4}\) of her homework, and Steve finished \(\frac{10}{12}\) of his homework. Which two students finished the same amount of homework?
_________

Answer: Jamal and Steve

Explanation:
As per the given data,
Jamal finished work = 5 /6 of his homework
Margaret finished work = 3 /4th of her homework
Steve finished work = 10/12 of his homework
Multiply the numerator and denominator of 5/6 with 2
Then, (2/2) x (5/6) = 10/12
Then, Jamal and Steve finished the same amount of homework.

Question 12.
Sophia’s vegetable garden is divided into 12 equal sections. She plants carrots in 8 of the sections. Write two fractions that are equivalent to the part of Sophia’s garden that is planted with carrots.
Type below:
_________

Answer: 2/3 and 4/6

Explanation:
As per the given data,
Sophia’s vegetable garden is divided into 12 equal sections
She plants carrots in 8 of the sections out of 12 sections = 8/12
By simplifying the 8/12, we will get 4/6
Again simplify the 4 /6 by dividing method, you will get 2 /3
2/3 = (2/2) x (2/3)
= 4/6
Then, the equivalent fractions are 2/3, 4 /6

Common Core – Fraction Equivalence and Comparison – Page No. 114

Question 1.
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{6}\)
d. \(\frac{3}{4}\)

Answer: \(\frac{1}{4}\)

Explanation:
As per the given data,
A rectangle is divided into 8 equal parts
Two parts are shaded
Then, the shaded area of rectangle = 2/8
By simplifying the 2/8, you will get 1/4
So, the shaded area of rectangle = 1/4
Thus the correct answer is option a.

Question 2.
Jeff uses 3 fifth-size strips to model \(\frac{3}{5}\). He wants to use tenth-size strips to model an equivalent fraction. How many tenth-size strips will he need?
Options:
a. 10
b. 6
c. 5
d. 3

Answer: 6

Explanation:
From the given data,
Jeff uses 3 fifth –size strips to model = 3 / 5 size strips
If he wants to use tenth – size strips to an equivalent fraction = 1 / 10 size strips
The number of strips = x
(1/10) x = 3/5
x = 30/5
then, the required number of tenth size trips = 6
Thus the correct answer is option b.

Question 3.
Cassidy places 40 stamps on each of 8 album pages. How many stamps does she place in all?
Options:
a. 300
b. 320
c. 360
d. 380

Answer: 320

Explanation:
As per the given data,
Cassidy places 40 stamps on each of 8 album pages = 8 x 40 = 320
So, totally placed stamps on album pages by Cassidy = 320 stamps
Thus the correct answer is option b.

Question 4.
Maria and 3 friends have 1,200 soccer cards. If they share the soccer cards equally, how many will each person receive?
Options:
a. 30
b. 40
c. 300
d. 400

Answer: 300

Explanation:
As per the given data,
Maria and 3 friends have 1200 soccer cards
If soccer cards shared equally by four members = 1200/4 = 300
Then, each person received soccer cards = 300
Thus the correct answer is option c.

Question 5.
Six groups of students sell 162 balloons at the school carnival. There are 3 students in each group. If each student sells the same number of balloons, how many balloons does each student sell?
Options:
a. 9
b. 18
c. 27
d. 54

Answer: 9

Explanation:
As per the given, data,
Six groups of students sell 162 balloons at the school carnival
There are 3 students in each group
Then, total number of students in 6 groups = 6 x 3 = 18
If each student sells the same number of balloons = 162 / 18 = 9
Number of balloons sells by each student = 9
Thus the correct answer is option a.

Question 6.
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
Who made an error and included a composite number?
Options:
a. Eric
b. Maya
c. Bella
d. Jordan

Answer: Jordan

Explanation:
As per the given data,
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
21 is not a prime number.
So, An error made by Jordan.
Thus the correct answer is option d.

Common Core – Fraction Equivalence and Comparison – Page No. 115

Write two equivalent fractions for each.

Question 1.

Question 2.
\(\frac{2}{3}\)
Type below:
_________

Answer: 4/6 and 8/12

Explanation:
2/3
(2/3) x (2/2) = 4/6
(2/3) x (4/4) = 8/12
Then, the equivalent fractions of 2/3 = 4/6 and 8/12

Question 3.
\(\frac{1}{2}\)
Type below:
_________

Answer: 2/4 and 4/8

Explanation:
1/2
(1/2) x (2/2) = 2/4
(1/2) x (4/4) = 4/8
Then, the equivalent fractions of 1/2 = 2/4, 4/8

Question 4.
\(\frac{4}{5}\)
Type below:
_________

Answer: 8/10 and 80/100

Explanation:
4/5
(4/5) x (2/2) = 8/10
(4/5) x (20/20) = 80/100
Then, the equivalent fractions of 4/5 = 8/10 and 80/100

Tell whether the fractions are equivalent. Write # or ≠.

Question 5.
\(\frac{1}{4}\) _____ \(\frac{3}{12}\)

Answer: \(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
So, 1/4 = 3/12

Question 6.
\(\frac{4}{5}\) _____ \(\frac{5}{10}\)

Answer: \(\frac{4}{5}\) ≠ \(\frac{5}{10}\)

Explanation:
4/5
Multiply numerator and denominator of 4/5 with 2
(4/5) x (2/2) = 8/10
Then 4/5 ≠ 5/10

Question 7.
\(\frac{3}{8}\) _____ \(\frac{2}{6}\)

Answer: \(\frac{3}{8}\) ≠ \(\frac{2}{6}\)

Explanation:
3/8 ≠ 2/6

Question 8.
\(\frac{3}{4}\) _____ \(\frac{6}{8}\)

Answer: \(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
Then, (3/4) x (2/2) = 6/8
So, 3/4 = 6/8

Question 9.
\(\frac{5}{6}\) _____ \(\frac{10}{12}\)

Answer: \(\frac{5}{6}\) = \(\frac{10}{12}\)

Explanation:
5/6
Multiply the numerator and denominator with 2
(5/6) x (2/2) = 10/12
So, 5/6 = 10/12

Question 10.
\(\frac{6}{12}\) _____ \(\frac{5}{8}\)

Answer: \(\frac{6}{12}\) ≠ \(\frac{5}{8}\)

Explanation:
6/12 ≠ 5/8

Question 11.
\(\frac{2}{5}\) _____ \(\frac{4}{10}\)

Answer: \(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 2
(2/5) x (2/2) = 4/10
So, 2/5 = 4/10

Question 12.
\(\frac{2}{4}\) _____ \(\frac{3}{12}\)

Answer: \(\frac{2}{4}\) ≠ \(\frac{3}{12}\)

Explanation:
2/4
Multiply the numerator and denominator of 2/4 with 3
(2/4) x (3/3) = 6/12
So, 2/4 ≠ 3/ 12

Question 13.
Jan has a 12-ounce milkshake. Four ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fraction of the milkshake that is vanilla?
Type below:
_________

Answer: 1/3 and 2/6

Explanation:
As per the given data,
Jan has a 12-ounce milkshake
Four ounces in the milkshake are vanilla = 4/12 = 1/3
Then, 8-ounces in milkshake are chocolate = 8/12 = 2/3
4/12 = 1/3
By multiplying 1/3 with 2
(1/3) x (2/2) = 2/6
So, the equivalent fractions of vanilla milkshake are 1/3 and 2/6.

Question 14.
Kareem lives \(\frac{4}{10}\) of a mile from the mall. Write two equivalent fractions that show what fraction of a mile Kareem lives from the mall.
Type below:
_________

Answer: 2/5 and 8/20

Explanation:
As per the given data,
Kareem lives 4/10 of a mile from the mall
To find the equivalent fractions of 4/10
Simplify the 4/10 = 2/5
Multiply the numerator and denominator of 2/5 with 4
(2/5) x (4/4) = 8/20
Then, the equivalent fraction of a mile Kareem lives from the mall = 2/5 and 8/20

Common Core – Fraction Equivalence and Comparison – Page No. 116

Question 1.
Jessie colored a poster. She colored \(\frac{2}{5}\) of the poster red. Which fraction is equivalent to \(\frac{2}{5}\) ?
Options:
a. \(\frac{4}{10}\)
b. \(\frac{7}{10}\)
c. \(\frac{4}{5}\)
d. \(\frac{2}{2}\)

Answer: \(\frac{4}{10}\)

Explanation:
As per the given data,
Jessie colored a poster
She colored 2/5th of the poster red
Multiply the numerator and denominator of 2/5 with 2
Then, (2/5) x (2/2) = 4 /10
So, the equivalent fraction of 2/5 is 4/10.
Thus the correct answer is option a.

