# Eureka Math Grade 5 Module 3 Lesson 2 Answer Key

## Engage NY Eureka Math 5th Grade Module 3 Lesson 2 Answer Key

### Eureka Math Grade 5 Module 3 Lesson 2 Sprint Answer Key

A
Find the Missing Numerator or Denominator

Question 1.
$$\frac{1}{2}$$ = $$\frac{}{4}$$
$$\frac{1}{2}$$ = $$\frac{2}{4}$$
Explanation :
$$\frac{1}{2}$$ = $$\frac{x}{4}$$
x = $$\frac{1}{2}$$ Ã— 4
x = $$\frac{4}{2}$$
x = 2 .

Question 2.
$$\frac{1}{5}$$ = $$\frac{2}{}$$
$$\frac{1}{5}$$ = $$\frac{2}{10}$$
Explanation :
$$\frac{1}{5}$$ = $$\frac{2}{x}$$
x = $$\frac{5}{1}$$ Ã— 2
x = 10 .

Question 3.
$$\frac{2}{5}$$ = $$\frac{}{10}$$
$$\frac{2}{5}$$ = $$\frac{4}{10}$$
Explanation :
$$\frac{2}{5}$$ = $$\frac{x}{10}$$
x = $$\frac{2}{5}$$ Ã— 10
x = $$\frac{20}{5}$$
x = 4 .

Question 4.
$$\frac{3}{5}$$ = $$\frac{}{10}$$
$$\frac{3}{5}$$ = $$\frac{6}{10}$$
Explanation :
$$\frac{3}{5}$$ = $$\frac{x}{10}$$
x = $$\frac{3}{5}$$ Ã— 10
x = $$\frac{30}{5}$$
x = 6 .

Question 5.
$$\frac{4}{5}$$ = $$\frac{}{10}$$
$$\frac{4}{5}$$ = $$\frac{8}{10}$$
Explanation :
$$\frac{4}{5}$$ = $$\frac{x}{10}$$
x = $$\frac{4}{5}$$ Ã— 10
x = $$\frac{40}{5}$$
x = 8 .

Question 6.
$$\frac{1}{3}$$ = $$\frac{2}{}$$
$$\frac{1}{3}$$ = $$\frac{2}{}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{2}{x}$$
x = $$\frac{3}{1}$$ Ã— 2
x = 3 Ã— 2
x = 6 .

Question 7.
$$\frac{2}{3}$$ = $$\frac{}{9}$$
$$\frac{2}{3}$$ = $$\frac{6}{9}$$
Explanation :
$$\frac{2}{3}$$ = $$\frac{x}{9}$$
x = $$\frac{2}{3}$$ Ã— 9
x = $$\frac{18}{3}$$
x = 6 .

Question 8.
$$\frac{1}{3}$$ = $$\frac{3}{}$$
$$\frac{1}{3}$$ = $$\frac{3}{9}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{3}{x}$$
x = $$\frac{3}{1}$$ Ã— 3
x = 3 Ã— 3
x = 9 .

Question 9.
$$\frac{2}{3}$$ = $$\frac{}{9}$$
$$\frac{2}{3}$$ = $$\frac{6}{9}$$
Explanation :
$$\frac{2}{3}$$ = $$\frac{x}{9}$$
x = $$\frac{2}{3}$$ Ã— 9
x = $$\frac{18}{3}$$
x = 6 .

Question 10.
$$\frac{1}{4}$$ = $$\frac{}{8}$$
$$\frac{1}{4}$$ = $$\frac{2}{8}$$
Explanation :
$$\frac{1}{4}$$ = $$\frac{x}{8}$$
x = $$\frac{1}{4}$$ Ã— 8
x = $$\frac{8}{4}$$
x = 2 .

Question 11.
$$\frac{3}{4}$$ = $$\frac{}{8}$$
$$\frac{3}{4}$$ = $$\frac{6}{8}$$
Explanation :
$$\frac{3}{4}$$ = $$\frac{x}{8}$$
x = $$\frac{3}{4}$$ Ã— 8
x = $$\frac{24}{4}$$
x = 6 .

Question 12.
$$\frac{1}{4}$$ = $$\frac{3}{}$$
$$\frac{1}{4}$$ = $$\frac{3}{12}$$
Explanation :
$$\frac{1}{4}$$ = $$\frac{3}{x}$$
x = $$\frac{4}{1}$$ Ã— 3
x = 4 Ã— 3
x = 12 .

Question 13.
$$\frac{3}{4}$$ = $$\frac{9}{}$$
$$\frac{3}{4}$$ = $$\frac{9}{12}$$
Explanation :
$$\frac{3}{4}$$ = $$\frac{9}{x}$$
x = $$\frac{4}{3}$$ Ã— 9
x = $$\frac{36}{3}$$
x = 12 .

Question 14.
$$\frac{2}{4}$$ = $$\frac{}{2}$$
$$\frac{2}{4}$$ = $$\frac{1}{2}$$
Explanation :
$$\frac{2}{4}$$ = $$\frac{x}{2}$$
x = $$\frac{2}{4}$$ Ã— 2
x = $$\frac{4}{4}$$
x = 1 .

