Engage NY Eureka Math 5th Grade Module 3 Lesson 3 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 3 Problem Set Answer Key

Question 1.
Draw a rectangular fraction model to find the sum. Simplify your answer, if possible.
a. $$\frac{1}{2}$$ + $$\frac{1}{3}$$ =
b. $$\frac{1}{3}$$ + $$\frac{1}{5}$$ =
c. $$\frac{1}{4}$$ + $$\frac{1}{3}$$ =
d. $$\frac{1}{3}$$ + $$\frac{1}{7}$$ =
e. $$\frac{3}{4}$$ + $$\frac{1}{5}$$ =
f. $$\frac{2}{3}$$ + $$\frac{2}{7}$$ =
a.
$$\frac{1}{2}$$ + $$\frac{1}{3}$$
L.c.m of 2 and 3 is 6
$$\frac{3}{6}$$ + $$\frac{2}{6}$$ = $$\frac{5}{6}$$ .

Explanation :
Divide the first rectangle into 2 parts using vertical lines as first fraction is $$\frac{1}{2}$$ and each vertical section represents $$\frac{1}{2}$$ and 1 part is shaded.
Divide the SecondÂ  rectangle into 3 parts using horizontal lines as Second fraction is $$\frac{1}{3}$$ and each horizontal fraction represent $$\frac{1}{3}$$ and 1 part is shaded.
As 2 and 3 have 6 lcm now divide both the rectangles into 6 parts .
First rectangle divided into 6 parts by drawing 2 horizontal lines and second rectangle into 6 parts by drawing 1 vertical line

b.
$$\frac{1}{3}$$ + $$\frac{1}{5}$$
L.c.m of 3 and 5 is 15 .
$$\frac{5}{15}$$ + $$\frac{3}{15}$$ = $$\frac{8}{15}$$

Explanation :
Divide the first rectangle into 3 parts using vertical lines as first fraction is $$\frac{1}{3}$$ and each vertical section represents $$\frac{1}{2}$$ and 1 part is shaded.
Divide the SecondÂ  rectangle into 5 parts using horizontal lines as Second fraction is $$\frac{1}{5}$$ and each horizontal fraction represent $$\frac{1}{5}$$ and 1 part is shaded.
As 5 and 3 have 15 lcm now divide both the rectangles into 15 parts .
First rectangle divided into 15 parts by drawing 4 horizontal lines and second rectangle into 15 parts by drawing 2 vertical line

c.
$$\frac{1}{4}$$ + $$\frac{1}{3}$$
l.cm of 4 and 3 is 12 .
$$\frac{3}{12}$$ + $$\frac{4}{12}$$ = $$\frac{7}{12}$$

Explanation :
Divide the first rectangle into 4 parts using vertical lines as first fraction is $$\frac{1}{4}$$ and each vertical section represents $$\frac{1}{4}$$ and 1 part is shaded.
Divide the SecondÂ  rectangle into 3 parts using horizontal lines as Second fraction is $$\frac{1}{3}$$ and each horizontal fraction represent $$\frac{1}{3}$$ and 1 part is shaded.
As 4 and 3 have 12 lcm now divide both the rectangles into 12 parts .
First rectangle divided into 12 parts by drawing 2 horizontal lines and second rectangle into 12 parts by drawing 3 vertical line

d.
$$\frac{1}{3}$$ + $$\frac{1}{7}$$
l.c.m of 3 and 7 is 21
$$\frac{7}{21}$$ + $$\frac{3}{21}$$ = $$\frac{10}{21}$$
Explanation :
Divide the first rectangle into 3 parts using vertical lines as first fraction is $$\frac{1}{3}$$ and each vertical section represents $$\frac{1}{3}$$ and 1 part is shaded.
Divide the SecondÂ  rectangle into 7 parts using horizontal lines as Second fraction is $$\frac{1}{7}$$ and each horizontal fraction represent $$\frac{1}{7}$$ and 1 part is shaded.
As 7 and 3 have 21 lcm now divide both the rectangles into 21 parts .
First rectangle divided into 21 parts by drawing 6 horizontal lines and second rectangle into 21 parts by drawing 2 vertical line

e.
$$\frac{3}{4}$$ + $$\frac{1}{5}$$
l.c.m of 4 and 5 is 20.
$$\frac{15}{20}$$ + $$\frac{4}{20}$$ = $$\frac{19}{20}$$

