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## Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers

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**Lesson: 1 – Multiples of Unit Fractions**

- Common Core – Multiply Fractions by Whole Numbers – Page No. 157
- Common Core – Multiply Fractions by Whole Numbers – Page No. 158

**Lesson: 2 – Multiples of Fractions**

- Common Core – Multiply Fractions by Whole Numbers – Page No. 159
- Common Core – Multiply Fractions by Whole Numbers – Page No. 160

**Lesson: 3 – Multiply a Fraction by a Whole Number Using Models**

- Common Core – Multiply Fractions by Whole Numbers – Page No. 161
- Common Core – Multiply Fractions by Whole Numbers – Page No. 162

**Lesson: 4 – Multiply a Fraction or Mixed Number by a Whole Number.**

- Common Core – Multiply Fractions by Whole Numbers – Page No. 163
- Common Core – Multiply Fractions by Whole Numbers – Page No. 164

**Lesson: 5 – Problem Solving Comparison**

- Common Core – Multiply Fractions by Whole Numbers – Page No. 165
- Common Core – Multiply Fractions by Whole Numbers – Page No. 166

**Lesson: 6**

- Common Core – Multiply Fractions by Whole Numbers – Page No. 167
- Common Core – Multiply Fractions by Whole Numbers – Page No. 168

### Common Core – Multiply Fractions by Whole Numbers – Page No. 157

**Multiples of Unit Fractions**

**Write the fraction as a product of a whole number and a unit fraction.**

Question 1.

Explanation:

Given that 5/6 or 5 sixth-size parts.

Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.

You can use unit fractions to show 5/6

5/6 = 5 x 1/6.

Question 2.

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

Type below:

_________

Answer:

7 x 1/8

Explanation:

Given that 7/8 or 7 eighth-size parts.

Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.

You can use unit fractions to show 7/8

7/8 = 7 x 1/8.

Question 3.

\(\frac{5}{3}\)

Type below:

_________

Answer:

5 x 1/3

Explanation:

Given that 5/3 or 5 third-size parts.

Each third-size part of the given fraction can be shown by the unit fraction 1/3.

You can use unit fractions to show 5/6

5/3 = 5 x 1/3.

Question 4.

\(\frac{9}{10}\)

Type below:

_________

Answer:

9 x 1/10

Explanation:

Given that 9/10 or 9 tenth-size parts.

Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.

You can use unit fractions to show 9/10

9/10 = 9 x 1/10.

Question 5.

\(\frac{3}{4}\)

Type below:

_________

Answer:

3 x 1/4

Explanation:

Given that 3/4 or 3 fourth-size parts.

Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.

You can use unit fractions to show 5/6

3/4 = 3 x 1/4.

Question 6.

\(\frac{11}{12}\)

Type below:

_________

Answer:

11 x 1/12

Explanation:

Given that 11/12 or 11 twelve-size parts.

Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.

You can use unit fractions to show 5/6

11/12 = 11 x 1/12.

Question 7.

\(\frac{4}{6}\)

Type below:

_________

Answer:

4 x 1/6

Explanation:

Given that 4/6 or 4 sixth-size parts.

Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.

You can use unit fractions to show 4/6

4/6 = 4 x 1/6.

Question 8.

\(\frac{8}{20}\)

Type below:

_________

Answer:

8 x 1/20

Explanation:

Given that 8/20 or 8 twenty-size parts.

Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.

You can use unit fractions to show 8/20

8/20 = 8 x 1/20.

Question 9.

\(\frac{13}{100}\)

Type below:

_________

Answer:

13 x 1/100

Explanation:

Given that 13/100 or 13 hundred-size parts.

Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.

You can use unit fractions to show 13/100

13/100 = 13 x 1/100.

**List the next four multiples of the unit fraction.**

Question 10.

\(\frac{1}{5}\),

Type below:

_________

Answer:

2/5, 3/5, 4/5, 5/5

Explanation:

2/5, 3/5, 4/5, 5/5

Question 11.

\(\frac{1}{8}\),

Type below:

_________

Answer:

2/8, 3/8, 4/8, 5/8

Explanation:

2/8, 3/8, 4/8, 5/8

**Problem Solving**

Question 12.