Question 15.
$$\frac{2}{6}$$ = $$\frac{1}{}$$
$$\frac{2}{6}$$ = $$\frac{1}{3}$$
Explanation :
$$\frac{2}{6}$$ = $$\frac{1}{x}$$
x = $$\frac{6}{2}$$ Ã— 1
x = $$\frac{6}{2}$$
x = 3 .

Question 16.
$$\frac{2}{10}$$ = $$\frac{1}{}$$
$$\frac{2}{10}$$ = $$\frac{1}{5}$$
Explanation :
$$\frac{2}{10}$$ = $$\frac{1}{x}$$
x = $$\frac{10}{2}$$ Ã— 1
x = 5 .

Question 17.
$$\frac{4}{10}$$ = $$\frac{}{5}$$
$$\frac{4}{10}$$ = $$\frac{2}{5}$$
Explanation :
$$\frac{4}{10}$$ = $$\frac{x}{5}$$
x = $$\frac{4}{10}$$ Ã— 5
x = $$\frac{20}{10}$$
x = 2 .

Question 18.
$$\frac{8}{10}$$ = $$\frac{}{5}$$
$$\frac{8}{10}$$ = $$\frac{4}{5}$$
Explanation :
$$\frac{8}{10}$$ = $$\frac{x}{5}$$
x = $$\frac{8}{10}$$ Ã— 5
x = $$\frac{40}{10}$$
x = 4 .

Question 19.
$$\frac{3}{9}$$ = $$\frac{}{3}$$
$$\frac{3}{9}$$ = $$\frac{1}{3}$$
Explanation :
$$\frac{3}{9}$$ = $$\frac{x}{3}$$
x = $$\frac{3}{9}$$ Ã— 3
x = $$\frac{9}{9}$$
x = 1 .

Question 20.
$$\frac{6}{9}$$ = $$\frac{}{3}$$
$$\frac{6}{9}$$ = $$\frac{2}{3}$$
Explanation :
$$\frac{6}{9}$$ = $$\frac{x}{3}$$
x = $$\frac{6}{9}$$ Ã— 3
x = $$\frac{18}{9}$$
x = 2 .

Question 21.
$$\frac{3}{12}$$ = $$\frac{1}{}$$
$$\frac{3}{12}$$ = $$\frac{1}{4}$$
Explanation :
$$\frac{3}{12}$$ = $$\frac{1}{x}$$
x = $$\frac{3}{12}$$ Ã— 1
x = 4 .

Question 22.
$$\frac{9}{12}$$ = $$\frac{}{4}$$
$$\frac{9}{12}$$ = $$\frac{3}{4}$$
Explanation :
$$\frac{9}{12}$$ = $$\frac{x}{4}$$
x = $$\frac{9}{12}$$ Ã— 4
x = $$\frac{36}{12}$$
x = 3 .

Question 23.
$$\frac{1}{3}$$ = $$\frac{}{12}$$
$$\frac{1}{3}$$ = $$\frac{4}{12}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{x}{12}$$
x = $$\frac{1}{3}$$ Ã— 12
x = $$\frac{12}{3}$$
x = 4 .

Question 24.
$$\frac{2}{3}$$ = $$\frac{}{12}$$
$$\frac{2}{3}$$ = $$\frac{8}{12}$$
Explanation :
$$\frac{2}{3}$$ = $$\frac{x}{12}$$
x = $$\frac{2}{3}$$ Ã— 12
x = $$\frac{24}{3}$$
x = 8 .

Question 25.
$$\frac{8}{12}$$ = $$\frac{}{3}$$
$$\frac{8}{12}$$ = $$\frac{2}{3}$$
Explanation :
$$\frac{8}{12}$$ = $$\frac{x}{3}$$
x = $$\frac{8}{12}$$ Ã— 3
x = $$\frac{24}{12}$$
x = 2 .

Question 26.
$$\frac{12}{16}$$ = $$\frac{3}{}$$
$$\frac{12}{16}$$ = $$\frac{3}{4}$$
Explanation :
$$\frac{12}{16}$$ = $$\frac{3}{x}$$
x = $$\frac{16}{12}$$ Ã— 3
x = 4 .

Question 27.
$$\frac{3}{5}$$ = $$\frac{}{25}$$
$$\frac{3}{5}$$ = $$\frac{15}{25}$$
Explanation :
$$\frac{3}{5}$$ = $$\frac{x}{25}$$
x = $$\frac{3}{5}$$ Ã— 25
x = 3 Ã— 5
x = 15 .

Question 28.
$$\frac{4}{5}$$ = $$\frac{28}{}$$
$$\frac{4}{5}$$ = $$\frac{28}{35}$$
Explanation :
$$\frac{4}{5}$$ = $$\frac{28}{x}$$
x = $$\frac{5}{4}$$ Ã— 28
x = 5 Ã— 7
x = 35 .

Question 29.
$$\frac{18}{24}$$ = $$\frac{3}{}$$
$$\frac{18}{24}$$ = $$\frac{3}{4}$$
Explanation :
$$\frac{18}{24}$$ = $$\frac{3}{x}$$
x = $$\frac{24}{18}$$ Ã— 3
x = $$\frac{24}{6}$$
x = 4 .

Question 30.
$$\frac{24}{30}$$ = $$\frac{}{5}$$
$$\frac{24}{30}$$ = $$\frac{4}{5}$$
Explanation :
$$\frac{24}{30}$$ = $$\frac{x}{5}$$
x = $$\frac{24}{30}$$ Ã— 5
x = $$\frac{24}{6}$$
x = 4 .

