## Engage NY Eureka Math 5th Grade Module 4 Lesson 8 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 8 Problem Set Answer Key

Question 1.

Laura and Sean find the product of \(\frac{2}{3}\) × 4 using different methods.

Laura: It’s 2 thirds of 4.

\(\frac{2}{3}\) × 4 = \(\frac{4}{3}\) + \(\frac{4}{3}\) = 2 × \(\frac{4}{3}\) = \(\frac{8}{3}\)

Sean: It’s 4 groups of 2 thirds.

\(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = 4 × \(\frac{2}{3}\) = \(\frac{8}{3}\)

Use words, pictures, or numbers to compare their methods in the space below.

Answer:

Laura:

2/3 * 4 = 4/3 + 4/3 = 2*4/3 = 8/3

Sean:

2/3 + 2/3 + 2/3 + 2/3 = 4 * 2/3 = 8/3

Both methods are correct. 2/3 *4 is 2 thirds of 4, and it will also have the same product as the 4 groups of 2 thirds.

Question 2.

Rewrite the following addition expressions as fractions as shown in the example.

Example: \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = (\(\frac{4 × 2}{3}\)) = \(\frac{8}{3}\)

a. \(\frac{7}{4}\) + \(\frac{7}{4}\) + \(\frac{7}{4}\) =

Answer:

21/4

Explanation:

The addition expression for the fraction given is :

7/4 + 7/4 + 7/4 = (3 × 7)/4 = 21/4

b. \(\frac{14}{5}\) + \(\frac{14}{5}\) =

Answer:

28/5

Explanation:

The addition expression for the fraction given is :

14/5 + 14/5 = (2×14)/5 = 28/5

c. \(\frac{4}{7}\) + \(\frac{4}{7}\) + \(\frac{4}{7}\) =

Answer:

12/7

Explanation:

4/7 +4/7 +4/7 = (3×4)/7 = 12/7

Question 3.

Solve and model each problem as a fraction of a set and as repeated addition.

a. \(\frac{1}{2}\) × 8 8 × \(\frac{1}{2}\)

Answer:

1 ×8/2 = 1×4 = 4

8 × 1/2 = (8×1)/2

= 8/2

= 4

b. \(\frac{3}{5}\) × 10 10 × \(\frac{3}{5}\)

Answer:

6

Explanation:

3 ×10/5 = 3 × 2 = 6

10 × 3/5 = (10×3)/5 = 30/5 = 6

Question 4.

Solve each problem in two different ways as modeled in the example.

a. 14 × \(\frac{3}{7}\) 14 × \(\frac{3}{7}\)

Answer:

6

Explanation:

(14×3)/7 = (7×2×3)/7 = (7×6)/7 = 6

(14 × 3)/7 = (2×3)/1 = 6

b. \(\frac{3}{4}\) × 36 \(\frac{3}{4}\) ×36

Answer:

27

Explanation:

(3×36)/4 = (3×4×9)/4 = (4×27)/4 = 27

(3×36)/4 = (3×9) = (3×9) = 27

c. 30 × \(\frac{13}{10}\) 30 × \(\frac{13}{10}\)

Answer:

39

Explanation:

(30×13)/10 = (10×3×13)/10 = (10×39)/10 = 39

(30 ×13)/10 = (3×13)/1 = 39

d. \(\frac{9}{8}\) ×32 \(\frac{9}{8}\) × 32

Answer:

36

Explanation:

(9×32)/8 = (9×4×8)/8 = (36×8)/8 = 36

(9×32)/8 = (9×32)/8 = (9×4)/1 = 36

Question 5.

Solve each problem any way you choose.

a. \(\frac{1}{2}\) × 60 \(\frac{1}{2}\) minute = __________ seconds

Answer:

30seconds

Explanation:

The answer and the procedure are explained clearly in the below steps.

1 minute = 60 seconds

(1×60)/2 = (1×30)/1 = 30

b. \(\frac{3}{4}\) × 60 \(\frac{3}{4}\) hour = __________ minutes

Answer:

45 minutes

Explanation:

The answer and the procedure are explained clearly in the below steps.

1 hour = 60 minutes

(3×60)/4 = (3×15)/1 = 45

c. \(\frac{3}{10}\) × 1,000 \(\frac{3}{10}\) kilogram = __________ grams”

Answer:

300 grams

Explanation:

The answer and the procedure are explained clearly in the below steps.

1 kilogram = 1000 grams

(3×1000)/1 = 300

d. \(\frac{4}{5}\) × 100 \(\frac{4}{5}\) meter = __________ centimeters

Answer:

80 centimeters

Explanation:

The answer and the procedure are explained clearly in the below steps.

1 meter

(4×100)/5 = (4×20)/1 = 80

### Eureka Math Grade 5 Module 4 Lesson 8 Exit Ticket Answer Key

Solve each problem in two different ways as modeled in the example.

a. \(\frac{2}{3}\) × 15 \(\frac{2}{3}\) × 15

Answer:

10

Explanation:

By solving the given question in two methods we could get the same answer i.e 10. The Explanation is given below.

