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

## HMH Into Math Grade 4 Module 16 Lesson 4 Answer Key Solve Problems Using Multiplication of a Fraction or Mixed Number by a Whole Number

I Can solve problems involving the multiplication of mixed numbers and whole numbers.

**Step It Out**

Question 1.

Armando is a plant biologist who works at an urban indoor vertical farm. He adds 1\(\frac{1}{4}\) gallons of plant food to each of 3 arugula trays. How much plant food does he use?

A. Write 1\(\frac{1}{4}\) as a fraction greater than 1.

Answer:

\(\frac{5}{4}\)

Explanation:

When the numerator of the fraction is greater than the denominator, it is a fraction greater than 1.

1\(\frac{1}{4}\) = \(\frac{5}{4}\)

B. Write a multiplication equation representing the product of the whole number and the fraction greater than 1.

Answer:

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

Explanation:

When the numerator of the fraction is greater than the denominator, it is a fraction greater than 1.

1\(\frac{1}{4}\) = 3 x \(\frac{5}{4}\) = \(\frac{15}{4}\)

C. Write the product as a mixed number.

Answer:

3 x \(\frac{5}{4}\)

Explanation:

1\(\frac{1}{4}\) = \(\frac{5}{4}\)

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

D. How much plant food does Armando use?

Answer:

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

Explanation:

Armando adds 1\(\frac{1}{4}\) gallons of plant food to each of 3 arugula trays.

Total plant food he use = 3 x \(\frac{5}{4}\) = \(\frac{15}{4}\)

**Turn and Talk** How could you use the Distributive Property to find the product using mental math?

Answer:

Distributive property means multiplying the sum of two or more addends by a number will give the same result. So, multiplying each addend individually by the number and then adding the products together.

Explanation:

8 x 34 = 272

8 ( 30 + 4) = 240 + 32 = 272

Question 2.

Each tray of herbs at the vertical farm uses 2\(\frac{3}{4}\) packets of seeds. How many packets are needed for 6 trays?

A. Rename 2\(\frac{3}{4}\) as a fraction greater than 1.

Answer:

\(\frac{11}{4}\)

Explanation:

When the numerator of the fraction is greater than the denominator, it is a fraction greater than 1.

2\(\frac{3}{4}\) = \(\frac{11}{4}\)

B. Write an equation to model the product of the whole number and the fraction greater than 1 and then solve it. Let p represent the number of packets needed.

Answer:

16 \(\frac{1}{2}\) packets needed.

Explanation:

P = 2\(\frac{3}{4}\)

p = \(\frac{11}{4}\)

number of packets needed = 6 x \(\frac{11}{4}\)

= \(\frac{66}{4}\) = 16\(\frac{1}{2}\)

C. Rename the product as a mixed number.

Answer:

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

Explanation:

for 1 tray = 2\(\frac{3}{4}\) = \(\frac{11}{4}\)

For 6 trays = 6 x \(\frac{11}{4}\)

= \(\frac{66}{4}\) = 16\(\frac{1}{2}\)

D. How many packets are needed for 6 trays?

Answer:

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

Explanation:

for 1 tray = 2\(\frac{3}{4}\) = \(\frac{11}{4}\)

for 6 trays = 6 x \(\frac{11}{4}\)

= \(\frac{66}{4}\) = 16\(\frac{1}{2}\)

**Turn and Talk** How could you find the product of this problem without renaming 2\(\frac{3}{4}\) as a fraction greater than 1?

Answer:

\(\frac{11}{4}\)

Explanation:

Convert the mixed fraction into improper fraction.

2\(\frac{3}{4}\) = \(\frac{11}{4}\)

**Check Understanding**

Question 1.

Tammi uses 2\(\frac{2}{3}\) gallons of water on her plants once a week. How much water does she use in 3 weeks?

Answer:

8 gallons

Explanation:

Tammi uses 2\(\frac{2}{3}\) gallons of water on her plants once a week.

Total gallons of water she use in 3 weeks,

2\(\frac{2}{3}\) = \(\frac{8}{3}\)

3 x \(\frac{8}{3}\) = \(\frac{24}{3}\) = 8 gallons

Question 2.

At an urban vertical farm, each tray of arugula makes about 3\(\frac{5}{8}\) pounds of edible plants. How many pounds will 5 trays make?

Answer:

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

Explanation:

Each tray of arugula makes about 3\(\frac{5}{8}\) pounds of edible plants.

5 trays will make = 5 x 3\(\frac{5}{8}\)

= 5 x \(\frac{29}{8}\) = \(\frac{145}{8}\)

= 18\(\frac{1}{8}\)

**Find the product.**

Question 3.