Question 31.
$$\frac{5}{6}$$ = $$\frac{35}{}$$
$$\frac{5}{6}$$ = $$\frac{35}{42}$$
Explanation :
$$\frac{5}{6}$$ = $$\frac{35}{x}$$
x = $$\frac{6}{5}$$ Ã— 35
x = 6 Ã— 7
x = 42 .

Question 32.
$$\frac{56}{63}$$ = $$\frac{}{9}$$
$$\frac{56}{63}$$ = $$\frac{8}{9}$$
Explanation :
$$\frac{56}{63}$$ = $$\frac{x}{9}$$
x = $$\frac{56}{63}$$ Ã— 9
x = $$\frac{56}{7}$$
x = 8 .

Question 33.
$$\frac{64}{72}$$ = $$\frac{8}{}$$
$$\frac{64}{72}$$ = $$\frac{8}{9}$$
Explanation :
$$\frac{64}{72}$$ = $$\frac{8}{x}$$
x = $$\frac{72}{64}$$ Ã— 8
x = $$\frac{72}{8}$$
x = 9 .

Question 34.
$$\frac{5}{8}$$ = $$\frac{}{64}$$
$$\frac{5}{8}$$ = $$\frac{40}{64}$$
Explanation :
$$\frac{5}{8}$$ = $$\frac{x}{64}$$
x = $$\frac{5}{8}$$ Ã— 64
x = 5 Ã— 8
x = 40 .

Question 35.
$$\frac{5}{6}$$ = $$\frac{45}{}$$
$$\frac{5}{6}$$ = $$\frac{45}{54}$$
Explanation :
$$\frac{5}{6}$$ = $$\frac{45}{x}$$
x = $$\frac{6}{5}$$ Ã— 45
x = 6 Ã— 9
x = 54 .

Question 36.
$$\frac{45}{81}$$ = $$\frac{}{9}$$
$$\frac{45}{81}$$ = $$\frac{5}{9}$$
Explanation :
$$\frac{45}{81}$$ = $$\frac{x}{9}$$
x = $$\frac{45}{81}$$ Ã— 9
x = $$\frac{45}{9}$$
x = 5 .

Question 37.
$$\frac{6}{7}$$ = $$\frac{48}{}$$
$$\frac{6}{7}$$ = $$\frac{48}{56}$$
Explanation :
$$\frac{6}{7}$$ = $$\frac{48}{x}$$
x = $$\frac{7}{6}$$ Ã— 48
x = 7 Ã— 8
x = 56 .

Question 38.
$$\frac{36}{81}$$ = $$\frac{}{9}$$
$$\frac{36}{81}$$ = $$\frac{4}{9}$$
Explanation :
$$\frac{36}{81}$$ = $$\frac{x}{9}$$
x = $$\frac{36}{81}$$ Ã— 9
x = $$\frac{36}{9}$$
x = 4 .

Question 39.
$$\frac{8}{56}$$ = $$\frac{1}{}$$
$$\frac{8}{56}$$ = $$\frac{1}{7}$$
Explanation :
$$\frac{8}{56}$$ = $$\frac{1}{x}$$
x = $$\frac{8}{56}$$ Ã— 1
x = 7 .

Question 40.
$$\frac{35}{63}$$ = $$\frac{5}{}$$
$$\frac{35}{63}$$ = $$\frac{5}{9}$$
Explanation :
$$\frac{35}{63}$$ = $$\frac{5}{x}$$
x = $$\frac{63}{35}$$ Ã— 5
x = $$\frac{63}{7}$$
x = 9 .

Question 41.
$$\frac{1}{6}$$ = $$\frac{12}{}$$
$$\frac{1}{6}$$ = $$\frac{12}{72}$$
Explanation :
$$\frac{1}{6}$$ = $$\frac{12}{x}$$
x = $$\frac{6}{1}$$ Ã— 12
x = 72 .

Question 42.
$$\frac{3}{7}$$ = $$\frac{36}{}$$
$$\frac{3}{7}$$ = $$\frac{36}{84}$$
Explanation :
$$\frac{3}{7}$$ = $$\frac{36}{x}$$
x = $$\frac{7}{3}$$ Ã— 36
x = 7 Ã— 12
x = 84 .

Question 43.
$$\frac{48}{60}$$ = $$\frac{4}{}$$
$$\frac{48}{60}$$ = $$\frac{4}{5}$$
Explanation :
$$\frac{48}{60}$$ = $$\frac{4}{x}$$
x = $$\frac{60}{48}$$ Ã— 4
x = $$\frac{60}{12}$$
x = 5 .

Question 44.
$$\frac{72}{84}$$ = $$\frac{}{7}$$
$$\frac{72}{84}$$ = $$\frac{6}{7}$$
Explanation :
$$\frac{72}{84}$$ = $$\frac{x}{7}$$
x = $$\frac{72}{84}$$ Ã— 7
x = $$\frac{72}{12}$$
x = 6 .

B
Find the Missing Numerator or Denominator

Question 1.
$$\frac{1}{5}$$ = $$\frac{2}{}$$
$$\frac{1}{5}$$ = $$\frac{2}{10}$$
Explanation :
$$\frac{1}{5}$$ = $$\frac{2}{x}$$
x = $$\frac{5}{1}$$ Ã— 2
x = 10 .