So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?

\(\frac{□}{□}\) of the book

Answer: 1/6 of the book

Explanation:

Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.

For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.

So far, Monica has read \(\frac{3}{8}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?

\(\frac{□}{□}\) pound of cheese

Answer: 1/8 pound of cheese

Explanation:

Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 158

**Lesson Check**

Question 1.

Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?

Options:

a. \(\frac{1}{3}\) mile

b. \(\frac{2}{3}\) mile

c. 1 \(\frac{1}{3}\) miles

d. 2 miles

Answer: a. 1/3 mile

Explanation:

Selena walks from home to school each morning and back home each afternoon.

Altogether, she walks 2/3 miles each day.

The distance between home and school will remain the same.

So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.

Thus the correct answer is option a.

Question 2.

Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?

Options:

a. \(\frac{1}{4}\) cup

b. \(\frac{1}{3}\) cup

c. 2 \(\frac{1}{3}\) cups

d. 3 cups

Answer: \(\frac{1}{4}\) cup

Explanation:

Will uses 3/4 cups of olive oil to make 3 batches of salad dressing.

To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3.

So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.

Thus the correct answer is option a.

**Spiral Review**

Question 3.

Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?

Options:

a. \(\frac{1}{8}\) pound

b. \(\frac{2}{8}\) pound

c. \(\frac{3}{8}\) pound

d. \(\frac{4}{8}\) pound

Answer: c. 3/8 pound

Explanation:

Liza bought 58 pound of trail mix. She gives 28 pounds of trail mix to Michael.

So, Liza has left 5/8 – 2/8 = 3/8 trail mix.

Thus the correct answer is option c.

Question 4.

Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?

Options:

a. \(\frac{11}{3}\) pound

b. \(\frac{15}{3}\) pound

c. \(\frac{20}{3}\) pound

d. \(\frac{62}{3}\) pound

Answer: c. 20/3

Explanation:

Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).

3 x 6 =18.

Add 18 + 2 =20.

Keep the Denominator the same i.e. 3.

The obtained fraction is 20/3.

Thus the correct answer is option c.

Question 5.

Randy’s house number is a composite number. Which of the following could be Randy’s house number?

Options:

a. 29

b. 39

c. 59

d. 79

Answer: b. 39

Explanation:

The composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divide by 13 and 3.

Thus the correct answer is option b.

Question 6.

Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?

Options:

a. \(\frac{1}{4}\)

b. \(\frac{1}{3}\)

c. \(\frac{2}{3}\)

d. \(\frac{3}{4}\)

Answer: a. 1/4

Explanation:

Mindy buys 12 cupcakes.

Nine of the cupcakes have chocolate frosting = 9/12.

The rest have vanilla frosting. So, there are 3 cups remained = 3/12 = 1/4.

1/4 cupcakes have vanilla frosting.

Thus the correct answer is option a.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 159

**Multiples of Fractions**

**List the next four multiples of the fraction.**

Question 1.

\(\frac{3}{5}\),

Type below:

_________

Answer:

6/5, 9/5, 12/5, 20/5

Explanation:

1 x 3/5 = 3/5.

2 x 3/5 = 6/5.

3 x 3/5 = 9/5.

4 x 3/5 = 12/5.

5 x 4/5 = 20/5.

The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.

\(\frac{2}{6}\),

Type below:

_________

Answer:

4/6, 6/6, 8/6, 10/6

Explanation:

1 x 2/6 = 2/6.

2 x 2/6 = 4/6.

3 x 2/6 = 6/6.

4 x 2/6 = 8/6.

5 x 2/6 = 10/6.

The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.

\(\frac{4}{8}\),

Type below:

_________

Answer:

8/8, 12/8, 16/8, 20/8

Explanation:

1 x 4/8 = 4/8.

2 x 4/8 = 8/8.

3 x 4/8 = 12/8.

4 x 4/8 = 16/8.

5 x 4/8 = 20/8.

The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.

\(\frac{5}{10}\),

Type below:

_________

Answer:

10/10, 15/10, 20/10, 25/10

Explanation:

1 x 5/10 = 5/10.