Question 2.
Jessie colored a poster. She colored \(\frac{1}{4}\) of the poster red. Which fraction is equivalent to \(\frac{1}{4}\) ?
Options:
a. \(\frac{2}{5}, \frac{3}{12}\)
b. \(\frac{2}{8}, \frac{4}{12}\)
c. \(\frac{3}{4}, \frac{6}{8}\)
d. \(\frac{2}{8}, \frac{3}{12}\)

Answer: \(\frac{2}{8}, \frac{3}{12}\)

Explanation:
As per the given data,
Marcus makes a punch that is 1/4th of cranberry juice
Multiply the numerator and denominator of 1/4 with 2
Then, (1/4) x (2/2) = 2/8
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
Equivalent fractions of 1/4 are 2/8 and 3/12.
Thus the correct answer is option d.

Question 3.
An electronics store sells a large flat screen television for $1,699. Last month, the store sold 8 of these television sets. About how much money did the store make on the television sets?
Options:
a. $160,000
b. $16,000
c. $8,000
d. $1,600

Answer: $16,000

Explanation:
As per the given data,
An electronics store sells a large flat-screen television for $1,699
Last month, the store sold 8 of these television sets = 8 x $1,699 = $13,952. The money is about to $16,000.
Thus the correct answer is option b.

Question 4.
Matthew has 18 sets of baseball cards. Each set has 12 cards. About how many baseball cards does Matthew have in all?
Options:
a. 300
b. 200
c. 150
d. 100

Answer: 200

Explanation:
From the given data,
Matthew has 18 sets of basketball cards
Each set has 12 cards = 12 x 18 = 216
Total number of basketball cards with Matthew = 216.
So, it is near to 200.
Thus the correct answer is option b.

Question 5.
Diana had 41 stickers. She put them in 7 equal groups. She put as many as possible in each group. She gave the leftover stickers to her sister. How many stickers did Diana give to her sister?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 6

Explanation:
As per the given data,
Diana has 41 stickers
She put them in 7 equal groups = 41/7
= 5 (remaining 6)
She gave the leftover stickers to her sister
The number of stickers Diana give to her sister = 6
Thus the correct answer is option d.

Question 6.
Christopher wrote the number pattern below. The first term is 8.
8, 6, 9, 7, 10, …
Which is a rule for the pattern?
Options:
a. Add 2, add 3.
b. Add 6, subtract 3.
c. Subtract 6, add 3.
d. Subtract 2, add 3

Answer: Subtract 2, add 3

Explanation:
From the given data,
Christopher wrote the number pattern = 8, 6, 9, 7, 10, …..
The first number in the pattern = 8
8 – 2 = 6 + 3 = 9 – 2 = 7 +3 = 10 ….
So, the rule for the above pattern is to subtract 2, add 3.
Thus the correct answer is option d.

Common Core – Fraction Equivalence and Comparison – Page No. 117

Write the fraction in simplest form.

Question 1.

Explanation:
To write the 6/10 in a simplest form
Divide the numerator and denominator of 6/10 with 2
(6 ÷2)/(10 ÷2) = 3/5
So, the simplest form of 6/10 = 3/5

Question 2.
\(\frac{6}{8}\) = \(\frac{□}{□}\)

Answer: \(\frac{3}{4}\)

Explanation:
To write the 6/8in a simplest form
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, the simplest form of 6/8 = 3/4

Question 3.
\(\frac{5}{5}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 5/5in a simplest form
Divide the numerator and denominator of 5/5 with 5
(5 ÷5)/(5 ÷5) = 1/1
So, the simplest form of 5/5 = 1

Question 4.
\(\frac{8}{12}\) = \(\frac{□}{□}\)

Answer: \(\frac{2}{3}\)

Explanation:
To write the 8/12in a simplest form
Divide the numerator and denominator of 8/12 with 4
(8 ÷4)/(12 ÷4) = 2/3
So, the simplest form of 8/12 = 2/3

Question 5.
\(\frac{100}{100}\) = \(\frac{□}{□}\)

Answer: 1

Explanation:
Any number divided by the same number will be always equal to 1.
The simplest form of 100/100 = 1

Question 6.
\(\frac{2}{6}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{3}\)

Explanation:
To write the 2/6in a simplest form
Divide the numerator and denominator of 2/6 with 2
(2 ÷2)/(6 ÷2) = 1/3
So, the simplest form of 2/6 = 1/3

Question 7.
\(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{4}\)

Explanation:
To write the 2/8in a simplest form
Divide the numerator and denominator of 2/8 with 2
(2 ÷2)/(8 ÷2) = 1/4
So, the simplest form of 2/8 = 1/4

Question 8.
\(\frac{4}{10}\) = \(\frac{□}{□}\)

Answer: \(\frac{2}{5}\)

Explanation:
To write the 4/10 in a simplest form
Divide the numerator and denominator of 4 /10 with 2
(4 ÷2)/(10 ÷2) = 2/5
So, the simplest form of 4/10 = 2/5

Tell whether the fractions are equivalent. Write = or ≠. (if you dont have ≠on your keyboard, copy and paste this one: ≠ )

Question 9.
\(\frac{6}{12}\) ______ \(\frac{1}{12}\)

Answer: \(\frac{6}{12}\) ≠ \(\frac{1}{12}\)

Explanation:
6/12 ≠ 1/12

Question 10.
\(\frac{3}{4}\) ______ \(\frac{5}{6}\)

Answer: \(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) ______ \(\frac{3}{5}\)

Answer: \(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/( 10 ÷ 2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{3}{12}\) ______ \(\frac{1}{3}\)

Answer: \(\frac{3}{12}\) ≠ \(\frac{1}{3}\)

Explanation:
3/12 ≠ 1/3

Question 13.
\(\frac{6}{10}\) ______ \(\frac{60}{100}\)

Answer: \(\frac{6}{10}\) = \(\frac{60}{100}\)

Explanation:
6/10
Multiply the numerator and denominator of 6/10 with 10
(6 x 10)/(10 x 10) = 60/100
So, 6/10 = 60/100

Question 14.
\(\frac{11}{12}\) ______ \(\frac{9}{10}\)

Answer: \(\frac{11}{12}\) ≠ \(\frac{9}{10}\)

Explanation:
11/12 ≠ 9/10

Question 15.
\(\frac{2}{5}\) ______ \(\frac{8}{20}\)

Answer: \(\frac{2}{5}\) = \(\frac{8}{20}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 4
(2 x 4)/(5 x 4) = 8/20
So, 2/5 = 8/20

Question 16.
\(\frac{4}{8}\) ______ \(\frac{1}{2}\)

Answer: \(\frac{4}{8}\) = \(\frac{1}{2}\)

Explanation:
4/8
Divide the numerator and denominator of 4/8 with 4
(4 x 4)/(8 x 4) = 1/2
So, 4/8 = 1/2

Question 17.
At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys. In simplest form, what fraction of the babies born on Tuesday were boys?
\(\frac{□}{□}\)

Answer: \(\frac{3}{4}\)

Explanation:
As per the given data,
At the memorial hospital, 9 of the 12 babies born on Tuesday were boys = 9/12
Divide the numerator and denominator of 9/12 with 3
(9 ÷ 3)/(12 ÷ 3) = 3/4
So, in the simplest form
3/4 of the babies born on Tuesday were boys.

Question 18.
Cristina uses a ruler to measure the length of her math textbook. She says that the book is \(\frac{4}{10}\) meter long. Is her measurement in simplest form? If not, what is the length of the book in simplest form?
\(\frac{□}{□}\)

Answer: \(\frac{2}{5}\)

Explanation:
As per the given data,
Cristiana uses a ruler to measure the length of her math textbook
She says that the book is 4/10meter long
It is not in the simplest form
Divide the numerator and denominator of 4/10 with 2
(4÷ 2)/( 10 ÷ 2) = 2/5
The length of the book in the simplest form = 2/5.

Common Core – Fraction Equivalence and Comparison – Page No. 118

Question 1.
Six out of the 12 members of the school choir are boys. In simplest form, what fraction of the choir is boys?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{6}{12}\)
c. \(\frac{1}{2}\)
d. \(\frac{12}{6}\)

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

Explanation:
As per the given data,
Six out of the 12 members of the school choir are boys = 6/12
To write the simplest form of 6/12, divide the numerator and denominator with 6
Then, (6 ÷ 6)/(12 ÷ 6) = 1/2
In the simplest form, 1/2 of the choir is boys.
Thus the correct answer is option c.

Question 2.
Six out of the 12 members of the school choir are boys. In simplest form, what fraction of the choir is boys?
Options:
a. \(\frac{5}{6}\)
b. \(\frac{6}{8}\)
c. \(\frac{8}{10}\)
d. \(\frac{2}{12}\)

Answer: \(\frac{5}{6}\)

Explanation:
5/6 is in the simplest form
6/8 simplest form = 3/4
8/10 simplest form = 4/5
2/12 simplest form = 1/6
Thus the correct answer is option a.