Question 2.
$$\frac{2}{5}$$ = $$\frac{}{10}$$
$$\frac{2}{5}$$ = $$\frac{4}{10}$$
Explanation :
$$\frac{2}{5}$$ = $$\frac{x}{10}$$
x = $$\frac{2}{5}$$ Ã— 10
x = 4 .

Question 3.
$$\frac{3}{5}$$ = $$\frac{}{10}$$
$$\frac{3}{5}$$ = $$\frac{6}{10}$$
Explanation :
$$\frac{3}{5}$$ = $$\frac{x}{10}$$
x = $$\frac{3}{5}$$ Ã— 10
x = 6 .

Question 4.
$$\frac{4}{5}$$ = $$\frac{}{10}$$
$$\frac{4}{5}$$ = $$\frac{8}{10}$$
Explanation :
$$\frac{4}{5}$$ = $$\frac{x}{10}$$
x = $$\frac{4}{5}$$ Ã— 10
x = 8 .

Question 5.
$$\frac{1}{3}$$ = $$\frac{2}{}$$
$$\frac{1}{3}$$ = $$\frac{2}{6}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{2}{x}$$
x = $$\frac{3}{1}$$ Ã— 2
x = 6

Question 6.
$$\frac{1}{3}$$ = $$\frac{}{6}$$
$$\frac{1}{3}$$ = $$\frac{2}{6}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{x}{6}$$
x = $$\frac{1}{3}$$ Ã— 6
x = 2

Question 7.
$$\frac{2}{3}$$ = $$\frac{4}{}$$
$$\frac{2}{3}$$ = $$\frac{4}{12}$$
Explanation :
$$\frac{2}{3}$$ = $$\frac{4}{x}$$
x = $$\frac{3}{2}$$ Ã— 4
x = 6

Question 8.
$$\frac{1}{3}$$ = $$\frac{}{9}$$
$$\frac{1}{3}$$ = $$\frac{3}{9}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{x}{9}$$
x = $$\frac{1}{3}$$ Ã— 9
x = 3

Question 9.
$$\frac{2}{3}$$ = $$\frac{6}{}$$
$$\frac{2}{3}$$ = $$\frac{6}{9}$$
Explanation :
$$\frac{2}{3}$$ = $$\frac{6}{x}$$
x = $$\frac{3}{2}$$ Ã— 6
x = 9

Question 10.
$$\frac{1}{4}$$ = $$\frac{2}{}$$
$$\frac{1}{4}$$ = $$\frac{2}{8}$$
Explanation :
$$\frac{1}{4}$$ = $$\frac{2}{x}$$
x = $$\frac{4}{1}$$ Ã— 2
x = 8

Question 11.
$$\frac{3}{4}$$ = $$\frac{6}{}$$
$$\frac{3}{4}$$ = $$\frac{6}{8}$$
Explanation :
$$\frac{3}{4}$$ = $$\frac{6}{x}$$
x = $$\frac{4}{3}$$ Ã— 6
x = 8

Question 12.
$$\frac{1}{4}$$ = $$\frac{}{12}$$
$$\frac{1}{4}$$ = $$\frac{3}{12}$$
Explanation :
$$\frac{1}{4}$$ = $$\frac{x}{12}$$
x = $$\frac{1}{4}$$ Ã— 12
x = 3

Question 13.
$$\frac{3}{4}$$ = $$\frac{}{12}$$
$$\frac{3}{4}$$ = $$\frac{9}{12}$$
Explanation :
$$\frac{3}{4}$$ = $$\frac{x}{12}$$
x = $$\frac{3}{4}$$ Ã— 12
x = 9

Question 14.
$$\frac{2}{4}$$ = $$\frac{1}{}$$
$$\frac{2}{4}$$ = $$\frac{1}{2}$$
Explanation :
$$\frac{2}{4}$$ = $$\frac{1}{x}$$
x = $$\frac{4}{2}$$ Ã— 1
x = 2

Question 15.
$$\frac{2}{6}$$ = $$\frac{}{3}$$
$$\frac{2}{6}$$ = $$\frac{4}{12}$$
Explanation :
$$\frac{2}{6}$$ = $$\frac{x}{12}$$
x = $$\frac{2}{6}$$ Ã— 12
x = 4

Question 16.
$$\frac{2}{10}$$ = $$\frac{}{5}$$
$$\frac{2}{10}$$ = $$\frac{1}{5}$$
Explanation :
$$\frac{2}{10}$$ = $$\frac{x}{5}$$
x = $$\frac{2}{10}$$ Ã— 5
x = 1

Question 17.
$$\frac{4}{10}$$ = $$\frac{2}{}$$
$$\frac{4}{10}$$ = $$\frac{2}{5}$$
Explanation :
$$\frac{4}{10}$$ = $$\frac{2}{x}$$
x = $$\frac{10}{4}$$ Ã— 2
x = 5

Question 18.
$$\frac{8}{10}$$ = $$\frac{4}{}$$
$$\frac{8}{10}$$ = $$\frac{4}{5}$$
Explanation :
$$\frac{8}{10}$$ = $$\frac{4}{x}$$
x = $$\frac{10}{8}$$ Ã— 4
x = 5