2 x 5/10 = 10/10.

3 x 5/10 = 15/10.

4 x 5/10 = 20/10.

5 x 5/10 = 25/10.

The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

**Write the product as the product of a whole number and a unit fraction.**

Question 5.

2 × \(\frac{4}{5}\) =

Type Below:

_________

Answer: 8/5 = 8 x 1/5

Explanation:

1 group of 4/5 = 4/5

2 groups of 4/5 = 8/5

2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.

5 × \(\frac{2}{3}\) =

Type below:

_________

Answer:

10/3 = 10 x 1/3

Explanation:

1 group of 2/3 = 2/3

2 group of 2/3 = 4/3

3 group of 2/3 = 6/3

4 group of 2/3 = 8/3

5 group of 2/3 = 10/3

5 x 2/3 = 10/3 = 10 x 1/3.

**Problem Solving**

Question 7.

Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?

_____ times

Answer: 6 times

Explanation:

Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.

For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.

Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.

So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.

A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?

_____ times

Answer: 12 times

Explanation:

A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.

If they have 1/8 teaspoon measuring spoon, 12 x 1/8.

So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 160

**Lesson Check**

Question 1.

Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?

Options:

a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)

b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)

c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)

d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer: b. 5/8, 10/8, 15/8, 20/8, 25/8

Explanation:

1 x 5/8 = 5/8.

2 x 5/8 = 10/8.

3 x 5/8 = 15/8.

4 x 5/8 = 20/8.

5 x 5/8 = 25/8.

The next four multiples of 5/8 are \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)

Thus the correct answer is option b.

Question 2.

David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?

Options:

a. 5

b. 10

c. 15

d. 20

Answer: c. 15

Explanation:

David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.

His measuring cup only holds 1/4 quart.

So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.

Thus the correct answer is option c.

**Spiral Review**

Question 3.

Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?

Options:

a. 12

b. 14

c. 16

d. 18

Answer: c. 16

Explanation:

Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.

128/8 = 16 stamps on each page.

So, there are 16 stamps on each page.

Thus the correct answer is option b.

Question 4.

Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?

Options:

a. $ 8

b. $ 18

c. $ 48

d. $ 180

Answer: b. $ 18

Explanation:

Ryan is saving up for a bike that costs $198.

So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.

$198 – $180 = $18 need in order to buy the bike.

Thus the correct answer is option b.

Question 5.

Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric leftover. How many yards of material did Tina use?

Options:

a. 1 \(\frac{4}{8}\)

b. 2 \(\frac{1}{8}\)

c. 2 \(\frac{4}{8}\)

d. 5 \(\frac{2}{8}\)

Answer: c. 2 4/8

Explanation:

Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric leftover.

3 -1 = 2; 7/8 – 3/8 = 4/8.

So, the answer is 2 \(\frac{4}{8}\).

Thus the correct answer is option c.

Question 6.

Which list shows the fractions in order from least to greatest?

Options:

a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)

b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)

c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)

d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer: d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:

2/3 = 0.666

3/4 = 0.75

7/12 = 0.5833

\(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Thus the correct answer is option d.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 161

**Multiply a Fraction by a Whole Number Using Models**

**Multiply.**

Question 1.

Question 2.

3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:

3 x 2/5 = 6/5

Question 3.

7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:

7 x 3/10 = 21/10

Question 4.

3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:

3 x 5/12 = 15/12

Question 5.

6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:

6 x 3/4 = 18/4

Question 6.

4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:

4 x 2/8 = 8/8

Question 7.

5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:

5 x 2/3 = 10/3

Question 8.

2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:

2 x 7/8 = 14/8

Question 9.

6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:

6 x 4/5 = 28/5

**Problem Solving**

Question 10.

Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?

\(\frac{□}{□}\)

Answer: 25/8 miles

Explanation:

Matthew walks 5/8 mile to the bus stop each morning.

In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.

Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?

\(\frac{□}{□}\)

Answer: 6/3 cups of milk

Explanation:

Emily uses a 2/3 cup of milk to make one batch of muffins.

Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

### Common Core – Multiply Fractions by Whole Numbers – Page No. 162

**Lesson Check**

Question 1.

Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?

