We included **HMH Into Math Grade 4 Answer Key PDF** **Module 16 Lesson 3 Represent Multiplication of a Fraction by a Whole Number **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 16 Lesson 3 Answer Key Represent Multiplication of a Fraction by a Whole Number

I Can find the product of a whole number and a fraction using a visual representation or an equation.

**Spark Your Learning**

Ari and his band practice for \(\frac{2}{5}\) hour each day. It is 4 days until the school talent show. How many hours will the band practice in 4 days?

Show how you found your answer.

Answer:

4 x \(\frac{2}{5}\) = \(\frac{8}{5}\)

Explanation:

Ari and his band practice for \(\frac{2}{5}\) hour each day.

It is 4 days until the school talent show.

Number of hours will the band practice in 4 days = 4 x \(\frac{2}{5}\)

= \(\frac{4×2}{5}\) = \(\frac{8}{5}\)

**Turn and Talk** What if Ari and his band practice for 7 days? Is the product 7 × \(\frac{2}{5}\) greater than or less than the factor 7? Is the product greater than or less than the factor \(\frac{2}{5}\)? Explain.

Answer:

7 x \(\frac{2}{5}\) = \(\frac{14}{5}\)

product is greater than the factor \(\frac{2}{5}\)

Explanation:

Ari and his band practice for \(\frac{2}{5}\) hour each day.

It is 7 days until the school talent show.

Number of hours will the band practice in 7 days = 7 x \(\frac{2}{5}\)

= \(\frac{7×2}{5}\) = \(\frac{14}{5}\)

**Build Understanding**

Question 1.

Hayley is making 5 batches of goop to use in her science demonstration. How much corn starch does she need to make 5 batches?

Draw a visual model to show the product 5 × \(\frac{3}{4}\).

Answer:

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

A. How many equal groups of \(\frac{3}{4}\) did you draw? Explain.

Answer:

5 equal groups.

Explanation:

Each group is divided into four parts,

\(\frac{3}{4}\) corn starch is used in each group.

B. How can you describe the amount of corn starch needed for 1 batch, 2 batches, 3 batches, 4 batches, and 5 batches using groups?

Answer:

1batch \(\frac{3}{4}\) corn starch is needed,

2 batches \(\frac{3}{4}\) corn starch is needed,

3 batches \(\frac{3}{4}\) corn starch is needed,

4 batches \(\frac{3}{4}\) corn starch is needed,

5 batches \(\frac{3}{4}\) corn starch is needed.

Explanation:

1 group of \(\frac{3}{4}\) cup = \(\frac{3}{4}\)

2 groups of \(\frac{3}{4}\) cup = \(\frac{3×2}{4}\) = \(\frac{6}{4}\)

3 groups of \(\frac{3}{4}\) cup = \(\frac{3×3}{4}\) = \(\frac{9}{4}\)

4 groups of \(\frac{3}{4}\) cup = \(\frac{3×4}{4}\) = \(\frac{12}{4}\)

5 groups of \(\frac{3}{4}\) cup = \(\frac{3×5}{4}\) = \(\frac{15}{4}\)

C. How much corn starch does Hayley need to make 5 batches?

Answer:

\(\frac{15}{4}\)

Explanation:

5 x \(\frac{3}{4}\) = \(\frac{3×5}{4}\) = \(\frac{15}{4}\)

Question 2.

Kelvin is ordering balloons to make balloon animals. He purchases 4 packets of balloons. If each packet weighs \(\frac{3}{8}\) pound, how many pounds of balloons does Kelvin order?

Draw a fraction model to show how many groups of \(\frac{1}{2}\) there are in 4 packets.

Answer:

Explanation:

4 x \(\frac{1}{2}\) = \(\frac{4}{2}\) = 2

A. How does your fraction model show how many groups of \(\frac{3}{8}\) pound represent the total weight of the balloons?

Answer:

4 x \(\frac{3}{8}\)

Explanation:

4 x \(\frac{3}{8}\) = \(\frac{12}{8}\)

B. How can you use multiplication to describe a way to solve the problem?

Answer:

By using multiplication operations.

Explanation:

Firstly read and understand what is asked in the problem.

Write the multiplication equation by using the multiplication property.

C. How can you write a multiplication equation to model the number of pounds of balloons Kelvin orders?

Let w = the total weight of balloons. .

Answer:

4 x \(\frac{3}{8}\)

Explanation:

w = the total weight of balloons.

weight of 1 balloon = \(\frac{3}{8}\)

Total weight of 4 balloons = 4 x \(\frac{3}{8}\)

D. How many pounds of balloons does Kelvin order?

Answer:

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

Explanation:

weight of 1 balloon = \(\frac{3}{8}\)

Total weight of 4 balloons = 4 x \(\frac{3}{8}\) = \(\frac{12}{8}\)

**Turn and Talk** Describe how to find the product 6 × \(\frac{2}{5}\) without using a picture or repeated addition.

Answer:

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

Explanation:

6 x \(\frac{2}{5}\) = \(\frac{6×2}{5}\) = \(\frac{12}{5}\)

**Step It Out**

Question 3.