Question 19.
$$\frac{3}{9}$$ = $$\frac{1}{}$$
$$\frac{3}{9}$$ = $$\frac{1}{3}$$
Explanation :
$$\frac{3}{9}$$ = $$\frac{1}{x}$$
x = $$\frac{9}{3}$$ Ã— 1
x = 3

Question 20.
$$\frac{6}{9}$$ = $$\frac{2}{}$$
$$\frac{6}{9}$$ = $$\frac{2}{3}$$
Explanation :
$$\frac{6}{9}$$ = $$\frac{2}{x}$$
x = $$\frac{9}{6}$$ Ã— 2
x = 3

Question 21.
$$\frac{1}{4}$$ = $$\frac{}{12}$$
$$\frac{1}{4}$$ = $$\frac{3}{12}$$
Explanation :
$$\frac{1}{4}$$ = $$\frac{x}{12}$$
x = $$\frac{1}{4}$$ Ã— 12
x = 3

Question 22.
$$\frac{9}{12}$$ = $$\frac{3}{}$$
$$\frac{9}{12}$$ = $$\frac{3}{}$$
Explanation :
$$\frac{6}{9}$$ = $$\frac{2}{x}$$
x = $$\frac{9}{6}$$ Ã— 2
x = 3

Question 23.
$$\frac{1}{3}$$ = $$\frac{4}{}$$
$$\frac{1}{3}$$ = $$\frac{4}{12}$$
Explanation :
$$\frac{1}{3}$$ = $$\frac{4}{x}$$
x = $$\frac{3}{1}$$ Ã— 4
x = 12

Question 24.
$$\frac{2}{3}$$ = $$\frac{8}{}$$
$$\frac{2}{3}$$ = $$\frac{8}{12}$$
Explanation :
$$\frac{2}{3}$$ = $$\frac{8}{x}$$
x = $$\frac{3}{2}$$ Ã— 8
x = 12

Question 25.
$$\frac{8}{12}$$ = $$\frac{2}{}$$
$$\frac{8}{12}$$ = $$\frac{2}{3}$$
Explanation :
$$\frac{8}{12}$$ = $$\frac{2}{x}$$
x = $$\frac{12}{8}$$ Ã— 2
x = 3

Question 26.
$$\frac{12}{16}$$ = $$\frac{}{4}$$
$$\frac{12}{16}$$ = $$\frac{3}{4}$$
Explanation :
$$\frac{12}{16}$$ = $$\frac{x}{4}$$
x = $$\frac{12}{16}$$ Ã— 4
x = 3

Question 27.
$$\frac{3}{5}$$ = $$\frac{15}{}$$
$$\frac{3}{5}$$ = $$\frac{15}{25}$$
Explanation :
$$\frac{3}{5}$$ = $$\frac{15}{x}$$
x = $$\frac{5}{3}$$ Ã— 15
x = 25

Question 28.
$$\frac{4}{5}$$ = $$\frac{}{35}$$
$$\frac{4}{5}$$ = $$\frac{28}{35}$$
Explanation :
$$\frac{4}{5}$$ = $$\frac{x}{35}$$
x = $$\frac{4}{5}$$ Ã— 35
x = 28

Question 29.
$$\frac{18}{24}$$ = $$\frac{}{4}$$
$$\frac{18}{24}$$ = $$\frac{3}{4}$$
Explanation :
$$\frac{18}{24}$$ = $$\frac{x}{4}$$
x = $$\frac{18}{24}$$ Ã— 4
x = 3

Question 30.
$$\frac{24}{30}$$ = $$\frac{4}{}$$
$$\frac{24}{30}$$ = $$\frac{4}{5}$$
Explanation :
$$\frac{24}{30}$$ = $$\frac{4}{x}$$
x = $$\frac{30}{24}$$ Ã— 4
x = 5

Question 31.
$$\frac{5}{6}$$ = $$\frac{}{42}$$
$$\frac{5}{6}$$ = $$\frac{35}{42}$$
Explanation :
$$\frac{5}{6}$$ = $$\frac{x}{42}$$
x = $$\frac{5}{6}$$ Ã— 42
x = 35

Question 32.
$$\frac{56}{63}$$ = $$\frac{8}{}$$
$$\frac{56}{63}$$ = $$\frac{8}{9}$$
Explanation :
$$\frac{56}{63}$$ = $$\frac{8}{x}$$
x = $$\frac{63}{56}$$ Ã— 8
x = 9

Question 33.
$$\frac{64}{72}$$ = $$\frac{}{9}$$
$$\frac{64}{72}$$ = $$\frac{8}{9}$$
Explanation :
$$\frac{64}{72}$$ = $$\frac{x}{9}$$
x = $$\frac{64}{72}$$ Ã— 9
x = 8

Question 34.
$$\frac{5}{8}$$ = $$\frac{40}{}$$
$$\frac{5}{8}$$ = $$\frac{40}{64}$$
Explanation :
$$\frac{5}{8}$$ = $$\frac40}{x}$$
x = $$\frac{8}{5}$$ Ã— 40
x = 64

Question 35.
$$\frac{5}{6}$$ = $$\frac{}{54}$$
$$\frac{5}{6}$$ = $$\frac{45}{54}$$
Explanation :
$$\frac{5}{6}$$ = $$\frac{x}{54}$$
x = $$\frac{5}{6}$$ Ã— 54
x = 45

