## 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) + (____ × \(\frac{4}{5}\))

Answer:

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___)

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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?

Answer:

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?

Answer:

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__ × \(\frac{2}{3}\))

Answer:

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

Answer:

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__ × \(\frac{4}{7}\))

Answer:

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__)

Answer:

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\(\frac{2}{7}\)

Answer:

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

Answer:

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\(\frac{7}{9}\)

Answer:

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

Answer:

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

Answer:

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

Answer:

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?

Answer:

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?

Answer:

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?

Answer:

The number of ounces of juice does the teacher needs to buy = 215.625 ounces.

Explanation:

In the above-given question,

given that,

At the class party, each student will be given a container filled with 8(5/8) ounces of juice.

There are 25 students in the class.

8(5/8) = 64 + 5/8.

64 + 5 = 69.

69/8 = 8.625.

8.625 x 25 = 215.625.