2/3 × 15 = (2 ×15)/3 = 30/3 = 10

2/3 ×15 = (2×15)/3 = (2×5) = 10

b. \(\frac{5}{4}\) × 12 \(\frac{5}{4}\) × 12

Answer:

15

Explanation:

By solving the given question in two methods we could get the same answer i.e 15. The process for the question is done below.

5/4 × 12 = (5×12)/4 = (60)/4 =15

5/4 ×12 = ( 5×12)/4 = (5×3) =15

### Eureka Math Grade 5 Module 4 Lesson 8 Homework Answer Key

Question 1.

Rewrite the following expressions as shown in the example.

Example: \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = (\(\frac{4 × 2}{3}\)) = \(\frac{8}{3}\)

a. \(\frac{5}{3}\) + \(\frac{5}{3}\) + \(\frac{5}{3}\)

Answer:

5

Explanation:

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

b. \(\frac{13}{5}\) + \(\frac{13}{5}\)

Answer:

\(\frac{26}{5}\)

Explanation:

(\(\frac{2 × 13}{5}\)) = \(\frac{26}{5}\)

c. \(\frac{9}{4}\) + \(\frac{9}{4}\) + \(\frac{9}{4}\)

Answer:

\(\frac{27}{4}\)

Expalanation:

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

Question 2.

Solve each problem in two different ways as modeled in the example.

a. \(\frac{3}{4}\) × 16 \(\frac{3}{4}\) × 16

Answer:

12

Explanation:

(\(\frac{3 × 16}{4}\)) = \(\frac{48}{4}\) = 12

(\(\frac{3 × 16}{4}\)) = \(\frac{3 × 4}{1}\) = 12

b. \(\frac{4}{3}\) × 12 \(\frac{4}{3}\) × 12

Answer:

16

Explanation:

(\(\frac{4 × 12}{3}\)) = \(\frac{48}{3}\) = 16

(\(\frac{4 × 12}{3}\)) = \(\frac{4 × 12}{1}\) = 16

c. 40 × \(\frac{11}{10}\) 40 × \(\frac{11}{10}\)

Answer:

44

Explanation:

(\(\frac{40 × 11}{10}\)) = \(\frac{440}{10}\) = 44

(\(\frac{40× 11}{10}\)) = \(\frac{4 × 11}{1}\) = \(\frac{44}{1}\) = 44

d. \(\frac{7}{6}\) × 36 \(\frac{7}{6}\)× 36

Answer:

42

Explanation:

(\(\frac{7 × 36}{6}\)) = \(\frac{252}{6}\) = 42

(\(\frac{7 × 36}{6}\)) = \(\frac{7 × 6}{1}\) = 42

e. 24 × \(\frac{5}{8}\) 24 × \(\frac{5}{8}\)

Answer:

15

Explanation:

(\(\frac{24 × 5}{8}\)) = \(\frac{126}{8}\) = 15

(\(\frac{24 × 5}{8}\)) = \(\frac{3 × 5}{1}\) = 15

f. 18 × \(\frac{5}{12}\) 18 × \(\frac{5}{12}\)

Answer:

7 1/2

Explanation:

(\(\frac{18 × 5}{12}\)) = \(\frac{90}{12}\) = 7 6/12 = 7 1/2

(\(\frac{18 × 5}{12}\)) = \(\frac{3 × 5 }{2}\) = \(\frac{15}{2}\)= 7 1/2

g. \(\frac{10}{9}\) × 21 \(\frac{10}{9}\) × 21

Answer:

23 3/9 = 23 1/3

Explanation:

(\(\frac{10 × 21}{9}\)) = \(\frac{210}{9}\) = 23 3/9 = 23 1/3

(\(\frac{10 × 21}{9}\)) = \(\frac{10 × 7}{3}\) = \(\frac{70}{3}\) = 23 1/3

Question 3.

Solve each problem any way you choose.

a. \(\frac{1}{3}\) × 60 \(\frac{1}{3}\) minute = _________ seconds

Answer:

20 seconds

Explanation:

(\(\frac{1 × 60}{3}\)) = \(\frac{60}{3\) = 20

b. \(\frac{4}{5}\) × 60 \(\frac{4}{5}\) hour = _________ minutes

Answer:

48 minutes

Explanation:

(\(\frac{4 × 60}{5}\)) = \(\frac{48}{1\) = 48

c. \(\frac{7}{10}\) × 1000 \(\frac{7}{10}\) kilogram = _________ grams

Answer:

700 grams

Explanation:

(\(\frac{7 × 1000}{10}\)) = \(\frac{700}{1\) = 700

d. \(\frac{3}{5}\)× 100 \(\frac{3}{5}\) meter = _________ centimeters

Answer:

60 centimeres

Explanation:

(\(\frac{3 × 100}{5}\)) = \(\frac{60}{1\) = 60