Question 36.
$$\frac{45}{81}$$ = $$\frac{5}{}$$
$$\frac{45}{81}$$ = $$\frac{5}{9}$$
Explanation :
$$\frac{45}{81}$$ = $$\frac{x}{9}$$
x = $$\frac{45}{81}$$ Ã— 9
x = 9

Question 37.
$$\frac{6}{7}$$ = $$\frac{}{56}$$
$$\frac{6}{7}$$ = $$\frac{48}{56}$$
Explanation :
$$\frac{6}{7}$$ = $$\frac{x}{56}$$
x = $$\frac{7}{6}$$ Ã— 56
x = 48

Question 38.
$$\frac{36}{81}$$ = $$\frac{4}{}$$
$$\frac{36}{81}$$ = $$\frac{4}{9}$$
Explanation :
$$\frac{36}{81}$$ = $$\frac{4}{x}$$
x = $$\frac{81}{36}$$Â  Ã— 4
x = 9

Question 39.
$$\frac{8}{56}$$ = $$\frac{}{7}$$
$$\frac{8}{56}$$ = $$\frac{1}{7}$$
Explanation :
$$\frac{8}{56}$$ = $$\frac{x}{7}$$
x = $$\frac{8}{56}$$ Ã— 7
x = 1

Question 40.
$$\frac{35}{63}$$ = $$\frac{}{9}$$
$$\frac{35}{63}$$ = $$\frac{5}{9}$$
Explanation :
$$\frac{35}{63}$$ = $$\frac{x}{9}$$
x = $$\frac{35}{63}$$ Ã— 9
x = 5

Question 41.
$$\frac{1}{6}$$ = $$\frac{}{72}$$
$$\frac{1}{6}$$ = $$\frac{12}{72}$$
Explanation :
$$\frac{1}{6}$$ = $$\frac{x}{72}$$
x = $$\frac{1}{6}$$ Ã— 72
x = 12

Question 42.
$$\frac{3}{7}$$ = $$\frac{}{84}$$
$$\frac{3}{7}$$ = $$\frac{36}{84}$$
Explanation :
$$\frac{3}{7}$$ = $$\frac{x}{84}$$
x = $$\frac{3}{7}$$ Ã— 84
x = 36

Question 43.
$$\frac{48}{60}$$ = $$\frac{}{5}$$
$$\frac{48}{60}$$ = $$\frac{4}{5}$$
Explanation :
$$\frac{48}{60}$$ = $$\frac{x}{5}$$
x = $$\frac{48}{60}$$ Ã— 5
x = 4

Question 44.
$$\frac{72}{84}$$ = $$\frac{6}{}$$
$$\frac{72}{84}$$ = $$\frac{6}{7}$$
Explanation :
$$\frac{72}{84}$$ = $$\frac{6}{x}$$
x = $$\frac{84}{72}$$Â  Ã— 6
x = 7

### Eureka Math Grade 5 Module 3 Lesson 2 Problem Set Answer Key

Question 1.
Show each expression on a number line. Solve.
a. $$\frac{2}{5}$$+ $$\frac{1}{5}$$
b. $$\frac{1}{3}$$ + $$\frac{1}{3}$$+ $$\frac{1}{3}$$
c. $$\frac{3}{10}$$ + $$\frac{3}{10}$$ + $$\frac{3}{10}$$
d. 2 Ã— $$\frac{3}{4}$$ + $$\frac{1}{4}$$
a. $$\frac{2}{5}$$+ $$\frac{1}{5}$$ = $$\frac{3}{5}$$

Explanation :
Number line is represented from 0 to 1 and is divided into 5 parts .$$\frac{2}{5}$$ is marked from 0 and then $$\frac{1}{5}$$ is marked from it to get sum of $$\frac{3}{5}$$.
b. $$\frac{1}{3}$$ + $$\frac{1}{3}$$+ $$\frac{1}{3}$$ = $$\frac{3}{3}$$ = 1

Explanation :
Number line is represented from 0 to 1 and is divided into 3 parts .$$\frac{1}{3}$$ is marked from 0 and then $$\frac{1}{3}$$ is marked from it and again $$\frac{1}{3}$$ is marked to get sum of $$\frac{3}{3}$$ = 1
c. $$\frac{3}{10}$$ + $$\frac{3}{10}$$ + $$\frac{3}{10}$$= $$\frac{9}{10}$$

Explanation :
Number line is represented from 0 to 1 and is divided into 10 parts .$$\frac{3}{10}$$ is marked from 0 and then $$\frac{3}{10}$$ is marked from it and again $$\frac{3}{10}$$ is marked to get sum of $$\frac{9}{10}$$.
d. 2 Ã— $$\frac{3}{4}$$ + $$\frac{1}{4}$$
$$\frac{3}{4}$$ + $$\frac{3}{4}$$ + $$\frac{1}{4}$$ = $$\frac{7}{4}$$

Explanation :
Number line is represented from 0 to 2 and is divided into 8 parts .$$\frac{3}{4}$$ is marked from 0 and then $$\frac{3}{4}$$ is marked from it and again $$\frac{1}{4}$$ is marked to get sum of $$\frac{7}{4}$$.