Question 3.
Each of the 23 students in Ms. Evans’ class raised $45 for the school by selling coupon books. How much money did the class raise in all?
Options:
a. $207
b. $225
c. $1,025
d. $1,035

Answer: $1,035

Explanation:
As per the given data,
Each of the 23 students in Ms. Evan’s class raised $45 for the school by selling coupon books
= 23 x $45
= $1,035
Thus the correct answer is option d.

Question 4.
Which pair of numbers below have 4 and 6 as common factors?
Options:
a. 12, 18
b. 20, 24
c. 28, 30
d. 36, 48

Answer: 36, 48

Explanation:
36, 48
Here, 36 = 4 x 9
= 2 x 2 x 3 x 3
48 = 6 x 8
= 2 x 3 x 4 x 2
Thus the correct answer is option d.

Question 5.
Bart uses \(\frac{3}{12}\) cup milk to make muffins. Which fraction is equivalent to \(\frac{3}{12}\) ?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{1}{2}\)
d. \(\frac{2}{3}\)

Answer: \(\frac{1}{4}\)

Explanation:
As per the given data,
Bart uses 3/12 cup milk to make muffins
Divide the fraction with 3
(3 ÷ 3)/(12 ÷ 3) = 1/4
So, the equivalent fraction for 3/12 = 1/4
Thus the correct answer is option a.

Question 6.
Ashley bought 4 packages of juice boxes. There are 6 juice boxes in each package. She gave 2 juice boxes to each of 3 friends. How many juice boxes does Ashley have left?
Options:
a. 24
b. 22
c. 18
d. 12

Answer: 18

Explanation:
As per the given data,
Ashley bought 4 packages of juice boxes
There are 6 juice boxes in each package = 6 x 4 = 24
She gave 2 juice boxes to each of 3 friends = 2 x 3 = 6 juice boxes
So, 24 – 6 = 18
Total number of juice boxes left with Ashley = 18
Thus the correct answer is option c.

Common Core – Fraction Equivalence and Comparison – Page No. 119

Write the pair of fractions as a pair of fractions with a common denominator.

Question 1.
\(\frac{2}{3} \text { and } \frac{3}{4}\)

Explanation:
2/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
Common multiple of 3 and 4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 3 x 12 ) ÷ ( 4 x 12)
So, common pair of fractions = 8/12 and 9/12

Question 2.
\(\frac{1}{4} \text { and } \frac{2}{3}\)
Type below:
_________

Answer: 3/4 and 8/12

Explanation:
1/4 and 2/3
List the multiples of 4 = 4, 8, 12, 16, 20, …
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
Common multiple of 4 and 3 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 2 x 12 ) ÷ ( 3 x 12)
So, common pair of fractions = 3/12 and 8/12

Question 3.
\(\frac{3}{10} \text { and } \frac{1}{2}\)
Type below:
_________

Answer: 3/10 and 5/10

Explanation:
3/10 and 1/2
List the multiples of 10 = 10, 20, 30, 40, 50, ….
List the multiples of 2 = 2, 4, 6, 8, 10, 12, 14, ….
Common multiple of 10 and 2 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 10 x 10) and ( 1 x 10 ) ÷ ( 2 x 10)
So, common pair of fractions = 3/10 and 5/10

Question 4.
\(\frac{3}{5} \text { and } \frac{3}{4}\)
Type below:
_________

Answer: 12/20 and 15/20

Explanation:
3/5 and 3/4
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
Common multiple of 5 and 4 is 20
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 20) ÷( 5 x 20) and ( 3 x 20 ) ÷ ( 4 x 20)
So, common pair of fractions = 12/20 and 15/20

Question 5.
\(\frac{2}{4} \text { and } \frac{7}{8}\)
Type below:
_________

Answer: 4/8 and 7/8

Explanation:
2/4 and 7/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 8 = 8, 16, 24, 32, 40, ….
Common multiple of 4 and 8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 8) ÷( 4 x 8) and ( 7 x 8 ) ÷ ( 8 x 8)
So, common pair of fractions = 4/8 and 7/8

Question 6.
\(\frac{2}{3} \text { and } \frac{5}{12}\)
Type below:
_________

Answer: 8/12 and 5/12

Explanation:
2/3 and 5/12
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 12 = 12, 24, 36, 48, 60, …
Common multiple of 3 and 12 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 5 x 12 ) ÷ ( 12 x 12)
So, common pair of fractions = 8/12 and 5/12

Question 7.
\(\frac{1}{4} \text { and } \frac{1}{6}\)
Type below:
_________

Answer: 3/12 and 2/12

Explanation:
1/4 and 1/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, …
Common multiple of 4 and 6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 1 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 2/12.

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{1}{2}\) ______ \(\frac{2}{5}\)

Answer: \(\frac{1}{2}\) ≠ \(\frac{2}{5}\)

Explanation:
Multiply the numerator and denominator of 1/2 with 2
(1 x 2) ÷ (2 x 2) = 2/4
So, 1/2 ≠ 2/5

Question 9.
\(\frac{1}{2}\) ______ \(\frac{3}{6}\)

Answer: \(\frac{1}{2}\) = \(\frac{3}{6}\)

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 3
(1 x 3) ÷ (2 x 3) = 3/6
So, 1/2 = 3/6

Question 10.
\(\frac{3}{4}\) ______ \(\frac{5}{6}\)

Answer: \(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) ______ \(\frac{3}{5}\)

Answer: \(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/(10 ÷2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{6}{8}\) ______ \(\frac{3}{4}\)

Answer: \(\frac{6}{8}\) = \(\frac{3}{4}\)

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, 6/8 = 3/4

Question 13.
\(\frac{3}{4}\) ______ \(\frac{2}{3}\)

Answer: \(\frac{3}{4}\) ≠ \(\frac{2}{3}\)

Explanation:
3/4 ≠ 2/3

Question 14.
\(\frac{2}{10}\) ______ \(\frac{4}{5}\)

Answer: \(\frac{2}{10}\) ≠ \(\frac{4}{5}\)

Explanation:
2/10
Divide the numerator and denominator of 2/10 with 8
(8 ÷ 2)/(10 ÷ 2) = 4/5
So, 2/10 ≠ 4/5

Question 15.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer: \(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
(1 x 3)/(4 x 3) = 3/12
So, 1/4 = 3/12

Question 16.
Adam drew two same size rectangles and divided them into the same number of equal parts. He shaded \(\frac{1}{3}\) of one rectangle and \(\frac{1}{4}\) of other rectangle. What is the least number of parts into which both rectangles could be divided?
_________

Answer: 12 parts

Explanation:
As per the given data,
Adam drew two same size rectangles and divided them into the same number of equal parts
He shaded 1/3 of one rectangle
1/4 of another rectangle
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
A common multiple of 3 and 4 is 12
So, the least number of parts which rectangles could be divided = 12 parts

Question 17.
Mera painted equal sections of her bedroom wall to make a pattern. She painted \(\frac{2}{5}\) of the wall white and \(\frac{1}{2}\) of the wall lavender. Write an equivalent fraction for each using a common denominator.
Type below:
_________

Answer: 1/2 are 4/10 and 5/10

Explanation:
As per the given data,
Mera painted equal sections of her bedroom wall to make a pattern
She painted 2/5 of the wall white and 1/2 of the wall lavender
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
List the multiples of 2 = 2 ,4, 6, 8, 10, 12, 14, …
The common denominator of 2/5 and 1/2 = 10
Multiply the 2/5 and 1/2 with 10
(2 x 10)/(5 x 10) and (1 x 10)/(2 x 10)
4/10 and 5/10
So, common fractions of 2/5 and 1/2 are 4/10 and 5/10.

Common Core – Fraction Equivalence and Comparison – Page No. 120

Question 1.
Which of the following is a common denominator of \(\frac{1}{4}\) and \(\frac{5}{6}\) ?
Options:
a. 8
b. 9
c. 12
d. 15

Answer: 12

Explanation:
The common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, ….
So, the common denominator of 1/4 and 5/6 is 12
The correct answer is option c.

Question 2.
Two fractions have a common denominator of 8. Which of the following could be the two fractions?
Options:
a. \(\frac{1}{2} \text { and } \frac{2}{3}\)
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)
c. \(\frac{3}{4} \text { and } \frac{1}{6}\)
d. \(\frac{1}{2} \text { and } \frac{4}{5}\)

Answer: \(\frac{1}{4} \text { and } \frac{1}{2}\)

Explanation:
As per the given data,
Two fractions have a common denominator of 8
a. 1/2 and 2/3
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 3 = 3, 6, 9, 12, …
There is no common denominator of 8 for 1/2 and 2/3
b. 1/4 and 1 /2
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 4 = 4, 8, 12, 16, …
Here, the common denominator of 1 /4 and 1 /2 is 8
So, the answer is 1/4 and 1/2
The correct answer is option b.

Question 3.
Which number is 100,000 more than seven hundred two thousand, eighty-three?
Options:
a. 703,083
b. 712,083
c. 730,083
d. 802,083

Answer: 802,083

Explanation:
100,000 + 702,083 = 802,083
The correct answer is option d.