Cara is preparing a kung fu demonstration for the talent show. She practices \(\frac{2}{3}\) hour each day for 5 days. How many hours does she practice over the 5 days?

A. Describe a visual representation that you could use to solve the problem.

Answer:

5 x \(\frac{2}{3}\)

B. Write an equation to model the problem. Let h = the total number of hours she practices.

Answer:

h = \(\frac{10}{3}\)

C. Find the product of the whole number and the numerator to find the number of thirds.

h =

Answer:

h =

D. How many hours does Cara practice over the 5 days?

Answer:

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

Explanation:

Cara practices \(\frac{2}{3}\) hour each day for 5 days.

Total hours she practice over the 5 days = 5\(\frac{2}{3}\)

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

**Check Understanding**

Question 1.

Jo is making smoothies. She uses \(\frac{5}{6}\) cup of strawberries in each smoothie. She makes 4 smoothies. How many cups of strawberries does she use?

Answer:

4 x \(\frac{5}{6}\) = \(\frac{20}{6}\)

Explanation:

Jo uses \(\frac{5}{6}\) cup of strawberries in each smoothie.

She makes 4 smoothies.

Total cups of strawberries she use = \(\frac{20}{6}\)

**Find the product.**

Question 2.

7 × \(\frac{3}{8}\) = ____________

Answer:

\(\frac{21}{8}\)

Explanation:

7 x \(\frac{3}{8}\) = \(\frac{3×7}{8}\) = \(\frac{21}{8}\)

Question 3.

3 × \(\frac{5}{6}\) = ____________

Answer:

\(\frac{15}{6}\)

Explanation:

3 x \(\frac{5}{6}\) = \(\frac{3×5}{6}\) = \(\frac{15}{6}\)

Question 4.

5 × \(\frac{3}{5}\) = ____________

Answer:

\(\frac{15}{5}\)

Explanation:

5 x \(\frac{3}{5}\) = \(\frac{5×3}{5}\) = \(\frac{15}{5}\)

Question 5.

9 × \(\frac{3}{4}\) = ____________

Answer:

\(\frac{27}{5}\)

Explanation:

9 x \(\frac{3}{4}\) = \(\frac{9×3}{4}\) = \(\frac{27}{4}\)

**On Your Own**

Question 6.

Art Pedro is making sand sculptures to display at the school art show. For each sculpture, he uses one bag of sand as shown. How many pounds of sand does he use for 4 sculptures?

Answer:

\(\frac{28}{10}\) pounds

Explanation:

1 bag of sand = \(\frac{7}{10}\) pounds

For each sculpture, he uses one bag of sand as shown.

Total pounds of sand he use for 4 sculptures = 4 x \(\frac{7}{10}\)

= \(\frac{7×4}{10}\) = \(\frac{28}{10}\) pounds

Question 7.

**Model with Mathematics** Emile walks \(\frac{7}{12}\) mile to school each morning. How far will he walk in 5 mornings? Model the problem with an equation and then solve.

Answer:

\(\frac{35}{12}\) mile

Explanation:

Emile walks \(\frac{7}{12}\) mile to school each morning.

How far will he walk in 5 mornings = 5 x \(\frac{7}{12}\) mile

= \(\frac{7×5}{12}\) mile = \(\frac{35}{12}\) mile

Question 8.

**Use Structure** Clarissa is making 4 bandanas as part of her costume for the school talent show. She uses \(\frac{3}{5}\) yard of fabric for each bandana. How much fabric does she need for 4 bandanas?

Answer:

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

Explanation:

Clarissa is making 4 bandanas as part of her costume for the school talent show.

She uses \(\frac{3}{5}\) yard of fabric for each bandana.

Total fabric she need for 4 bandanas = 4 x \(\frac{3}{5}\)

= \(\frac{3×4}{5}\) = \(\frac{12}{5}\)

Question 9.

**Model with Mathematics** Lana bakes banana bread for a fundraiser. She uses \(\frac{3}{4}\) cup of bananas in each loaf. She bakes 5 loaves. How rany cups of bananas does she use? Describe a fraction model you could draw to represent the problem. Then, model it with an equation and solve the problem.

Answer:

\(\frac{15}{4}\)

Explanation:

Lana uses \(\frac{3}{4}\) cup of bananas in each loaf.

She bakes 5 loaves.

Total cups of bananas she use = 5 x \(\frac{3}{4}\)

= \(\frac{3×5}{4}\) = \(\frac{15}{4}\)

**Find the product.**

Question 10.