Question 2.
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show Part (a) on a number line.
a. $$\frac{6}{7}$$
b. $$\frac{9}{2}$$
c. $$\frac{12}{10}$$
d. $$\frac{27}{5}$$
a. $$\frac{6}{7}$$ = $$\frac{2}{7}$$ + $$\frac{2}{7}$$ + $$\frac{2}{7}$$Â  = 3Ã—Â $$\frac{2}{7}$$

Explanation :
Number line is represented from 0 to 1 and is divided into 7 parts .$$\frac{2}{7}$$ is marked from 0 and then $$\frac{2}{7}$$ is marked from it and again $$\frac{2}{7}$$ is marked to get sum of $$\frac{6}{7}$$.
b. $$\frac{9}{2}$$ = $$\frac{3}{2}$$ + $$\frac{3}{2}$$ + $$\frac{3}{2}$$ .= 3 Ã— $$\frac{3}{2}$$
c. $$\frac{12}{10}$$ = $$\frac{6}{10}$$ +$$\frac{6}{10}$$= 2Ã—$$\frac{6}{10}$$
d. $$\frac{27}{5}$$ = $$\frac{9}{5}$$ + $$\frac{9}{5}$$ + $$\frac{9}{5}$$Â  = 3Ã—$$\frac{9}{5}$$

Question 3.
Express each of the following as the sum of a whole number and a fraction. Show Parts (c) and (d) on number lines.
a. $$\frac{9}{7}$$
c. $$\frac{32}{7}$$
d. $$\frac{24}{9}$$
a. $$\frac{9}{7}$$ =$$\frac{7}{7}$$ + $$\frac{2}{7}$$ .
c. $$\frac{32}{7}$$ = $$\frac{28}{7}$$ + $$\frac{4}{7}$$ = 4 + $$\frac{4}{7}$$.

Explanation :
Number line is represented from 0 to 5 and each whole is divided into 7 parts .4 is marked from 0 and then $$\frac{4}{7}$$ is marked from it to get sum of $$\frac{32}{7}$$.
d. $$\frac{24}{9}$$ = $$\frac{18}{9}$$ + $$\frac{6}{9}$$ = 2 + $$\frac{6}{9}$$ .

Explanation :
Number line is represented from 0 to 3 and each 1 whole divided into 9 parts .2 is marked from 0 and then $$\frac{6}{9}$$ is marked from it to get sum of $$\frac{24}{9}$$.

Question 4.
Marisela cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of ribbon did she cut? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.

Explanation :
Length of each ribbon = $$\frac{5}{8}$$.
Number of ribbons = 4
Total Length of ribbon = $$\frac{5}{8}$$ + $$\frac{5}{8}$$ + $$\frac{5}{8}$$ + $$\frac{5}{8}$$ = $$\frac{20}{8}$$ .
$$\frac{20}{8}$$ = 2 + $$\frac{4}{8}$$ .

### Eureka Math Grade 5 Module 3 Lesson 2 Exit Ticket Answer Key

Question 1.
Show each expression on a number line. Solve.
a. $$\frac{5}{5}$$ + $$\frac{2}{5}$$
b. $$\frac{6}{3}$$+ $$\frac{2}{3}$$
a. $$\frac{5}{5}$$ + $$\frac{2}{5}$$ = $$\frac{7}{5}$$

Explanation :
Number line is represented from 0 to 2 and each 1 whole divided into 5 parts .1 is marked from 0 and then $$\frac{2}{5}$$ is marked from it to get sum of $$\frac{7}{5}$$.
b. $$\frac{6}{3}$$+ $$\frac{2}{3}$$ = 2 + $$\frac{2}{3}$$ = $$\frac{8}{3}$$

Explanation :
Number line is represented from 0 to 3 and each 1 whole divided into 3 parts .2 is marked from 0 and then $$\frac{2}{3}$$ is marked from it to get sum of $$\frac{8}{3}$$.

Question 2.
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show Part (b) on a number line.
a. $$\frac{6}{9}$$
b. $$\frac{15}{4}$$
a. $$\frac{6}{9}$$ = $$\frac{3}{9}$$ + $$\frac{3}{9}$$ = 2 Ã— $$\frac{3}{9}$$
b. $$\frac{15}{4}$$ = $$\frac{4}{4}$$ + $$\frac{4}{4}$$ + $$\frac{4}{4}$$ + $$\frac{3}{4}$$ = 3 + $$\frac{3}{4}$$ .

Explanation :
Number line is represented from 0 to 4 and each 1 whole divided into 4 parts .3 is marked from 0 and then $$\frac{3}{4}$$ is marked from it to get sum of $$\frac{15}{4}$$.

### Eureka Math Grade 5 Module 3 Lesson 2 Homework Answer Key

Question 1.
Show each expression on a number line. Solve.
a. $$\frac{4}{9}$$ + $$\frac{1}{9}$$
b. $$\frac{1}{4}$$ + $$\frac{1}{4}$$ + $$\frac{1}{4}$$ + $$\frac{1}{4}$$
c. $$\frac{2}{7}$$ + $$\frac{2}{7}$$ + $$\frac{2}{7}$$
d. 2 Ã— $$\frac{3}{5}$$ + $$\frac{1}{5}$$
a. $$\frac{4}{9}$$ + $$\frac{1}{9}$$ = $$\frac{5}{9}$$ .