5 × 3\(\frac{4}{5}\) = __________

Answer:

\(\frac{95}{5}\) = 19

Explanation:

5 x 3\(\frac{4}{5}\) = 5 x \(\frac{19}{5}\)

= \(\frac{95}{5}\) = 19

Question 4.

4 × 3\(\frac{2}{3}\) = ___________

Answer:

\(\frac{44}{3}\)

Explanation:

4 x 3\(\frac{2}{3}\) = 4 x \(\frac{11}{3}\)

= \(\frac{44}{3}\)

**On Your Own**

Question 5.

**Model with Mathematics** Mr. Dayton uses 3\(\frac{3}{8}\) gallons of diesel fuel in his tractor each time he plows one of his four 50-acre fields. If he plows 4 fields, how much diesel fuel does he use? Model the problem with an equation, and then solve it.

Answer:

13\(\frac{4}{8}\) = 13.5gallon

Explanation:

Dayton uses 3\(\frac{3}{8}\) gallons of diesel fuel in his tractor each time 50-acre field.

If he plows 4 fields, how much diesel fuel does he use = 4 x 3\(\frac{3}{8}\)

= 4 x \(\frac{27}{8}\) = \(\frac{27×4}{8}\)

= \(\frac{108}{8}\) = 13\(\frac{4}{8}\) = 13.5gallon

Question 6.

**Use Structure** Ms. Abad purchases 7 packages of prewashed spinach to make a large salad for a school potluck dinner. Each package contains 1\(\frac{1}{4}\) pounds of spinach. How many pounds of spinach does Ms. Abad purchase?

Answer:

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

Explanation:

Ms. Abad purchases 7 packages of prewashed spinach to make a large salad for a school potluck dinner.

Each package contains 1\(\frac{1}{4}\) pounds of spinach.

Total pounds of spinach Ms. Abad purchase = 7 x 1\(\frac{1}{4}\)

= 7 x \(\frac{5}{4}\) = \(\frac{35}{4}\) = 8\(\frac{3}{4}\)

Question 7.

**Use Repeated Reasoning** Lanny is planting radishes in 4 garden plots.. He uses 8\(\frac{2}{5}\) ounces of radish seeds in each plot. How many ounces of seeds does he use?

Answer:

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

Explanation:

Lanny is planting radishes in 4 garden plots.

He uses 8\(\frac{2}{5}\) ounces of radish seeds in each plot.

Total ounces of seeds he use = 4 x 8\(\frac{2}{5}\)

= 4 x \(\frac{42}{5}\) = \(\frac{42×4}{5}\)

= \(\frac{168}{5}\) = 33\(\frac{3}{5}\)

Question 8.

**Critique Reasoning** Darrin says he can find 4 × 3\(\frac{2}{5}\) by finding (4 × 3) + (4 × \(\frac{2}{5}\)). Is Darrin correct? Explain.

Answer:

Darrin is wrong.

Explanation:

4 × 3\(\frac{2}{5}\) = (4 × 3) + (4 × \(\frac{2}{5}\)).

4 × \(\frac{17}{5}\) = (12) + (\(\frac{22}{5}\)).

\(\frac{17×4}{5}\) = (12×5) + (\(\frac{22}{5}\)).

\(\frac{68}{5}\) = \(\frac{60+22}{5}\)

\(\frac{68}{5}\) = \(\frac{82}{5}\)

**Find the product. If possible, write your answer as a mixed number.**

Question 9.

4 × 3\(\frac{5}{6}\) = ___________

Answer:

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

Explanation:

4 × 3\(\frac{5}{6}\) = 4 x \(\frac{23}{6}\)

\(\frac{92}{6}\) = 15\(\frac{2}{6}\)

Question 10.

10 × 2\(\frac{3}{4}\) = ___________

Answer:

27\(\frac{2}{4}\) = 27.5

Explanation:

10 × 2\(\frac{3}{4}\) = 10 x \(\frac{11}{4}\)

\(\frac{110}{4}\) = 27\(\frac{2}{4}\)

Question 11.

8 × 5\(\frac{2}{3}\) = ___________

Answer:

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

Explanation:

8 × 5\(\frac{2}{3}\) = 8 x \(\frac{17}{3}\)

\(\frac{136}{3}\) = 45\(\frac{1}{3}\)

Question 12.

2 × 2\(\frac{7}{12}\) = ___________

Answer:

5\(\frac{2}{12}\)

Explanation:

2 × 2\(\frac{7}{12}\) = 2 x \(\frac{31}{12}\)

\(\frac{62}{12}\) = 5\(\frac{2}{12}\)

Question 13.