Explanation :
Divide the first rectangle into 4 parts using vertical lines as first fraction is $$\frac{3}{4}$$ and each vertical section represents $$\frac{1}{4}$$ and 3 parts are shaded.
Divide the SecondÂ  rectangle into 5 parts using horizontal lines as Second fraction is $$\frac{1}{5}$$ and each horizontal fraction represent $$\frac{1}{5}$$ and 1 part is shaded.
As 5 and 4 have 20 lcm now divide both the rectangles into 20 parts .
First rectangle divided into 20 parts by drawing 3 horizontal lines and second rectangle into 20 parts by drawing 3 vertical line

f.
$$\frac{2}{3}$$ + $$\frac{2}{7}$$
l.c.m of 3 and 7 is 21.
$$\frac{14}{21}$$ + $$\frac{6}{21}$$ = $$\frac{20}{21}$$

Explanation :
Divide the first rectangle into 3 parts using vertical lines as first fraction is $$\frac{2}{3}$$ and each vertical section represents $$\frac{1}{3}$$ and 2 parts are shaded.
Divide the SecondÂ  rectangle into 7 parts using horizontal lines as Second fraction is $$\frac{2}{7}$$ and each horizontal fraction represent $$\frac{1}{7}$$ and 2 parts are shaded.
As 7 and 3 have 21 lcm now divide both the rectangles into 21 parts .
First rectangle divided into 21 parts by drawing 6 horizontal lines and second rectangle into 21 parts by drawing 2 vertical line

Solve the following problems. Draw a picture and write the number sentence that proves the answer. Simplify your answer, if possible.
Question 2.
Jamal used $$\frac{1}{3}$$ yard of ribbon to tie a package and $$\frac{1}{6}$$ yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?

Explanation :
Length of ribbon used to tie package = $$\frac{1}{3}$$ yard
Length of ribbon used to tie bow = $$\frac{1}{6}$$ yard
Total length of ribbon used by jamal = $$\frac{1}{3}$$ + $$\frac{1}{6}$$ = $$\frac{2}{6}$$ + $$\frac{1}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$ .

Question 3.
Over the weekend, Nolan drank $$\frac{1}{6}$$ quart of orange juice, and Andrea drank $$\frac{3}{4}$$ quart of orange juice. How many quarts did they drink together?

Explanation :
Quantity of Orange juice drank by Nolan= $$\frac{1}{6}$$ quart
Quantity of Orange juice drank by Andrea = $$\frac{3}{4}$$ quart
Total Quantity of orange juice drank by both of them = $$\frac{1}{6}$$Â  + $$\frac{3}{4}$$ = $$\frac{2}{12}$$ $$\frac{9}{12}$$ = $$\frac{11}{12}$$ quarts .

Question 4.
Nadia spent $$\frac{1}{4}$$ of her money on a shirt and $$\frac{2}{5}$$ of her money on new shoes. What fraction of Nadiaâ€™s money has been spent? What fraction of her money is left?

consider total money = 1 whole .
Money spent on shirt = $$\frac{1}{4}$$
Money spent on new shoes = $$\frac{2}{5}$$
Total Money spent on Nadia = $$\frac{1}{4}$$ + $$\frac{2}{5}$$ = $$\frac{5}{20}$$ + $$\frac{8}{20}$$ = $$\frac{13}{20}$$
Fraction of money left = 1 – $$\frac{13}{20}$$ = $$\frac{20}{20}$$ – $$\frac{13}{20}$$ = $$\frac{7}{20}$$ .

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

Solve by drawing the rectangular fraction model.
Question 1.
$$\frac{1}{2}$$ + $$\frac{1}{5}$$ =
$$\frac{1}{2}$$ + $$\frac{1}{5}$$ = $$\frac{5}{10}$$ + $$\frac{2}{10}$$ = $$\frac{7}{10}$$

Question 2.
In one hour, Ed used $$\frac{2}{5}$$ of the time to complete his homework and $$\frac{1}{4}$$ of the time to check his email. How much time did he spend completing homework and checking email? Write your answer as a fraction. (Extension: Write the answer in minutes.)
Time used by Ed to complete his home work = $$\frac{2}{5}$$
Time used by Ed to check his email = $$\frac{1}{4}$$
Total Time Spent by Ed = $$\frac{2}{5}$$ + $$\frac{1}{4}$$ = $$\frac{8}{20}$$ +$$\frac{5}{20}$$ = $$\frac{13}{20}$$ .
1 hour =Â  $$\frac{20}{20}$$ = $$\frac{60}{60}$$ multiplied by 3
$$\frac{13}{20}$$ = $$\frac{39}{60}$$ that means 39 minutes .