Question 4.
Aiden baked 8 dozen muffins. How many total muffins did he bake?
Options:
a. 64
b. 80
c. 96
d. 104

Answer: 96

Explanation:
As per the given data,
Aiden baked 8 dozen muffins
1 dozen = 12
then, 8 dozens = 12 x 8 = 96
So, Aiden baked total 96 muffins.
The correct answer is option c.

Question 5.
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourthgrade students in her school. She put the photos in 5 equal rows. How many photos did she put in each row?
Options:
a. 21
b. 23
c. 25
d. 32

Answer: 23

Explanation:
As per the given data,
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth-grade students in her school
She put the photos in 5 equal rows
Then, number of photos in each row = 115/5 = 23
So, Ms. Gomez put photos in each row = 23
The correct answer is option b.

Question 6.
Judy uses 12 tiles to make a mosaic. Eight of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{4}\)
d. \(\frac{12}{18}\)

Answer: \(\frac{2}{3}\)

Explanation:
As per the given data,
Judy uses 12 tiles to make a mosaic
Eight of the tiles are blue = 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
The simplest form of 8/12 is 2/3
The correct answer is option a.

Common Core – Fraction Equivalence and Comparison – Page No. 121

Question 1.
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red?

Explanation:
Miranda is braiding her hair. Then she will attach beads to the braid. She wants 1/3 of the beads to be red. If the greatest number of beads that will fit on the braid is 12.
1/3 × 2/2 = 2/6
1/3 × 3/3 = 3/9
1/3 × 4/4 = 4/12

Question 2.
Ms. Groves has trays of paints for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction of the colors in 20 trays is purple?
\(\frac{□}{□}\)

Answer: \(\frac{1}{5}\)

Explanation:
Given,
Ms. Groves has trays of paints for students in her art class.
Each tray has 5 colors.
If you have 20 trays that are 100 colors with 20 being purple. 20/ 100 is 1/5.

Question 3.
Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle?
Type below:
_________

Answer: 1/3, 1/2, 2/3 and final locations

Explanation:
We have three fractions with different denominators: sixths, thirds, and halves.
The first step is to make all the denominators equal for 1/6, 1/3, 1/2.
In this case, we want sixths since LCM(2, 3, 6) = 6
since 1/3 = 2/6, and 1/2 = 3/6. Now we can start solving.
1. There are six tires at the following: 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6.
2. There are three cones at the following (G.C.F.): 2/6 (or 1/3), 4/6 (or 2/3), and 6/6 (or 3/3).
3. There are two hurdles at the following (G.C.F.): 3/6 (or 1/2) and 6/6 (or 2/2).
We look for common numbers.
1. On 2/6, there are two obstacles: a tire and a cone.
2. On 3/6, there are two obstacles: a tire and a hurdle.
3. On 4/6, there are two obstacles: a tire and a cone.
4. At 6/6, there are three obstacles: a tire, cone, and a hurdle.
2/6 = 1/3
3/6 = 1/2
4/6 = 2/3
6/6 = 1
The answers are 1/3, 1/2, 2/3, and 1.

Question 4.
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.

How many blueberry muffins should Preston put in a box with 36 muffins?
_________

Answer: 12 blueberry muffins

Explanation:
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.
So, he had 2 blueberry muffins out of 6 muffins.
2/6 × 2/2 = 4/12. 4 blueberry muffins out of 12 muffins.
2/6 × 4/4 = 8/24. 8 blueberry muffins out of 24 muffins.
2/6 × 6/6 = 12/36. 12 blueberry muffins out of 36 muffins.

Common Core – Fraction Equivalence and Comparison – Page No. 122

Question 1.
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade, how many books can she get from the store?
Options:
a. 9
b. 12
c. 18
d. 27

Answer: 12

Explanation:
A used bookstore will trade 2 of its books for 3 of yours.
If Val brings in 18 books to trade 2/3 × 6/6 = 12/18, she gets 12 books.
Thus the correct answer is option b.

Question 2.
Every \(\frac{1}{2}\) hour Naomi stretches her neck; every \(\frac{1}{3}\) hour she stretches her legs; and every \(\frac{1}{6}\) hour she stretches her arms. Which parts of her body will Naomi stretch when \(\frac{2}{3}\) of an hour has passed?
Options:
a. neck and legs
b. neck and arms
c. legs and arms
d. none

Answer: legs and arms

Explanation:
Summing \(\frac{1}{2}\)‘s only gives integer values giving 1, 2, 3, 4…or
integer values +\(\frac{1}{2}\) and 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\), 1 \(\frac{1}{2}\), 2 \(\frac{1}{2}\)…
So neck is excluded
Every \(\frac{1}{3}\): \(\frac{1}{3}\) + \(\frac{1}{2}\) = \(\frac{2}{3}\)
Legs will be stretched at \(\frac{2}{3}\) hour
Every \(\frac{1}{6}\): \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{4}{6}\)
Divide top and bottom by 2 giving:
(4 ÷ 2)/(6 ÷ 2) = \(\frac{2}{3}\)
Arms will be stretched at \(\frac{2}{3}\) hour.
Thus the correct answer is option c.

Question 3.
At the beginning of the year, the Wong family car had been driven 14,539 miles. At the end of the year, their car had been driven 21,844 miles. How many miles did the Wong family drive their car during that year?
Options:
a. 6,315 miles
b. 7,295 miles
c. 7,305 miles
d. 36,383 miles

Answer: 7,305 miles

Explanation:
If at the beginning of the year, the Wong family’s car had driven 14539 miles and at the end of the year, it had driven 21844 miles, then subtract 14539 from 21844 to determine the difference between the two values, which will tell you how many miles the Wong family drove their car for during the year.
21844 – 14539 = 7305 miles
Thus the correct answer is option c.

Question 4.
Widget Company made 3,600 widgets in 4 hours. They made the same number of widgets each hour. How many widgets did the company make in one hour?
Options:
a. 80
b. 90
c. 800
d. 900

Answer: 900

Explanation:
3,600 widgets in 4 hours therefore 3,600 / 4 for one hour = 900 widgets 900 widgets in one hour.
Thus the correct answer is option d.

Question 5.
Tyler is thinking of a number that is divisible by 2 and by 3. By which of the following numbers must Tyler’s number also be divisible?
Options:
a. 6
b. 8
c. 9
d. 12

Answer: 6

Explanation:
The number 6 is divisible by 2 and by 3.
Thus the correct answer is option a.

Question 6.
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. Which fraction is equivalent to the part of the circle that is shaded?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{3}{4}\)
c. \(\frac{10}{16}\)
d. \(\frac{12}{18}\)

Answer: \(\frac{3}{4}\)

Explanation:
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts.
6/8 = 3/4
Thus the correct answer is option b.

Common Core – Fraction Equivalence and Comparison – Page No. 123

Compare. Write < or > .

Question 1.

Answer:
18 < 610
Explanation:

Question 2.
\(\frac{4}{12}\) ______ \(\frac{4}{6}\)

Answer:
4/12 < 4/6

Explanation:
4/12 and 4/6
4/12 is less than 1/2
4/6 is greater than 1/2
So, 4/12 < 4/6

Question 3.
\(\frac{2}{8}\) ______ \(\frac{1}{2}\)

Answer:
2/8 < 1/2

Explanation:
2/8 and 1/2
2/8 is less than 1/2
1/2 is equal to 1/2
So, 2/8 < 1/2

Question 4.
\(\frac{3}{5}\) ______ \(\frac{3}{3}\)

Answer:
3/5 < 3/3

Explanation:
3/5 and 3/3
3/5 is greater than 1/2
3/3 is equal to 1
So, 3/5 < 3/3

Question 5.
\(\frac{7}{8}\) ______ \(\frac{5}{10}\)

Answer:
7/8 > 5/10

Explanation:
7/8 and 5/10
7/8 is greater than 1/2
5/10 is equal to 1/2
So, 5/10 < 7/8

Question 6.
\(\frac{9}{12}\) ______ \(\frac{1}{3}\)

Answer:
9/12 > 1/3

Explanation:
9/12 and 1/3
9/ 12 is greater than 1/2
1/3 is less than 1/2
1/3 < 9/12

Question 7.
\(\frac{4}{6}\) ______ \(\frac{7}{8}\)

Answer:
4/6 < 7/8

Explanation:
4/6 and 7/8
4/6 is greater than 1/2
7/8 is closer to 1
So, 4/6 < 7/8

Question 8.
\(\frac{2}{4}\) ______ \(\frac{2}{3}\)

Answer:
2/4 < 2/3

Explanation:
2/4 and 2/3
2/4 is equal to 1/2
2/3 is greater than 1/2
So, 2/4 < 2/3

Question 9.
\(\frac{3}{5}\) ______ \(\frac{1}{4}\)