Options:

a. \(\frac{8}{12}\) pound

b. 1 \(\frac{2}{8}\) pounds

c. \(\frac{12}{8}\) pounds

d. 4 \(\frac{3}{8}\) pounds

Answer: \(\frac{12}{8}\) pounds

Explanation:

Aleta’s puppy gained 3/8 pound each week.

It gained 4 x 3/8 = 12/8 pounds in 4 weeks.

Thus the correct answer is option c.

Question 2.

Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?

Options:

a. \(\frac{3}{20}\) teaspoon

b. \(\frac{4}{15}\) teaspoon

c. \(\frac{8}{4}\) teaspoons

d. \(\frac{15}{4}\) teaspoons

Answer: d. \(\frac{15}{4}\) teaspoons

Explanation:

If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.

Thus the correct answer is option d.

**Spiral Review**

Question 3.

Ivana has \(\frac{3}{4}\)pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?

Options:

a. \(\frac{1}{4}\) pound

b. \(\frac{1}{3}\) pound

c. 2 \(\frac{1}{4}\) pounds

d. 3 pounds

Answer: a. \(\frac{1}{4}\) pound

Explanation:

Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.

Each patty weighs the same amount. So, each hamburger patty weighs 1/4 pound.

Thus the correct answer is option a.

Question 4.

Which of the following expressions is NOT equal to \(\frac{7}{10}\)?

Options:

a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)

b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)

c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)

d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer: c. 3/10+3/10+2/10

Explanation:

a. 5/10+1/10+1/10 = 7/10

b. 2/10+2/10+3/10 = 7/10

c. 3/10+3/10+2/10 = 8/10

d. 4/10+2/10+1/10 = 7/10

The expression not equal to \(\frac{7}{10}\) is \(\frac{8}{10}\)

Thus the correct answer is option c.

Question 5.

Lance wants to find the total length of 3 boards. He uses the expression \(3 \frac{1}{2}+\left(2+4 \frac{1}{2}\right)\). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?

Options:

a. \(5+4 \frac{1}{2}\)

b. \(\left(3 \frac{1}{2}+2\right)+4 \frac{1}{2}\)

c. \(2+\left(3 \frac{1}{2}+4 \frac{1}{2}\right)\)

d. \(3 \frac{1}{2}+\left(4 \frac{1}{2}+2\right)\)

Answer: She can write as (3 1/2 + 2) + 4 1/2

Question 6.

Which of the following statements is true?

Options:

a. \(\frac{5}{8}>\frac{9}{10}\)

b. \(\frac{5}{12}>\frac{1}{3}\)

c. \(\frac{3}{6}>\frac{4}{5}\)

d. \(\frac{1}{2}>\frac{3}{4}\)

Answer: \(\frac{1}{2}>\frac{3}{4}\)

Explanation:

0.625 > 0.9

0.416 > 0.333

0.5 > 0.8

0.5 > 0.75

Thus the correct answer is option d.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 163

**Multiply a Fraction or Mixed Number by a Whole Number.**

**Multiply. Write the product as a mixed number.**

Question 1.

Answer:

1 5/10

Explanation:

5 × 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1 5/10

Question 2.

3 × \(\frac{3}{5}\) =

_____ \(\frac{□}{□}\)

Answer:

1 × 4/5

Explanation:

3 × 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1 4/5

Question 3.

5 × \(\frac{3}{4}\) =

_____ \(\frac{□}{□}\)

Answer:

3 3/4

Explanation:

15/4 = 3 and the remainder is 3. So, the mixed fraction is 3 3/4

Question 4.

4 × 1 \(\frac{1}{5}\) =

_____ \(\frac{□}{□}\)

Answer:

4 4/5

Explanation:

1 ×15 = 6/5.

4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4× 4/5

Question 5.

2 × 2 \(\frac{1}{3}\) =

_____ \(\frac{□}{□}\)

Answer:

4 2/3

Explanation:

2 13 = 7/3.

2 x 7/3 = 14/3.

14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.

5 × 1 \(\frac{1}{6}\) =

_____ \(\frac{□}{□}\)

Answer: 5 5/6

Explanation:

1 1/6 = 7/6

5 x 7/6 = 35/6.