2 × \(\frac{5}{6}\) = ____________

Answer:

\(\frac{10}{6}\) = \(\frac{5}{3}\)

Explanation:

2 x \(\frac{5}{6}\) = \(\frac{2×5}{6}\) = \(\frac{10}{6}\)

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

Question 11.

3 × \(\frac{2}{3}\) = ____________

Answer:

\(\frac{6}{3}\) = 2

Explanation:

3 x \(\frac{2}{3}\) = \(\frac{2×3}{3}\) = \(\frac{6}{3}\)

simplify we get 2.

Question 12.

7 × \(\frac{3}{5}\) = ____________

Answer:

\(\frac{21}{5}\)

Explanation:

7 x \(\frac{3}{5}\) = \(\frac{7×3}{5}\) = \(\frac{21}{5}\)

Question 13.

3 × \(\frac{5}{12}\) = ____________

Answer:

\(\frac{6}{3}\) = 2

Explanation:

3 x \(\frac{5}{12}\) = \(\frac{3×5}{12}\) = \(\frac{15}{12}\)

Question 14.

4 × \(\frac{9}{10}\) = ____________

Answer:

\(\frac{36}{10}\)

Explanation:

4 x \(\frac{9}{10}\) = \(\frac{4×9}{10}\) = \(\frac{36}{10}\)

Question 15.

8 × \(\frac{2}{6}\) = ____________

Answer:

\(\frac{16}{6}\)

Explanation:

8 x \(\frac{2}{6}\) = \(\frac{2×8}{6}\) = \(\frac{16}{6}\)

Question 16.

**Reason** Alana is making bean soup. The recipe for 1 batch calls for \(\frac{3}{4}\) cup of beans. She wants to make 4 batches of soup. Her measuring cup holds \(\frac{1}{4}\) cup. How many times must she use her \(\frac{1}{4}\) cup to measure beans to have enough for 4 batches of soup? Show your work.

Answer:

4\(\frac{3}{4}\) = \(\frac{12}{4}\)

Explanation:

The recipe for 1 batch calls for \(\frac{3}{4}\) cup of beans.

She wants to make 4 batches of soup.

Her measuring cup holds \(\frac{1}{4}\) cup.

Number of times she use her \(\frac{1}{4}\) cup to measure beans to have enough for 4 batches of soup = 4\(\frac{3}{4}\) = \(\frac{12}{4}\)

Question 17.

**Use Repeated Reasoning** Jeff’s gerbil eats \(\frac{5}{8}\) pound of food in 1 week. His rabbit eats \(\frac{7}{8}\) pound of food in 1 week. How many pounds of food do Jeff’s animals eat in 6 weeks? Show your work.

Answer:

\(\frac{72}{8}\)

Explanation:

Jeff’s gerbil eats \(\frac{5}{8}\) pound of food in 1 week.

His rabbit eats \(\frac{7}{8}\) pound of food in 1 week.

Gerbil and Rabbit eats = \(\frac{5}{8}\) + \(\frac{7}{8}\)

= \(\frac{12}{8}\)

Total pounds of food Jeff’s animals eat in 6 weeks = 6 x \(\frac{12}{8}\)

= \(\frac{72}{8}\)

**Find the product.**

Question 18.

6 × \(\frac{2}{5}\) = ____________

Answer:

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

Explanation:

6 x \(\frac{2}{5}\) = \(\frac{6×2}{5}\) = \(\frac{12}{5}\)

Question 19.

4 × \(\frac{5}{8}\) = ____________

Answer:

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

Explanation:

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

Question 20.

3 × \(\frac{11}{12}\) = ____________

Answer:

\(\frac{33}{12}\)

Explanation:

3 x \(\frac{11}{12}\) = \(\frac{3×11}{12}\) = \(\frac{33}{12}\)

Question 21.

7 × \(\frac{4}{5}\) = ____________

Answer:

\(\frac{28}{5}\)

Explanation:

7 x \(\frac{4}{5}\) = \(\frac{7×4}{5}\) = \(\frac{28}{5}\)

Question 22.

9 × \(\frac{3}{8}\) = ____________

Answer:

\(\frac{27}{8}\)

Explanation:

9 x \(\frac{3}{8}\) = \(\frac{9×3}{8}\) = \(\frac{27}{8}\)

Question 23.

2 × \(\frac{7}{8}\) = ____________

Answer:

\(\frac{14}{8}\)

Explanation:

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

**I’m in a Learning Mindset!**

When a strategy did not work, how did I adjust?

Answer:

By using “Hit and Trial” “Guess and Check Back” method.

Explanation:

Read the problem carefully, list all the components of the given data to solve the problem,

when a strategy did not work.