Answer: 35 > 14

Explanation:
3/5 and 1/4
3/5 is greater than 1/2
1/4 is less than 1/2
So, 1/4 < 3/5

Question 10.
\(\frac{6}{10}\) ______ \(\frac{2}{5}\)

Answer:
6/10 > 2/5

Explanation:
6/10 and 2/5
6/10 is greater than 1/2
2/5 is less than 1/2
So, 2/5 < 6/10

Question 11.
\(\frac{1}{8}\) ______ \(\frac{2}{10}\)

Answer:
1/8 < 2/10

Explanation:
1/8 and 2/10
1/8 is less than 1/2
2/10 is less than 1/2 but greater than 1/8
So, 1/8 < 2/10

Question 12.
\(\frac{2}{3}\) ______ \(\frac{5}{12}\)

Answer:
2/3 > 5/12

Explanation:
2/3 and 5/12
2/3 is greater than 1/2
5/12 is less than 1/2
So, 5/12 < 2/3

Question 13.
\(\frac{4}{5}\) ______ \(\frac{5}{6}\)

Answer:
4/5< 5/6

Explanation:
4/5 and 5/6
4/5 is greater than 1/2
5/6 is greater than 1/2
Common denominator is 30
(4×6)/(5×6) and (5×5)/(6×5)
24/30 and 25/30
24/30 < 25/30
So, 4/5 < 5/6

Question 14.
\(\frac{3}{5}\) ______ \(\frac{5}{8}\)

Answer:
3/5 < 5/8

Explanation:
3/5 and 5/8
3/5 is greater than 1/2
5/8 is greater than 1/2
Common denominator is 40
(3×8)/(5×8) and (5×5)/(8×5)
24/40 and 25/ 40
24/40 < 25/40
3/5 < 5/8

Question 15.
\(\frac{8}{8}\) ______ \(\frac{3}{4}\)

Answer:
8/8 > 3/4

Explanation:
8/8 and 3/4
8/8 is equal to 1
3/4 is less than 1
3/4 < 8/8

Question 16.
Erika ran \(\frac{3}{8}\) mile. Maria ran \(\frac{3}{4}\) mile. Who ran farther?
__________

Answer: Maria

Explanation:
As per the data,
Erika ran 3/8 mile
Maria ran 3/4 mile
Multiply the numerator and denominator of 3/4 with 2
(3×2)/(4×2) = 6/8
3/8 < 6/8
So, 3/8 < 3/4
So, Maria ran faster than Erika

Question 17.
Carlos finished \(\frac{1}{3}\) of his art project on Monday. Tyler finished \(\frac{1}{2}\) of his art project on Monday. Who finished more of his art project on Monday?
__________

Answer:
Tyler

Explanation:
From the given data,
Carlos finished 1/3 of his art project on Monday
Tyler finished ½ of his art project on Monday
1/3 is less than 1/2
1/2 is equal to 1/2
So, 1/3 < 1/2
Then, Tyler finished more of his work on Monday

Common Core – Fraction Equivalence and Comparison – Page No. 124

Question 1.
Which symbol makes the statement true?

Options:
a. >
b. <
c. =
d. none

Answer:
a. >

Explanation:
4/6 ? 3/8
By comparing 4/6 with 1/2, 4/6 > 1/2
By comparing 3/8 with 1/2, 3/8 < 1/2
So, 4/6 > 3/8
Thus the correct answer is option a.

Question 2.
Which of the following fractions is greater than \(\frac{3}{4}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{5}{6}\)
c. \(\frac{3}{8}\)
d. \(\frac{2}{3}\)

Answer: b. 5/6

Explanation:
From the given data,
By comparing the 3/4 with 1/2, 3/4 > 1/2
Same as above, compare the options with ½
a. 1/4 < 1/2
b. 5/6 > 1/2
c. 3/8 < 1/2
d. 2/3 > 1/2
5/6 and 2/3 are greater than the 1/2
So, compare the 5/6 with 2/3
Then, 5/6 > 2/3
So, 5/6 > 3/4
Thus the correct answer is option b.

Question 3.
Abigail is putting tiles on a table top. She needs 48 tiles for each of 8 rows. Each row will have 6 white tiles. The rest of the tiles will be purple. How many purple tiles will she need?
Options:
a. 432
b. 384
c. 336
d. 48

Answer:
c. 336

Explanation:
As per the given data
Abigail is putting tiles on a table top
Number of rows = 8
She needs 48 tiles for each of row = 48×8 = 384
Number of white tiles per row = 6×8 = 48
The rest of the tiles will be purple = 384 – 48 =336
So, the total number of purple color tiles = 336
Thus the correct answer is option c.

Question 4.
Each school bus going on the field trip holds 36 students and 4 adults. There are 6 filled buses on the field trip. How many people are going on the field trip?
Options:
a. 216
b. 240
c. 256
d. 360

Answer:
b. 240

Explanation:
From the given data,
Each school bus going on the field trip holds 36 students and 4 adults
There are 6 filled buses on the field trip
6 x (36 + 4) = 6 x 40 = 240
So, the total number of people on the field trip = 240
Thus the correct answer is option b.

Question 5.
Noah wants to display his 72 collector’s flags. He is going to put 6 flags in each row. How many rows of flags will he have in his display?
Options:
a. 12
b. 15
c. 18
d. 21

Answer:
a. 12

Explanation:
As mentioned in the data,
Noah wants to display his 72 collector’s flag
He is going to put 6 flags in each row = 6x = 72
X = 12
So, a total 12 number of rows of flags will have in his display.
Thus the correct answer is option a.

Question 6.
Julian wrote this number pattern on the board:
3, 10, 17, 24, 31, 38.
Which of the numbers in Julian’s pattern are composite numbers?
Options:
a. 3, 17, 31
b. 10, 24, 38
c. 10, 17, 38
d. 17, 24, 38

Answer:
b. 10, 24, 38

Explanation:
As per the given information
Julian wrote his number pattern on the board =3, 10, 17, 24, 31, 38
Factors of 3 = 1,3
Factors of 10 = 1,2,5,10
Factors of 17 = 1, 17
Factors of 24 = 1, 2, 3, 4, 6
Factors of 31 = 1, 31
Factors of 38 = 1, 2, 19, 38
So, the composite number is 10, 24, and 38, which numbers have more than 2 factors.
Thus the correct answer is option b.

Common Core – Fraction Equivalence and Comparison – Page No. 125

Compare. Write <, >, or =

Question 1.

Answer:
1/5 < 2/10

Explanation:

Question 2.
\(\frac{1}{5}\) ______ \(\frac{2}{10}\)

Answer:
1/5 = 2/10

Explanation:
1/5 and 2/10
Think: 10 is a common denominator
1/5 = (1×2) / (5×2) = 2/10
2/10 = 2/10
So, 1/5 = 2/10

Question 3.
\(\frac{2}{4}\) ______ \(\frac{2}{5}\)

Answer:
2/4 > 2/5

Explanation:
2/4 and 2/5
20 is a common denominator
2/4 = (2×5)/(4×5) = 10/20
2/5 = (2×4)/(5×4) = 8/20
10/20 > 8/20
So, 2/4 > 2/5

Question 4.
\(\frac{3}{5}\) ______ \(\frac{7}{10}\)

Answer:
3/5 < 7/10

Explanation:
3/5 and 7/10
10 is a common denominator
3/5 = (3×2)/(5×2) = 6/10
7/10
6/10 < 7/10
So, 3/5 < 7/10

Question 5.
\(\frac{4}{12}\) ______ \(\frac{1}{6}\)

Answer:
4/12 > 1/6

Explanation:
4/12 and 1/6
12 is a common denominator
4/12
1/6 = (1×2)/(6×2) = 2/12
4/12 > 2/12
So, 4/12 > 1/6

Question 6.
\(\frac{2}{6}\) ______ \(\frac{1}{3}\)

Answer:
2/6 = 1/3

Explanation:
2/6 and 1/3
6 is a common denominator
2/6
1/3 = (1×2)/(3×2) = 2/6
So, 2/6 =2/6
So, 2/6 = 1/3

Question 7.
\(\frac{1}{3}\) ______ \(\frac{2}{4}\)

Answer:
1/3 < 2/4

Explanation:
1/3 and 2/4
12 is a common denominator
1/3 = (1×4)/(3×4) = 4/12
2/4 = (2×3)/(4×3) = 6/12
4/12 < 6/12
So, 1/3 < 2/4

Question 8.
\(\frac{2}{5}\) ______ \(\frac{1}{2}\).