Question 1.
Draw a rectangular fraction model to find the sum. Simplify your answer, if possible.
a. $$\frac{1}{4}$$ + $$\frac{1}{3}$$ =
b. $$\frac{1}{4}$$ + $$\frac{1}{5}$$ =
c. $$\frac{1}{4}$$ + $$\frac{1}{6}$$ =
d. $$\frac{1}{5}$$ + $$\frac{1}{9}$$ =
e. $$\frac{1}{4}$$ + $$\frac{2}{5}$$ =
f. $$\frac{3}{5}$$ + $$\frac{3}{7}$$ =
a. $$\frac{1}{4}$$ + $$\frac{1}{3}$$ = $$\frac{3}{12}$$ + $$\frac{4}{12}$$ =$$\frac{7}{12}$$

b. latex]\frac{1}{4}[/latex] + $$\frac{1}{5}$$ = latex]\frac{5}{20}[/latex] + $$\frac{4}{20}$$ = latex]\frac{9}{20}[/latex]

c. $$\frac{1}{4}$$ + $$\frac{1}{6}$$ =$$\frac{3}{12}$$ + $$\frac{2}{12}$$ = $$\frac{5}{12}$$

d. $$\frac{1}{5}$$ + $$\frac{1}{9}$$ =$$\frac{9}{45}$$ + $$\frac{5}{45}$$ = $$\frac{13}{45}$$

e. latex]\frac{1}{4}[/latex] + $$\frac{2}{5}$$ = latex]\frac{5}{20}[/latex] + $$\frac{8}{20}$$ = latex]\frac{13}{20}[/latex]

f. $$\frac{3}{5}$$ + $$\frac{3}{7}$$ = $$\frac{21}{35}$$ + $$\frac{15}{35}$$ = $$\frac{36}{35}$$ = 1$$\frac{1}{35}$$

Solve the following problems. Draw a picture, and write the number sentence that proves the answer. Simplify your answer, if possible.
Question 2.
Rajesh jogged $$\frac{3}{4}$$ mile and then walked $$\frac{1}{6}$$ mile to cool down. How far did he travel?

Distance traveled by Rajesh by jogging = $$\frac{3}{4}$$ mile
Distance traveled by Rajesh by walking = $$\frac{1}{6}$$ mile
Total Distance traveled by Rajesh = $$\frac{3}{4}$$ + $$\frac{1}{6}$$ = $$\frac{9}{12}$$ + $$\frac{2}{12}$$ = $$\frac{11}{12}$$

Question 3.
Cynthia completed $$\frac{2}{3}$$ of the items on her to-do list in the morning and finished $$\frac{1}{8}$$ of the items during her lunch break. What fraction of her to-do list is finished by the end of her lunch break? (Extension: What fraction of her to-do list does she still have to do after lunch?)

Work done by Cynthia in the morning = $$\frac{2}{3}$$
Work done by Cynthia in the lunch break = $$\frac{1}{8}$$
Total work done = $$\frac{2}{3}$$Â  + $$\frac{1}{8}$$ = $$\frac{16}{24}$$ + $$\frac{3}{24}$$ = $$\frac{19}{24}$$.

Question 4.
Sam read $$\frac{2}{5}$$ of her book over the weekend and $$\frac{1}{6}$$ of it on Monday. What fraction of the book has she read? What fraction of the book is left?
Fraction of her book read by weekend = $$\frac{2}{5}$$
FractionÂ  of her read by Monday = $$\frac{1}{6}$$
Fraction of book read = $$\frac{2}{5}$$ + $$\frac{1}{6}$$ = $$\frac{12}{30}$$ + $$\frac{5}{30}$$ = $$\frac{17}{30}$$
Fraction of book left to read = 1 – $$\frac{17}{30}$$ = $$\frac{30 }{30}$$ – $$\frac{17}{30}$$ = $$\frac{13}{30}$$ .