Explanation :
Number line is represented from 0 to 1 and each 1 whole divided into 9 parts .$$\frac{4}{9}$$ is marked from 0 and then $$\frac{1}{9}$$ is marked from it to get sum of $$\frac{5}{9}$$.
b. $$\frac{1}{4}$$ + $$\frac{1}{4}$$ + $$\frac{1}{4}$$ + $$\frac{1}{4}$$ = $$\frac{4}{4}$$ = 1

Explanation :
Number line is represented from 0 to 1 and each 1 whole divided into 4 parts .$$\frac{1}{4}$$ is marked from 0 and then $$\frac{1}{4}$$ is marked againÂ  $$\frac{1}{4}$$ and $$\frac{1}{4}$$ from it to get sum of $$\frac{4}{4}$$.
c. $$\frac{2}{7}$$ + $$\frac{2}{7}$$ + $$\frac{2}{7}$$ = $$\frac{6}{7}$$

Explanation :
Number line is represented from 0 to 1 and each 1 whole divided into 7 parts .$$\frac{2}{7}$$ is marked from 0 and then $$\frac{2}{7}$$ is marked and again $$\frac{2}{7}$$ is marked from it to get sum of $$\frac{6}{7}$$.
d. 2 Ã— $$\frac{3}{5}$$ + $$\frac{1}{5}$$ = $$\frac{3}{5}$$ + $$\frac{3}{5}$$ + $$\frac{1}{5}$$ = $$\frac{7}{5}$$ .

Explanation :
Number line is represented from 0 to 2 and each 1 whole divided into 5 parts .$$\frac{3}{5}$$ is marked from 0 and then $$\frac{3}{5}$$ is marked and $$\frac{1}{5}$$ from it to get sum of $$\frac{7}{5}$$.

Question 2.
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show Part (a) on a number line.
a. $$\frac{6}{11}$$
b. $$\frac{9}{4}$$
c. $$\frac{12}{8}$$
d. $$\frac{27}{10}$$
a. $$\frac{6}{11}$$ = $$\frac{3}{11}$$ + $$\frac{3}{11}$$ = 2 Ã— $$\frac{3}{11}$$ .

b. $$\frac{9}{4}$$ = $$\frac{3}{4}$$ + $$\frac{3}{4}$$ + $$\frac{3}{4}$$ = 3 Ã— $$\frac{3}{4}$$
c. $$\frac{12}{8}$$ =$$\frac{4}{8}$$ + $$\frac{4}{8}$$ + $$\frac{4}{8}$$= 3 Ã— $$\frac{4}{8}$$
d. $$\frac{27}{10}$$ = $$\frac{9}{10}$$ + $$\frac{9}{10}$$ + $$\frac{9}{10}$$ = 3 Ã— $$\frac{9}{10}$$ .

Question 3.
Express each of the following as the sum of a whole number and a fraction. Show Parts (c) and (d) on number lines.
a. $$\frac{9}{5}$$
b. $$\frac{7}{2}$$
c. $$\frac{25}{7}$$
d. $$\frac{21}{9}$$
a. $$\frac{9}{5}$$ = $$\frac{5}{5}$$ + $$\frac{4}{5}$$ = 1 + $$\frac{4}{5}$$ .
b. $$\frac{7}{2}$$ = $$\frac{2}{2}$$ + $$\frac{2}{2}$$ + $$\frac{2}{2}$$ + $$\frac{1}{2}$$ =
1+ 1 + 1 + $$\frac{1}{2}$$ =Â  3 + $$\frac{1}{2}$$ .
c. $$\frac{25}{7}$$ = $$\frac{7}{7}$$ + $$\frac{7}{7}$$ + $$\frac{7}{7}$$ + $$\frac{4}{7}$$ =Â  Â  Â  1+ 1+ 1+ $$\frac{4}{7}$$ =3 + $$\frac{4}{7}$$ .

Explanation :
Number line is represented from 0 to 4 and each 1 whole divided into 7 parts .3 1′ are marked from 0 and then $$\frac{4}{7}$$ is marked from it to get sum of $$\frac{25}{7}$$.
d. $$\frac{21}{9}$$ = $$\frac{9}{9}$$ + $$\frac{9}{9}$$ + $$\frac{3}{9}$$ = 1+ 1+ $$\frac{3}{9}Â Â Â Â Â$$ = 2 + $$\frac{3}{9}$$ .

Explanation :
Number line is represented from 0 to 3 and each 1 whole divided into 9 parts .2 1’s are marked from 0 and then $$\frac{3}{9}$$ is marked from it to get sum of $$\frac{21}{9}$$.

Question 4.
Natalie sawed five boards of equal length to make a stool. Each was 9 tenths of a meter long. What is the total length of the boards she sawed? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
Length of each board = 9 tenthsÂ  = $$\frac{9}{10}$$ .
Total Length of board = 5 Ã— $$\frac{9}{10}$$ = $$\frac{45}{10}$$.
$$\frac{45}{10}$$ = $$\frac{10}{10}$$ + $$\frac{10}{10}$$ + $$\frac{10}{10}$$ + $$\frac{10}{10}$$ + $$\frac{5}{10}$$ = 1+ 1+ 1+ 1+ $$\frac{5}{10}$$ = 4 + $$\frac{5}{10}$$ .