Answer:
2/5 < 1/2

Explanation:
2/5 and 1/2
10 is a common denominator
2/5 = (2×2)/(5×2) = 4/10
1/2 = (1×5)/(2×5) = 5/10
4/10 < 5/10
So, 2/5 < 1/2

Question 9.
\(\frac{4}{8}\) ______ \(\frac{2}{4}\)

Answer:
4/8 = 2/4

Explanation:
4/8 and 2/4
8 is a common denominator
4/8
2/4 = (2×2)/(4×2) = 4/8
2/4 = 4/8
So, 4/8 = 2/4

Question 10.
\(\frac{7}{12}\) ______ \(\frac{2}{4}\)

Answer:
7/12 < 2/4

Explanation:
7/12 and 2/4
12 is a common denominator
7/12
2/4 = (2×3)/(4×3) = 6/12
7/12 < 6/12
So, 7/12 < 2/4

Question 11.
\(\frac{1}{8}\) ______ \(\frac{3}{4}\)

Answer:
1/8 < 3/4

Explanation:
1/8 and 3/4
8 is a common denominator
1/8
3/4 = (3×2)/(4×2) = 6/8
1/8 < 6/8
So, 1/8 < 3/4

Question 12.
A recipe uses \(\frac{2}{3}\) of flour and \(\frac{5}{8}\) cup of blueberries. Is there more flour or more blueberries in the recipe?
more _________

Answer: flour

Explanation:
From the given data,
A recipe uses 2/3 of flour and 5/8 cup of blueberries
The common denominator is 24
2/3 = (2×8)/(3×8) = 16/24
5/8 = (5×3)/(8×3) = 15/24
16/24 > 15/24
So, 2/3 > 5/8
So, flour is more in the recipe

Question 13.
Peggy completed \(\frac{5}{6}\) of the math homework and Al completed \(\frac{4}{5}\) of the math homework. Did Peggy or Al complete more of the math homework?
_________

Answer:
Peggy completed more work than Al

Explanation:
As per the given data,
Peggy completed 5/6 of the math homework
A1 completed 4/5 of the math homework
30 is a common denominator
5/6 = (5×5)/(6×5) = 25/30
4/5 = (4×6)/(5×6) =24/30
25/30 > 24/30
So, 5/6 > 4/5
So, Peggy completed more work than Al

Common Core – Fraction Equivalence and Comparison – Page No. 126

Question 1.
Pedro fills a glass \(\frac{2}{4}\) full with orange juice. Which of the following fractions is greater than \(\frac{2}{4}\)?
Options:
a. \(\frac{3}{8}\)
b. \(\frac{4}{6}\)
c. \(\frac{5}{12}\)
d. \(\frac{1}{3}\)

Answer:
b. 46

Explanation:
46 > 24
Thus the correct answer is option b.

Question 2.
Today Ian wants to run less than \(\frac{7}{12}\) mile. Which of the following distances is less than \(\frac{7}{12}\) mile?
Options:
a. \(\frac{3}{4}\) mile
b. \(\frac{2}{3}\) mile
c. \(\frac{5}{6}\) mile
d. \(\frac{2}{4}\) mile

Answer:
d. 2/4 mile

Explanation:
2/4 is less than 7/12
Thus the correct answer is option d.

Question 3.
Ms. Davis traveled 372,645 miles last year on business. What is the value of 6 in 372,645?
Options:
a. 6
b. 60
c. 600
d. 6,000

Answer:
c. 600

Explanation:
Ms. Davis traveled 372, 645 miles last year on business
The value of 6 in 372,645 is 600.
Thus the correct answer is option c.

Question 4.
One section of an auditorium has 12 rows of seats. Each row has 13 seats. What is the total number of seats in that section?
Options:
a. 25
b. 144
c. 156
d. 169

Answer:
c. 156

Explanation:
From the given information
One section of an auditorium has 12 rows of seats
Each row has 13 seats = 13×12 = 156 seats
So, the total number of seats in the auditorium = 156 seats
Thus the correct answer is option c.

Question 5.
Sam has 12 black-and-white photos and 18 color photos. He wants to put the photos in equal rows so each row has either black-and-white photos only or color photos only. In how many rows can Sam arrange the photos?
Options:
a. 1, 2, 3, or 6 rows
b. 1, 3, 6, or 9 rows
c. 1, 2, or 4 rows
d. 1, 2, 3, 4, 6, or 9 rows

Answer:
a. 1, 2, 3, or 6 rows

Explanation:
As per the given information
Sam has 12 black and white photos 18 color photos
He wants to put the photos in equal rows
So each row has either black and white photos only or color photos only
H.C.F of 12 and 18 is 6
Rows of 6.
2 rows of black equal 12.
3 rows of white equals 18.
Thus the correct answer is option a.

Question 6.
The teacher writes \(\frac{10}{12}\) on the board. He asks students to write the fraction in the simplest form. Who writes the correct answer?
Options:
a. JoAnn writes \(\frac{10}{12}\)
b. Karen writes \(\frac{5}{12}\)
c. Lynn writes \(\frac{6}{5}\)
d. Mark writes \(\frac{5}{6}\)

Answer:
d. Mark writes 56

Explanation:
As per the given data,
The teacher writes 10/12 on the board
He asks students to write the fraction in simplest form
For the simplest form of 10/12, divide the 10/12 with 2
(10÷2)/(12÷2) = 5/6
5/6 is the simplest form of 10/12
So, Mark writes the correct answer.
Thus the correct answer is option d.

Common Core – Fraction Equivalence and Comparison – Page No. 127

Write the fractions in order from least to greatest.

Question 1.
\(\frac{5}{8}, \frac{2}{12}, \frac{8}{10}\)

Answer:
2/12, 5/8, 8/10

Explanation:

Question 2.
\(\frac{1}{5}, \frac{2}{3}, \frac{5}{8}\)
Type below:
_________

Answer:
1/5, 5/8, 2/3

Explanation:

1/5, 2/3, 5/8
1/5 is closer to 0
2/3 is greater than 1/2
5/8 greater than 1/2
1/5 < 5/8 < 2/3

Question 3.
\(\frac{1}{2}, \frac{2}{5}, \frac{6}{10}\)
Type below:
_________

Answer:
2/5, 1/2, 6/10

Explanation:

1/2, 2/5, 6/10
1/2 is equal to 1/2
2/5 is less than 1/2
6/10 is greater than 1/2

Question 4.
\(\frac{4}{6}, \frac{7}{12}, \frac{5}{10}\)
Type below:
_________

Answer:
5/10 < 7/12 < 4/6

Explanation:

4/6, 7/12, 5/10
4/6 is closer to 1
7/12 is greater than 1/2
5/10 is equal to 1/2

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
Type below:
_________

Answer:
18 < 14 < 36

Explanation:

1/4, 3/6, 1/8
1/4 is less than 1/2
3/6 is equal to 1/2
1/8 is closer to 0

Question 6.
\(\frac{1}{8}, \frac{3}{6}, \frac{7}{12}\)
Type below:
_________

Answer:
1/8 < 7/12 < 3/6

Explanation:

1/8, 3/6, 7/12
1/8 is closer to 0
3/6 is equal to 1/2
7/12 is greater than 1/2

Question 7.
\(\frac{8}{100}, \frac{3}{5}, \frac{7}{10}\)
Type below:
_________

Answer:
8/100 < 3/5 < 7/10

Explanation:

8/100, 3/5, 7/10
8/100 is closer to 0
3/5 is greater than 1/2
7/10 is closer to 1

Question 8.
\(\frac{3}{4}, \frac{7}{8}, \frac{1}{5}\)
Type below:
_________

Answer:
15 < 34 < 78
Explanation:

3/4, 7/8, 1/5
3/4 is greater than 1/2
7/8 is closer to 1
1/5 is closer to 0

Question 9.
Amy’s math notebook weighs \(\frac{1}{2}\) pound, her science notebook weighs \(\frac{7}{8}\) pound, and her history notebook weighs \(\frac{3}{4}\) pound. What are the weights in order from lightest to heaviest?
Type below:
__________

Answer:
12 pound, 34 pound, 78 pound

Explanation:
From the given data,
Amy’s math notebook weighs 1/2 pound
Science notebook weighs 7/8 pound
History notebook weighs 3/4 pound
7/8 is closer to 1
3/4 is greater than 1/2
1/2 < 3/4 < 7/8
So, Amy’s math notebook weight < history notebook weight < science notebook

Question 10.
Carl has three picture frames. The thicknesses of the frames are \(\frac{4}{5}\) inch, \(\frac{3}{12}\) inch, and \(\frac{5}{6}\) inch. What are the thicknesses in order from least to greatest?
Type below:
__________

Answer:
3/12 inch, 4/5 inch, 5/6 inch

Explanation:
As per the given data,
Carl has three picture frames
The thickness of the frames are 4/5 inch, 3/12 inch, 5/6 inch
4/5 is greater than 1/2
3/12 is less than 1/2
5/6 is closer to 1
3/12 < 4/5 < 5/6

Common Core – Fraction Equivalence and Comparison – Page No. 128

Question 1.
Juan’s three math quizzes this week took him \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, and \(\frac{1}{5}\) hour to complete. Which list shows the lengths of time in order from least to greatest?
Options:
a. \(\frac{1}{3} hour, \frac{4}{6} hour, \frac{1}{5} hour\)
b. \(\frac{1}{5} hour, \frac{1}{3} hour, \frac{4}{6} hour\)
c. \(\frac{1}{3} hour, \frac{1}{5} hour, \frac{4}{6} hour\)
d. \(\frac{4}{6} hour, \frac{1}{3} hour, \frac{1}{5} hour\)

Answer:
b. 1/5 hour, 1/3 hour, 4/6 hour

Explanation:
From the given information
Juan’s three math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour
Compare 1/3 and 1/2
1/3 is less than 1/2
4/6 is greater than 1/2
1/5 is closer to 0
1/5 < 1/3 < 4/6
So, Juan’s math quizzes times from least to greatest is 1/5, 1/3, 4/6
Thus the correct answer is option b.

