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

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.
$$\frac{5}{4}$$
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.
$$\frac{15}{4}$$
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.
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?
$$\frac{15}{4}$$
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?
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.
$$\frac{11}{4}$$
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.
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.
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?
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?
$$\frac{11}{4}$$
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?
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?
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$$\frac{4}{5}$$ = __________
$$\frac{95}{5}$$ = 19
Explanation:
5 x 3$$\frac{4}{5}$$ = 5 x $$\frac{19}{5}$$
= $$\frac{95}{5}$$ = 19

Question 4.
4 × 3$$\frac{2}{3}$$ = ___________
$$\frac{44}{3}$$
Explanation:
4 x 3$$\frac{2}{3}$$ = 4 x $$\frac{11}{3}$$
= $$\frac{44}{3}$$

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.

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?
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?
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.
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$$\frac{5}{6}$$ = ___________
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$$\frac{3}{4}$$ = ___________
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$$\frac{2}{3}$$ = ___________
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$$\frac{7}{12}$$ = ___________
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$$\frac{4}{5}$$ = ___________
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$$\frac{3}{8}$$ = ___________
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?
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?
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.
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?
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$$\frac{5}{6}$$ = ___________
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$$\frac{3}{10}$$ = ___________
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$$\frac{9}{10}$$ = ___________
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$$\frac{3}{6}$$ = ___________
$$\frac{42}{6}$$ = 8
Explanation:
2 x 3$$\frac{3}{6}$$ = 2 x $$\frac{21}{6}$$
= $$\frac{42}{6}$$ = 8

Question 23.
7 × 2$$\frac{3}{4}$$ = ___________
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$$\frac{2}{3}$$ = ___________
$$\frac{72}{3}$$ = 24
9 x 2$$\frac{2}{3}$$ = 9 x $$\frac{8}{3}$$
= $$\frac{72}{3}$$ = 24