35/6 = 5 and the remainder is 5.

So, the mixed fraction is 5 5/6

Question 7.

2 × 2 \(\frac{7}{8}\) =

_____ \(\frac{□}{□}\)

Answer: 6 1/1

Explanation:

2 7/8 = 23/8

2 x 23/8 = 46/8 = 6 1/1

Question 8.

7 × 1 \(\frac{3}{4}\) =

_____ \(\frac{□}{□}\)

Answer: 9 3/4

Explanation:

1 3/4 = 7/4

7 x 7/4 = 39/4

39/4 = 9 and the remainder is 3.

So, the mixed fraction is 9 3/4

Question 9.

8 × 1 \(\frac{3}{5}\) =

_____ \(\frac{□}{□}\)

Answer: 12 4/5

Explanation:

1 3/5 = 8/5

8 x 8/5 = 64/5

64/5 = 12 and the remainder is 4.

So, the mixed fraction is 12 4/5

**Problem Solving**

Question 10.

Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?

_____ \(\frac{□}{□}\)

Answer: 4 2/4

Explanation:

6 x 3/4 = 18/4 = 4 and the remainder is 2.

So, the mixed fraction is 4 2/4.

Question 11.

A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?

_____ \(\frac{□}{□}\)

Answer: 10 2/3

Explanation:

quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.

So, 4 x 8/3 = 32/3 = 10 and the remainder is 2.

So, the mixed fraction is 10 2/3

### Common Core – Multiply Fractions by Whole Numbers – Page No. 164

**Lesson Check**

Question 1.

A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?

Options:

a. 4 \(\frac{3}{4}\) feet

b. 5 \(\frac{1}{4}\) feet

c. 5 \(\frac{1}{2}\) feet

d. 5 \(\frac{3}{4}\) feet

Answer: b. 5 1/4 feet

Explanation:

A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.

So, 3 x 7/4 = 21/4 = 5 and the remainder is 1.

The mixed fraction is 5 1/4 feet.

Thus the correct answer is option b.

Question 2.

The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?

Options:

a. 8 \(\frac{1}{3}\) feet

b. 8 \(\frac{3}{8}\) feet

c. 10 \(\frac{1}{3}\) feet

d. 10 \(\frac{2}{3}\) feet

Answer: d. 10 2/3 feet

Explanation:

The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 1/3 times the width of the banner.

So, 8 x 4/3 = 32/3 =10 and the remainder is 2.

The mixed fraction is 10 2/3 feet.

Thus the correct answer is option d.

**Spiral Review**

Question 3.

Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?

Options:

a. \(\frac{5}{40}\) mile

b. \(\frac{25}{40}\) mile

c. \(\frac{10}{8}\) miles

d. \(\frac{25}{8}\) miles

Answer: d. 25/8 miles

Explanation:

5 x 5/8 = 25/8.

Thus the correct answer is option d.

Question 4.

Which number is a multiple of \(\frac{4}{5}\)?

Options:

a. \(\frac{8}{10}\)

b. \(\frac{12}{15}\)

c. \(\frac{16}{20}\)

d. \(\frac{12}{5}\)

Answer: d. 12/5

Explanation:

The multiple of 45 has the denominator 5.

So, 12/5 is the correct answer.

Thus the correct answer is option d.

Question 5.

Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?

Options:

a. 5

b. 6

c. 7

d. 8

Answer: c. 7

Explanation:

Jo cut a key lime pie into 8 equal-size slices.

The next day, 78 of the pie is left. Jo puts each slice on its own plate.

She needs 7 plates.

Thus the correct answer is option c.

Question 6.

Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?

Options:

a. 3 hours

b. 2 \(\frac{3}{4}\) hours

c. 2 \(\frac{1}{2}\) hours

d. 2 hours

Answer: a. 3 hours

Explanation:

Given,

Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project.

5/4 + 7/4 = 12/4 = 3 hours

Thus the correct answer is option a.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 165

**Problem Solving Comparison**

**Problems with Fractions**

**Read each problem and solve.**

Question 1.

A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?

Answer: 5 feet

Explanation:

Question 2.