Question 2.
On three days last week, Maria ran \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, and \(\frac{3}{5}\) mile. What are the distances in order from least to greatest?
Options:
a. \(\frac{3}{4} mile, \frac{7}{8} mile, \frac{3}{5} mile\)
b. \(\frac{3}{5} mile, \frac{3}{4} mile, \frac{7}{8} mile\)
c. \(\frac{7}{8} mile, \frac{3}{4} mile, \frac{3}{5} mile\)
d. \(\frac{7}{8} mile, \frac{3}{5} mile, \frac{3}{4} mile\)

Answer:
b. 3/5 mile, 3/4 mile, 7/8 mile

Explanation:
As per the information
On three days last week, Maria ran 3/4 mile, 7/8 mile, and 3/5 mile
3/4 is greater than 1/2
7/8 is closer to 1
3/5 is greater than 1/2
Compare 3/5 and 3/4
3/4 is greater than 3/5
So, 3/5 < 3/4 < 7/8
Distance from least to greatest is 3/5, 3/4 , 7/8
Thus the correct answer is option b.

Question 3.
Santiago collects 435 cents in nickels. How many nickels does he collect?
Options:
a. 58
b. 78
c. 85
d. 87

Answer:
d. 87

Explanation:
As per the given data,
Santiago collects 435 cents in nickels
1 nickel worth is 5 cents
Then, nickels per 435 cents = 435/5 = 87
So, Santiago collects 87 nickels.
Thus the correct answer is option d.

Question 4.
Lisa has three classes that each last 50 minutes. What is the total number of minutes the three classes last?
Options:
a. 15 minutes
b. 150 minutes
c. 153 minutes
d. 156 minutes

Answer:
b. 150 minutes

Explanation:
From the given data,
Lisa has three classes that each last 50 minutes
The total number of minutes the three classes last = 3×50 =150 minutes.
Thus the correct answer is option b.

Question 5.
Some students were asked to write a composite number. Which student did NOT write a composite number?
Options:
a. Alicia wrote 2.
b. Bob wrote 9.
c. Arianna wrote 15.
d. Daniel wrote 21.

Answer:
a. Alicia wrote 2.

Explanation:
As per the information
Some students were asked to write a composite number
a. Alicia wrote 2
Factors of 2 is 1 and 2
b. Bob wrote 9
Factors of 9 is 1, 3, 9
c. Arianna wrote 15
Factors of 15 is 1, 3, 5, 15
d. Daniel wrote 21
Factors of 21 is 1,3,7,21
So, Alicia did not write a composite number.
Thus the correct answer is option a.

Question 6.
Mrs. Carmel serves \(\frac{6}{8}\) of a loaf of bread with dinner. Which fraction is equivalent to \(\frac{6}{8}\) ?
Options:
a. \(\frac{2}{4}\)
b. \(\frac{9}{16}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer: d. 3/4

Explanation:
As per the given information
Mrs. Carmel serves 6/8 of a loaf of bread with dinner
To find the equivalent fraction of 6/8, simplify the 6/8 by dividing with the 2
(6÷2)/(8÷2) = 3/4
So, the equivalent fraction of 6/8 is 3/4
Thus the correct answer is option d.

Common Core – Fraction Equivalence and Comparison – Page No. 129

Lesson 6.1

Tell whether the fractions are equivalent. Write = or ≠.

Question 1.
\(\frac{5}{10}\) ______ \(\frac{1}{2}\)

Answer: \(\frac{5}{10}\) = \(\frac{1}{2}\)

Explanation:
Divide \(\frac{5}{10}\) by 2
\(\frac{5}{10}\) ÷ 5 = \(\frac{1}{2}\)
So, \(\frac{5}{10}\) = \(\frac{1}{2}\)

Question 2.
\(\frac{2}{3}\) ______ \(\frac{3}{6}\)

Answer: \(\frac{2}{3}\) ≠ \(\frac{3}{6}\)

Explanation:
The fraction \(\frac{2}{3}\) is not equal to \(\frac{3}{6}\)

Question 3.
\(\frac{6}{8}\) ______ \(\frac{3}{4}\)

Answer: \(\frac{6}{8}\) = \(\frac{3}{4}\)

Explanation:
Divide \(\frac{6}{8}\) by 2.
\(\frac{6}{8}\) ÷ 2 = \(\frac{3}{4}\)
So, \(\frac{6}{8}\) = \(\frac{3}{4}\)

Question 4.
\(\frac{7}{12}\) ______ \(\frac{4}{6}\)

Answer: \(\frac{7}{12}\) ≠ \(\frac{4}{6}\)

Explanation:
The fraction \(\frac{7}{12}\) is not equal to \(\frac{4}{6}\).

Lesson 6.2

Write two equivalent fractions for each.

Question 5.
\(\frac{2}{3}\)
Type below:
_________

Answer: 4/6 and 8/12

Explanation:
2/3
(2/3) x (2/2) = 4/6
(2/3) x (4/4) = 8/12
Then, the equivalent fractions of 2/3 = 4/6 and 8/12

Question 6.
\(\frac{5}{10}\)
Type below:
_________

Answer: 1/2

Explanation:
\(\frac{5}{10}\) × 2/2 = 10/20
\(\frac{5}{10}\) ÷ 5 = 1/2

Question 7.
\(\frac{4}{12}\)
Type below:
_________

Answer: 1/3

Explanation:
\(\frac{4}{12}\) ÷ 3 = 1/3
\(\frac{4}{12}\) × 3/3 = 4/12

Question 8.
\(\frac{4}{5}\)
Type below:
_________

Answer:
8/10 and 80/100

Explanation:
4/5
(4/5) x (2/2) = 8/10
(4/5) x (20/20) = 80/100
Then, the equivalent fractions of 4/5 = 8/10 and 80/100

Lesson 6.3

Write the fraction in simplest form.

Question 9.
\(\frac{6}{12}\)
\(\frac{□}{□}\)

Answer:
1/2

Explanation:
6/12 in simplest form
Divide the 6/12 with 6
(6/6)/(12/6) = 1/2
So, the simplest form of 6/12 is 1/2

Question 10.
\(\frac{2}{10}\)
\(\frac{□}{□}\)

Answer:
1/5

Explanation:
2/10 in simplest form
Divide the 2/10 with 2
(2/2)/(10/2) = 1/5
So, the simplest form of 2/10 is 1/5

Question 11.
\(\frac{4}{6}\)
\(\frac{□}{□}\)

Answer:
2/3

Explanation:
4/6 in simplest form
Divide the 4/6 with 2
(4/2)/(6/2) = 2/3
So, the simplest form of 4/6 is 2/3

Question 12.
\(\frac{3}{12}\)
\(\frac{□}{□}\)

Answer: 1/4

Explanation:
3/12 in the simplest form
Divide 3/12 with 3.
3/12 ÷ 3 = 1/4
So the simplest form of \(\frac{3}{12}\) is \(\frac{1}{4}\)

Question 13.
\(\frac{6}{10}\)
\(\frac{□}{□}\)

Answer: 3/5

Explanation:
\(\frac{6}{10}\) in the simplest form.
Divide the \(\frac{6}{10}\) with 2
\(\frac{6}{10}\) ÷ 2 = \(\frac{3}{5}\)

Lesson 6.4

Write the pair of fractions as a pair of fractions with a common denominator.

Question 14.
\(\frac{2}{3} \text { and } \frac{5}{6}\)
Type below:
_________

Answer: 8/12 and 10/12

Explanation:
The common denominator of \(\frac{2}{3} \text { and } \frac{5}{6}\)
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21,….
List the multiples of 6 = 6, 12, 18, 24, 30, 36, ….
Then, the common denominator of \(\frac{2}{3} \text { and } \frac{5}{6}\) is 12
For the Common pair of fractions, multiply the common denominator with fractions
So, common pair of fractions = 8/12 and 10/12

Question 15.
\(\frac{3}{5} \text { and } \frac{1}{2}\)
Type below:
_________

Answer: 6/10 and 5/10

Explanation:
Common denominator of \(\frac{3}{5} \text { and } \frac{1}{2}\)
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …..
List the multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….
Then, the common denominator of \(\frac{3}{5} \text { and } \frac{1}{2}\) is 10.
For the Common pair of fractions, multiply the common denominator with fractions
So, the common pair of fractions = 6/10 and 5/10.

