## Engage NY Eureka Math 4th Grade Module 5 Lesson 38 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 38 Problem Set Answer Key

Question 1.
Fill in the unknown factors.
a. 7 × 3$$\frac{3}{4}$$ = (____ × 3) + (____ × $$\frac{4}{5}$$)

7 x 3$$\frac{3}{4}$$ = 26.6.

Explanation:
In the above-given question,
given that,
7 x 3(3/4).
7 x 3 + 7 x 4/5.
21 + 7 x 0.8.
21 + 5.6.
26.6.

b. 3 × 12$$\frac{7}{8}$$ = (3 × __12___) + (3 × __7/8___)

3 x 12$$\frac{7}{8}$$ = 38.625.

Explanation:
In the above-given question,
given that,
3 x 12(7/8).
3 x 12 + 3 x 7/8.
36 + 3 x 0.875.
36 + 2.625.
38.625.

Question 2.
Multiply. Use the distributive property.
a. 7 × 8$$\frac{2}{5}$$

7 x 8$$\frac{2}{5}$$ = 58.8.

Explanation:
In the above-given question,
given that,
7 x 8(2/5).
7 x 8 + 7 x 2/5.
56 + 7 x 0.4.
56 + 2.8.
58.8.

b. 4$$\frac{5}{6}$$ × 9

4 x 9$$\frac{5}{6}$$ = 6.33.

Explanation:
In the above-given question,
given that,
4 x 9(5/6).
4 x 9 + 4 x 5/6.
36 + 4 x 0.83.
36 + 3.33.
6.33.

c. 3 × 8$$\frac{11}{12}$$

3 x 8$$\frac{11}{12}$$ = 38.75.

Explanation:
In the above-given question,
given that,
3 x 8(11/12).
3 x 8 + 3 x 11/12.
24 + 3 x 0.916.
36 + 2.75.
38.75.

d. 5 × 20$$\frac{8}{10}$$

5 x 20$$\frac{8}{10}$$ = 104.

Explanation:
In the above-given question,
given that,
5 x 20(8/10).
5 x 20 + 5 x 8/10.
100 + 5 x 0.8.
100 + 4.
104.

e. 25$$\frac{4}{100}$$ × 4

25 x 4$$\frac{4}{100}$$ = 101.

Explanation:
In the above-given question,
given that,
25 x 4(4/100).
25 x 4 + 25 x 4/100.
100 + 25 x 0.04.
100 + 1.
101.

Question 3.
The distance around the park is 2 $$\frac{5}{10}$$ miles. Cecilia ran around the park 3 times. How far did she run?

The far she runs = 4 times.

Explanation:
In the above-given question,
given that,
The distance around the park is 2(5/10).
2 x 5/10.
5/10 = 1/2.
2 x 1/2.
2/2 = 1.
Cecilia ran around the park 3 times.
3 + 1 = 4.

Question 4.
Windsor the dog ate 4 $$\frac{3}{4}$$ snack bones each day for a week. How many bones did Windsor eat that week?

The number of bones did Windsor eat that week = 4.75.

Explanation:
In the above-given question,
given that,
Windsor the dog ate 4(3/4) snack bones each day for a week.
4(3/4).
16 + 3/4.
19/4 = 4.75.

### Eureka Math Grade 4 Module 5 Lesson 38 Exit Ticket Answer Key

Question 1.
Fill in the unknown factors.
a. 8 × 5$$\frac{2}{3}$$ = (__8__ × 5) + (__8__ × $$\frac{2}{3}$$)

8 x 5$$\frac{2}{3}$$ = 48.33.

Explanation:
In the above-given question,
given that,
8 x 5(2/3).
8 x 5 + 5 x 2/3.
40 + 5 x 0.6.
45 + 3.33.
48.33.

b. 6$$\frac{5}{8}$$ × 7

6 x 7$$\frac{5}{8}$$ = 48.