You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?

_________ miles

Answer: 7 miles

Explanation:

Given,

You run 1 \(\frac{3}{4}\) miles each day.

Your friend runs 4 times as far as you do.

4 x 7/4 = 7 miles each day

Question 3.

At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?

_____ \(\frac{□}{□}\) pounds

Answer: 2 2/3 pounds

Explanation:

Given,

At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey.

Tasha buys 2 times as much ground turkey as Ayla.

2 x 4/3 = 8/3 = 2 and the remainder is 2.

The mixed fraction is 2 2/3 pounds.

Question 4.

When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?

\(\frac{□}{□}\) hours

Answer: 4/5 hours

Explanation:

Given,

When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour.

When Nathan walks to school, it takes him 4 times as long to get to school.

4 x 1/5 = 4/5 hour

It takes 4/5 hour Nathan to walk to school.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 166

**Lesson Check**

Question 1.

A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?

Options:

a. \(\frac{4}{21}\) foot

b. 2 \(\frac{1}{3}\) feet

c. 7 \(\frac{1}{3}\) feet

d. 9 \(\frac{1}{3}\) feet

Answer: d. 9 1/3 feet

Explanation:

Given,

A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet.

A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel.

Convert from mixed fraction to the improper fraction.

1 1/3 = 4/3.

7 x 4/3 = 28/3 feet = 9 and the remainder is 1.

The mixed fraction is 9 1/3

Thus the correct answer is option d.

Question 2.

The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?

Options:

a. \(\frac{9}{80}\) mile

b. \(\frac{72}{80}\) mile

c. 1 \(\frac{7}{10}\) miles

d. 7 \(\frac{2}{10}\) miles

Answer: d. 7 2/10 miles

Explanation:

Given,

The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile.

The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far.

8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2.

The mixed fraction is 7 2/10 miles.

Thus the correct answer is option d.

**Spiral Review**

Question 3.

Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?

Options:

a. \(3 \times \frac{9}{4}\)

b. (3 × 2) + (3 × \(\frac{1}{4}\))

c. 6 \(\frac{3}{4}\)

d. 3 × 2 + \(\frac{1}{4}\)

Answer: d. 3 × 2 + 14

Explanation:

3 × 2 14 = 3 x 9/4 = 27/4

a. 3 × 94 = 27/4

b. (3 × 2) + (3 × 14) = 6 + 3/4 = 27/4

c. 6 3/4 = 27/4

d. 3 × 2 + 14 = 6 + 1/4 = 25/4

Thus the correct answer is option d.

Question 4.

At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?

Options:

a. \(\frac{2}{8}\)

b. \(\frac{12}{16}\)

c. \(\frac{12}{8}\)

d. \(\frac{35}{8}\)

Answer: c. 12/8

Explanation:

Given,

At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie.

7/8 + 5/8 = 12/8

The bake sale 12/8 pie.

Thus the correct answer is option c.

Question 5.

On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?

Options:

a. \(\frac{1}{16}\) inch

b. \(\frac{1}{8}\) inch

c. \(\frac{11}{16}\) inch

d. \(\frac{15}{16}\) inch

Answer: c. 11/16 inch

Explanation:

Subtract \(\frac{3}{16}\) inch and \(\frac{7}{8}\)

Make denominators as common.

\(\frac{7}{8}\) × \(\frac{2}{2}\) = \(\frac{14}{16}\)

\(\frac{14}{16}\) – \(\frac{3}{16}\) = \(\frac{11}{16}\) inch.

Thus the correct answer is option c.

Question 6.

Which of the following numbers is composite?

Options:

a. 4

b. 3

c. 2

d. 1

Answer:

a. 4

Explanation:

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.

The factors of 4 are 1, 2, 4.

4 has more than 2 factors.

Thus the correct answer is option a.

### Common Core – Multiply Fractions by Whole Numbers – Page No. 167

**Lesson 8.1**

**Write the fraction as a product of a whole number and a unit fraction.**

Question 1.

\(\frac{5}{6}\) =

Type below:

________

Answer: 5 x 1/6

Explanation:

Given that 5/6 or 5 sixth-size parts.

Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.

You can use unit fractions to show 5/6

\(\frac{5}{6}\) = 5 x 1/6.

Question 2.

\(\frac{7}{8}\) =

Type below:

________

Answer: 7 x 1/8

Explanation:

Given that 7/8 or 7 eighth-size parts.

Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.

You can use unit fractions to show 7/8

\(\frac{7}{8}\) = 7 x 1/8.

Question 3.

\(\frac{3}{5}\) =

Type below:

________

Answer: 5 x 1/3

Explanation:

Given that 5/3 or 5 third-size parts.

Each third-size part of the given fraction can be shown by the unit fraction 1/3.

You can use unit fractions to show 5/6

5/3 = 5 x 1/3.

**List the next four multiples of the unit fraction**

Question 4.

\(\frac{1}{2}\),

Type below:

________

Answer: 2/2, 3/2, 4/2, 5/2

Explanation:

1 x 1/2 = 1/2.

2 x 1/2 = 2/2.

3 x 1/2 = 3/2.

4 x 1/2 = 4/2.

5 x 1/2 = 5/2.

The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 5.

\(\frac{1}{6}\),

Type below:

________

Answer: 2/6, 3/6, 4/6, 5/6,6/6.

Explanation:

1 x 1/6 = 1/6.

2 x 1/6 = 2/6.

3 x 1/6 = 3/6.

4 x 1/6 = 4/6.

5 x 1/6 = 5/6.

6 x 1/6 = 6/6.

The next four multiples of 1/6 are 2/6, 3/6, 4/6, 5/6,6/6.

**Lesson 8.2**

**List the next four multiples of the fraction.**

Question 6.

\(\frac{3}{10}\),

Type below:

________

Answer: 6/10, 9/10, 12/10, 15/10

Explanation:

1 × 3/10 = 3/10

2 × 3/10 = 6/10

3 × 3/10 = 9/10

4 × 3/10 = 12/10

5 × 3/10 = 15/10

Question 7.

\(\frac{7}{12}\),

Type below:

________

Answer: 7/12, 14/12, 21/12, 28/12, 35/12

Explanation:

1 × 7/12 = 7/12

2 × 7/12 = 14/12

3 × 7/12 = 21/12

4 × 7/12 = 28/12

5 × 7/12 = 35/12

**Write the product as the product of a whole number and a unit fraction.**

Question 8.

2 × \(\frac{3}{6}\) =

Type below:

________

Answer:

1 group of \(\frac{3}{6}\) is \(\frac{3}{6}\)

2 groups of \(\frac{3}{6}\) is \(\frac{6}{6}\)

2 × \(\frac{3}{6}\) = \(\frac{6}{6}\)

Question 9.

3 × \(\frac{2}{8}\) =

Type below:

________

Explanation:

1 group of \(\frac{2}{8}\) is \(\frac{2}{8}\)

2 group of \(\frac{2}{8}\) is \(\frac{4}{8}\)

3 group of \(\frac{2}{8}\) is \(\frac{6}{8}\)

3 × \(\frac{2}{8}\) = \(\frac{6}{8}\)

### Common Core – Multiply Fractions by Whole Numbers – Page No. 168

**Lesson 8.3**

**Multiply.**

Question 1.

3 × \(\frac{7}{10}\) =

\(\frac{□}{□}\)

Answer: \(\frac{21}{10}\)

Explanation:

Multiply 7 and 3

3 × 7 = 21

3 × \(\frac{7}{10}\) = \(\frac{21}{10}\)

Question 2.

5 × \(\frac{4}{8}\) =

\(\frac{□}{□}\)

Answer: 20/8

Explanation:

Multiply 5 and 4

5 × 4 = 20

5 × \(\frac{4}{8}\) = \(\frac{20}{8}\)

Question 3.

4 × \(\frac{6}{12}\) =

\(\frac{□}{□}\)

Answer: 24/12

Explanation:

Multiply 4 and 6

4 × 6 = 24

4 × \(\frac{6}{12}\) = \(\frac{24}{12}\)

Question 4.

