## 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.
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. $$\frac{7}{4}$$ + $$\frac{7}{4}$$ + $$\frac{7}{4}$$ =
21/4

Explanation:
The addition expression for the fraction given is :
7/4 + 7/4 + 7/4 = (3 × 7)/4 = 21/4

b. $$\frac{14}{5}$$ + $$\frac{14}{5}$$ =
28/5

Explanation:
The addition expression for the fraction given is :
14/5 + 14/5 = (2×14)/5 = 28/5

c. $$\frac{4}{7}$$ + $$\frac{4}{7}$$ + $$\frac{4}{7}$$ =
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 × $$\frac{1}{2}$$
1 ×8/2 = 1×4 = 4
8 × 1/2 = (8×1)/2
= 8/2
= 4

b. $$\frac{3}{5}$$ × 10 10 × $$\frac{3}{5}$$
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 × $$\frac{3}{7}$$
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
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 × $$\frac{13}{10}$$
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
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
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
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”
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
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
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
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. $$\frac{5}{3}$$ + $$\frac{5}{3}$$ + $$\frac{5}{3}$$
5

Explanation:
($$\frac{3 × 5}{3}$$) = $$\frac{15}{3}$$ =5

b. $$\frac{13}{5}$$ + $$\frac{13}{5}$$
$$\frac{26}{5}$$

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

c. $$\frac{9}{4}$$ + $$\frac{9}{4}$$ + $$\frac{9}{4}$$
$$\frac{27}{4}$$

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
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
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 × $$\frac{11}{10}$$
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
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 × $$\frac{5}{8}$$
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 × $$\frac{5}{12}$$
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
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
20 seconds

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

b. $$\frac{4}{5}$$ × 60 $$\frac{4}{5}$$ hour = _________ minutes
48 minutes

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

c. $$\frac{7}{10}$$ × 1000 $$\frac{7}{10}$$ kilogram = _________ grams
($$\frac{7 × 1000}{10}$$) = $$\frac{700}{1$$ = 700
d. $$\frac{3}{5}$$× 100 $$\frac{3}{5}$$ meter = _________ centimeters
($$\frac{3 × 100}{5}$$) = $$\frac{60}{1$$ = 60