Question 16.
\(\frac{1}{4} \text { and } \frac{5}{12}\)
Type below:
_________

Answer: 3/12 and 5/12

Explanation:
The common denominator of \(\frac{1}{4} \text { and } \frac{5}{12}\)
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 12 = 12, 24, 36, 48…
Then, the common denominator of \(\frac{1}{4} \text { and } \frac{5}{12}\) is 12
For the Common pair of fractions, multiply the common denominator with fractions
So, common pair of fractions = 3/12 and 5/12.

Question 17.
\(\frac{7}{8} \text { and } \frac{3}{4}\)
Type below:
_________

Answer: 7/8 and 6/8

Explanation:
Common denominator of \(\frac{7}{8} \text { and } \frac{3}{4}\)
List the multiples of 8 = 8, 16, 24, 32, . . . .
List the multiples of 4 = 4, 8, 12, 16,….
Then, the common denominator of \(\frac{7}{8} \text { and } \frac{3}{4}\) is 8
For the Common pair of fractions, multiply the common denominator with fractions
So, the common pair of fractions = 7/8 and 6/8

Question 18.
\(\frac{3}{10} \text { and } \frac{1}{5}\)
Type below:
_________

Answer: \(\frac{3}{10} \text { and } \frac{2}{10}\)

Explanation:
Common denominator of \(\frac{3}{10} \text { and } \frac{1}{5}\)
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …..
List the multiples of 10 = 10, 20, 30, 40, 50 ….
Then, the common denominator of \(\frac{3}{10} \text { and } \frac{1}{5}\) is 10
For the Common pair of fractions, multiply the common denominator with fractions
So, the common pair of fractions = \(\frac{3}{10} \text { and } \frac{2}{10}\)

Question 19.
\(\frac{3}{4} \text { and } \frac{1}{3}\)
Type below:
_________

Answer: 9/12 and 4/12

Explanation:
The common denominator of \(\frac{3}{4} \text { and } \frac{1}{3}\)
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of \(\frac{3}{4} \text { and } \frac{1}{3}\) is 12
For the Common pair of fractions, multiply the common denominator with fractions
So, the common pair of fractions = 9/12 and 4/12

Common Core – Fraction Equivalence and Comparison – Page No. 130

Lesson 6.5

Question 1.
Mr. Renner is decorating a bulletin board with groups of shapes. Each group has 3 shapes, and \(\frac{2}{3}\) of the shapes are snowflakes. If Mr. Renner is using 4 groups of shapes, how many snowflakes will he need? Complete the table to find the fraction of the shapes for each number of group that are

How many snowflake shapes will Mr. Renner use?
_______ snowflakes shapes

Answer: 8 snowflakes shapes

Explanation:
Given,
Mr. Renner is decorating a bulletin board with groups of shapes.
Each group has 3 shapes, and \(\frac{2}{3}\) of the shapes are snowflakes.
There are 4 groups and in every group, there are 2 snowflakes so in total there are 8. because 4 × 2=8
Mr. Renner uses 8 snowflakes shapes.

Question 2.
Nell made a pizza. She cut the pizza into fourths. Then she cut each fourth into four pieces. Nell and her friends ate 6 of the smaller pieces of the pizza.
What fraction of the pizza did Nell and her friends eat?
What fraction of the pizza did Nell and her friends NOT eat?

Answer:
okay so four is slice, and then do it again. the answer is at the bottom,

pizza: 16 pieces
Nell and her friends ate 6 smaller pizza
3/8 is the answer.

Lesson 6.6 – 6.7

Compare. Write <,>, or =.

Question 3.
\(\frac{2}{6}\) ______ \(\frac{3}{4}\)

Answer: \(\frac{2}{6}\) < \(\frac{3}{4}\)

Explanation:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
\(\frac{1}{3}\) is less than \(\frac{3}{4}\)
So, \(\frac{2}{6}\) < \(\frac{3}{4}\)

Question 4.
\(\frac{6}{8}\) ______ \(\frac{1}{4}\)

Answer: \(\frac{6}{8}\) > \(\frac{1}{4}\)

Explanation:
\(\frac{6}{8}\) = \(\frac{3}{4}\)
\(\frac{3}{4}\) is greater than \(\frac{1}{4}\)
So, \(\frac{6}{8}\) > \(\frac{1}{4}\)

Question 5.
\(\frac{5}{6}\) ______ \(\frac{2}{4}\)

Answer: \(\frac{5}{6}\) > \(\frac{2}{4}\)

Explanation:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
\(\frac{5}{6}\) is greater than \(\frac{1}{2}\)
So, \(\frac{5}{6}\) > \(\frac{2}{4}\)

Question 6.
\(\frac{1}{3}\) ______ \(\frac{4}{12}\)

Answer: \(\frac{1}{3}\) = \(\frac{4}{12}\)

Explanation:
\(\frac{4}{12}\) = \(\frac{1}{3}\)
\(\frac{1}{3}\) = \(\frac{4}{12}\)

Question 7.
\(\frac{1}{6}\) ______ \(\frac{1}{8}\)

Answer: \(\frac{1}{6}\) > \(\frac{1}{8}\)

Explanation:
Given the fractions \(\frac{1}{6}\) and \(\frac{1}{8}\)
Here the numerators are same so we have to compare the denominators.
The denominator with the smallest number will be the greatest fraction.
\(\frac{1}{6}\) is greater than \(\frac{1}{8}\)
So, \(\frac{1}{6}\) > \(\frac{1}{8}\)

Question 8.
\(\frac{2}{3}\) ______ \(\frac{4}{6}\)

Answer: \(\frac{2}{3}\) = \(\frac{4}{6}\)

Explanation:
\(\frac{4}{6}\) ÷ 2 = \(\frac{2}{3}\)
\(\frac{2}{3}\) = \(\frac{2}{3}\)
So, \(\frac{2}{3}\) = \(\frac{4}{6}\)

Question 9.
\(\frac{3}{10}\) ______ \(\frac{3}{12}\)

Answer: \(\frac{3}{10}\) > \(\frac{3}{12}\)

Explanation:
Given the fractions \(\frac{3}{10}\) and \(\frac{3}{12}\)
Here the numerators are same so we have to compare the denominators.
The denominator with the smallest number will be the greatest fraction.
Thus \(\frac{3}{10}\) > \(\frac{3}{12}\)

Question 10.
\(\frac{7}{8}\) ______ \(\frac{4}{4}\)

Answer: \(\frac{7}{8}\) < \(\frac{4}{4}\)

Explanation:
\(\frac{4}{4}\) = 1
1 is greater than \(\frac{7}{8}\)
Thus \(\frac{7}{8}\) < \(\frac{4}{4}\)

Lesson 6.8

Write the fractions in order from least to greatest.

Question 12.
\(\frac{1}{2}, \frac{1}{4}, \frac{5}{8}\)
Type below:
__________

Answer: 1/4, 5/8 and 1/2

Explanation:
1/4 × 2/2 = 2/8
5/8 × 1/1 = 5/8
1/2 × 4/4 = 4/8
Compare the numerators of the above fractions.
The numerator with the largest number will be the greatest fraction.
The fraction from least to greatest is 1/4, 5/8 and 1/2

Question 13.
\(\frac{2}{3}, \frac{1}{6}, \frac{9}{10}\)
Type below:
__________

Answer: 1/6, 2/3 and 9/10

Explanation:
Given the fractions \(\frac{2}{3}, \frac{1}{6}, \frac{9}{10}\)
2/3 × 10/10 = 20/30
1/6 × 5/5 = 5/30
9/10 × 3/3 = 27/30
Compare the numerators of the above fractions.
The numerator with the largest number will be the greatest fraction.
The fraction from least to greatest is 1/6, 2/3 and 9/10.

Question 14.
\(\frac{3}{5}, \frac{3}{4}, \frac{3}{8}\)
Type below:
__________

Answer: \(\frac{3}{8}, \frac{3}{5}, \frac{3}{4}\)

Explanation:
Given the fractions \(\frac{3}{5}, \frac{3}{4}, \frac{3}{8}\)
Here the numerators are the same so we have to compare the denominators.
The denominator with the smallest number will be the greatest fraction.
Thus the fractions from least to greatest are \(\frac{3}{8}, \frac{3}{5}, \frac{3}{4}\).

Conclusion:

I think the explained answers provided in this chapter are important for all 4th-grade students. Make sure to share these pdf links with our friends and assist them while practicing mathematical concepts. In case, do you feel anything is missing in Homework Practice FL, you can refer to the Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison. Try solving these chapter problems and enhance your subject knowledge.