Explanation:
In the above-given question,
given that,
6 x 7(5/8).
6 x 7 + 6 x 5/8.
42 + 6 x 1.
42 + 6.
48.

### Eureka Math Grade 4 Module 5 Lesson 38 Homework Answer Key

Question 1.
Fill in the unknown factors.
a. 8 × 4$$\frac{4}{7}$$ = (__8__ × 4) + (__8__ × $$\frac{4}{7}$$)

8 x 4$$\frac{4}{7}$$ = 36.

Explanation:
In the above-given question,
given that,
8 x 4(4/7).
8 x 4 + 8 x 4/7.
32 + 8 x 0.5.
32 + 4.
36.

b. 9 × 7$$\frac{7}{10}$$ = (9 × __7__) + (9 × __7/10__)

9 x 7$$\frac{7}{10}$$ = 69.3.

Explanation:
In the above-given question,
given that,
9 x 7(7/10).
9 x 7 + 9 x 7/10.
63 + 9 x 0.7.
63 + 6.3.
69.3.

Question 2.
Multiply. Use the distributive property.
a. 6 × 8$$\frac{2}{7}$$

6 x 8$$\frac{2}{7}$$ = 49.2.

Explanation:
In the above-given question,
given that,
6 x 8(2/7).
6 x 8 + 6 x 2/7.
48 + 6 x 0.2.
48 + 1.2.
49.2.

b. 7$$\frac{3}{4}$$ × 9

7 x 9$$\frac{3}{4}$$ = 68.25.

Explanation:
In the above-given question,
given that,
7 x 9(3/4).
7 x 9 + 7 x 3/4.
63 + 7 x 0.75.
63 + 5.25.
68.25.

c. 9 × 8$$\frac{7}{9}$$

9 x 8$$\frac{7}{9}$$ = 78.3.

Explanation:
In the above-given question,
given that,
9 x 8(7/9).
9 x 8 + 9 x 7/9.
72 + 9 x 0.7.
72 + 6.3.
78.3.

d. 25$$\frac{7}{8}$$ × 3

25 x 3$$\frac{7}{8}$$ = 96.8.

Explanation:
In the above-given question,
given that,
25 x 3(7/8).
25 x 3 + 25 x 7/8.
75 + 25 x 0.875.
75 + 21.875.
96.8.

e. 4 × 20$$\frac{8}{12}$$

4 x 20$$\frac{8}{12}$$ = 82.4.

Explanation:
In the above-given question,
given that,
4 x 20(8/12).
4 x 20 + 4 x 8/12.
80 + 4 x 0.6.
80 + 2.4.
82.4.

f. 30$$\frac{3}{100}$$ × 12

30 x 12$$\frac{3}{100}$$ = 360.9.

Explanation:
In the above-given question,
given that,
30 x 12(3/100).
30 x 12 + 30 x 3/100.
360 + 30 x 0.03.
360 + 0.9.
360.9.

Question 3.
Brandon is cutting 9 boards for a woodworking project. Each board is 4 $$\frac{5}{8}$$ feet long. What is the total length of the boards?

The total length of the boards = 41.4 feet.

Explanation:
In the above-given question,
given that,
Brandon is cutting 9 boards for a woodworking project.
Each board is 4(5/8) feet long.
4(5/8) = 32 + 5/8.
37/8 = 4.625
4.6 x 9 = 41.4

Question 4.
Rocky the collie ate 3 $$\frac{1}{4}$$ cups of dog food each day for two weeks. How much dog food did Rocky eat in that time?

The dog food did Rocky eat in that time = 42.25 cups.

Explanation:
In the above-given question,
given that,
Rocky the collie ate 3(1/4) cups of dog food each day for two weeks.
3(1/4) = 12 + 1/4.
13/4 = 3.25.
3.25 x 13 = 42.25.

Question 5.
At the class party, each student will be given a container filled with 8 $$\frac{5}{8}$$ ounces of juice. There are 25 students in the class. How many ounces of juice does the teacher need to buy?