4 × 2\(\frac{4}{5}\) = ___________

Answer:

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

Explanation:

4 × 2\(\frac{4}{5}\) = 4 x \(\frac{14}{5}\)

\(\frac{56}{5}\) = 11\(\frac{1}{5}\)

Question 14.

3 × 3\(\frac{3}{8}\) = ___________

Answer:

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

Explanation:

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

\(\frac{81}{8}\) = 10\(\frac{1}{8}\)

Question 15.

**Reason** David takes care of two horses. One horse eats 1\(\frac{1}{4}\) bags of oats each week. The other horse eats 11 bags of oats each week. How many bags of oats does David feed the two horses over 7 weeks?

Answer:

96\(\frac{1}{4}\)

Explanation:

One horse eats 1\(\frac{1}{4}\) bags of oats each week.

The other horse eats 11 bags of oats each week.

Total bags of oats David feed the two horses over 1 week = 11 x 1\(\frac{1}{4}\)

= 11 x \(\frac{5}{4}\) = \(\frac{55}{4}\) = 13\(\frac{3}{4}\) bags

Total bags of oats David feed the two horses over 7 weeks = 7 x 13\(\frac{3}{4}\)

7 x \(\frac{55}{4}\) = \(\frac{385}{4}\) = 96\(\frac{1}{4}\)

Question 16.

**Use Structure** Langston has 8 packets of corn seeds that he wants to plant in a community garden. Each packet contains 2\(\frac{2}{3}\) ounces of seeds. How many ounces of seeds does he have?

Answer:

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

Explanation:

Langston has 8 packets of corn seeds.

Each packet contains 2\(\frac{2}{3}\) ounces of seeds.

Total ounces of seeds he have in all = 8 x 2\(\frac{2}{3}\)

= 8 x \(\frac{8}{3}\) = \(\frac{64}{3}\) = 21\(\frac{1}{3}\)

Question 17.

**Model with Mathematics** A recipe for 1 loaf of bread calls for 1\(\frac{1}{4}\) cups of milk. Wade wants to make 4 loaves. How much milk does he need? Model the problem with an equation and then solve it. Let c represent the amount of milk he needs for 4 loaves.

Answer:

5 cups of milk

Explanation:

A recipe for 1 loaf of bread calls for 1\(\frac{1}{4}\) cups of milk.

Wade wants to make 4 loaves.

Total milk he need for 4 loaves = 4 x 1\(\frac{1}{4}\)

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

Question 18.

Gordon is building a wooden table. Each leg is 3\(\frac{3}{8}\) feet long. What length of wood does he need for 4 legs?

Answer:

13\(\frac{4}{8}\) or 13 .5 feet long

Explanation:

Each leg is 3\(\frac{3}{8}\) feet long.

length of wood he need for 4 legs = 4 x 3\(\frac{3}{8}\)

= 4 x \(\frac{27}{8}\) = \(\frac{108}{8}\)

= 13\(\frac{4}{8}\) = 13 .5 feet long

**Find the product. If possible, write your answer as a mixed number.**

Question 19.

3 × 2\(\frac{5}{6}\) = ___________

Answer:

8\(\frac{3}{6}\)

Explanation:

3 x 2\(\frac{5}{6}\) = 3 x \(\frac{17}{6}\)

= \(\frac{51}{6}\) = 8\(\frac{3}{6}\)

Question 20.

4 × 4\(\frac{3}{10}\) = ___________

Answer:

17\(\frac{2}{10}\)

Explanation:

4 x 4\(\frac{3}{10}\) = 4 x \(\frac{43}{10}\)

= \(\frac{172}{10}\) = 17\(\frac{2}{10}\)

Question 21.

6 × 2\(\frac{9}{10}\) = ___________

Answer:

17\(\frac{4}{10}\)

Explanation:

6 x 2\(\frac{9}{10}\) = 6 x \(\frac{29}{10}\)

= \(\frac{174}{10}\) = 17\(\frac{4}{10}\)

Question 22.

2 × 3\(\frac{3}{6}\) = ___________

Answer:

\(\frac{42}{6}\) = 8

Explanation:

2 x 3\(\frac{3}{6}\) = 2 x \(\frac{21}{6}\)

= \(\frac{42}{6}\) = 8

Question 23.

7 × 2\(\frac{3}{4}\) = ___________

Answer:

19\(\frac{1}{4}\)

Explanation:

7 x 2\(\frac{3}{4}\) = 7 x \(\frac{11}{4}\)

= \(\frac{77}{4}\) = 19\(\frac{1}{4}\)

Question 24.

9 × 2\(\frac{2}{3}\) = ___________

Answer:

\(\frac{72}{3}\) = 24

Explanation:

9 x 2\(\frac{2}{3}\) = 9 x \(\frac{8}{3}\)

= \(\frac{72}{3}\) = 24