2 × \(\frac{3}{4}\) =

\(\frac{□}{□}\)

Answer: 6/4

Explanation:

Multiply 2 and 3

2 × 3 = 6

2 × \(\frac{3}{4}\) = \(\frac{6}{4}\)

Question 5.

6 × \(\frac{3}{5}\) =

\(\frac{□}{□}\)

Answer: 18/5

Explanation:

Multiply 6 and 3

6 × 3 =18

6 × \(\frac{3}{5}\) = \(\frac{18}{5}\)

Question 6.

7 × \(\frac{2}{10}\) =

\(\frac{□}{□}\)

Answer: 14/10

Explanation:

Multiply 7 and 2.

7 × 2 =14

7 × \(\frac{2}{10}\) = \(\frac{14}{10}\)

**Lesson 8.4**

**Multiply. Write the product as a mixed number.**

Question 7.

4 × \(\frac{8}{10}\) =

_____ \(\frac{□}{□}\)

Answer: 3 2/10

Explanation:

Given,

4 × \(\frac{8}{10}\)

First multiply 4 and 8

4 × 8 = 32

4 × \(\frac{8}{10}\) = 32/10

Now convert from improper fraction to the mixed fraction.

32/10 = 3 \(\frac{2}{10}\)

Question 8.

3 × \(\frac{5}{6}\) =

_____ \(\frac{□}{□}\)

Answer: 2 3/6

Explanation:

Given,

3 × \(\frac{5}{6}\)

First multiply 3 and 5.

3 × 5 =15

3 × \(\frac{5}{6}\) = 15/6

Now convert from improper fraction to the mixed fraction.

15/6 = 2 3/6

Question 9.

2 × 3 \(\frac{1}{3}\) =

_____ \(\frac{□}{□}\)

Answer: 6 2/3

Explanation:

Given,

2 × 3 \(\frac{1}{3}\)

3 \(\frac{1}{3}\) = 10/3

2 × 10/3 = 20/3

Now convert from improper fraction to the mixed fraction.

20/3 = 6 2/3

Question 10.

4 × 2 \(\frac{2}{5}\) =

_____ \(\frac{□}{□}\)

Answer: 9 3/5

Explanation:

Given,

4 × 2 \(\frac{2}{5}\)

2 \(\frac{2}{5}\) = 4/5

4 × 12/5 = 48/5

Now convert from improper fraction to the mixed fraction.

48/5 = 9 3/5

Question 11.

5 × 1 \(\frac{7}{8}\) =

_____ \(\frac{□}{□}\)

Answer: 9 3/8

Explanation:

Given,

5 × 1 \(\frac{7}{8}\)

5 × 15/5 = 75/5

Now convert from improper fraction to the mixed fraction.

75/5 = 9 3/8

Question 12.

3 × 3 \(\frac{3}{4}\) =

_____ \(\frac{□}{□}\)

Answer: 11 1/4

Explanation:

Given,

3 × 3 \(\frac{3}{4}\)

3 × 15/4 = 45/4

Now convert from improper fraction to the mixed fraction.

45/4 = 11 1/4

**Lesson 8.5**

Question 13.

A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall. A small tree in her back yard is 7 times as tall as the shrub. About how tall is the tree?

_____ \(\frac{□}{□}\) feet

Answer: 9 5/2 feet.

Explanation:

Given,

A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall.

A small tree in her back yard is 7 times as tall as the shrub.

9.625 ft because 1 3/8 × 7 is equal to 9 5/2 feet

Therefore the tree is 9 5/2 feet.

Question 14.

A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much. How much does the mother weigh?

_____ \(\frac{□}{□}\) pounds

Answer: 7 \(\frac{2}{10}\) pounds

Explanation:

Given,

A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much.

\(\frac{9}{10}\) × 8 = 72/10

Convert from improper fraction to the mixed fraction.

72/10 = 7 \(\frac{2}{10}\) pounds

Thus the mother weigh 7 \(\frac{2}{10}\) pounds.

*Conclusion:*

Refer HMH Go Math Solution Key for Grade 4 Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers to secure good marks in the exams. Most of the students believe that fractions are difficult but it is easiest of all the chapters if you understand the logic and tricks to solve. Get more number of questions from Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers.