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

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

A

Find the Missing Numerator or Denominator

Question 1.

\(\frac{1}{2}\) = \(\frac{}{4}\)

Answer:

\(\frac{1}{2}\) = \(\frac{2}{4}\)

Explanation :

\(\frac{1}{2}\) = \(\frac{x}{4}\)

x = \(\frac{1}{2}\) Ã— 4

x = \(\frac{4}{2}\)

x = 2 .

Question 2.

\(\frac{1}{5}\) = \(\frac{2}{}\)

Answer:

\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation :

\(\frac{1}{5}\) = \(\frac{2}{x}\)

x = \(\frac{5}{1}\) Ã— 2

x = 10 .

Question 3.

\(\frac{2}{5}\) = \(\frac{}{10}\)

Answer:

\(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation :

\(\frac{2}{5}\) = \(\frac{x}{10}\)

x = \(\frac{2}{5}\) Ã— 10

x = \(\frac{20}{5}\)

x = 4 .

Question 4.

\(\frac{3}{5}\) = \(\frac{}{10}\)

Answer:

\(\frac{3}{5}\) = \(\frac{6}{10}\)

Explanation :

\(\frac{3}{5}\) = \(\frac{x}{10}\)

x = \(\frac{3}{5}\) Ã— 10

x = \(\frac{30}{5}\)

x = 6 .

Question 5.

\(\frac{4}{5}\) = \(\frac{}{10}\)

Answer:

\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation :

\(\frac{4}{5}\) = \(\frac{x}{10}\)

x = \(\frac{4}{5}\) Ã— 10

x = \(\frac{40}{5}\)

x = 8 .

Question 6.

\(\frac{1}{3}\) = \(\frac{2}{}\)

Answer:

\(\frac{1}{3}\) = \(\frac{2}{}\)

Explanation :

\(\frac{1}{3}\) = \(\frac{2}{x}\)

x = \(\frac{3}{1}\) Ã— 2

x = 3 Ã— 2

x = 6 .

Question 7.

\(\frac{2}{3}\) = \(\frac{}{9}\)

Answer:

\(\frac{2}{3}\) = \(\frac{6}{9}\)

Explanation :

\(\frac{2}{3}\) = \(\frac{x}{9}\)

x = \(\frac{2}{3}\) Ã— 9

x = \(\frac{18}{3}\)

x = 6 .

Question 8.

\(\frac{1}{3}\) = \(\frac{3}{}\)

Answer:

\(\frac{1}{3}\) = \(\frac{3}{9}\)

Explanation :

\(\frac{1}{3}\) = \(\frac{3}{x}\)

x = \(\frac{3}{1}\) Ã— 3

x = 3 Ã— 3

x = 9 .

Question 9.

\(\frac{2}{3}\) = \(\frac{}{9}\)

Answer:

\(\frac{2}{3}\) = \(\frac{6}{9}\)

Explanation :

\(\frac{2}{3}\) = \(\frac{x}{9}\)

x = \(\frac{2}{3}\) Ã— 9

x = \(\frac{18}{3}\)

x = 6 .

Question 10.

\(\frac{1}{4}\) = \(\frac{}{8}\)

Answer:

\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation :

\(\frac{1}{4}\) = \(\frac{x}{8}\)

x = \(\frac{1}{4}\) Ã— 8

x = \(\frac{8}{4}\)

x = 2 .

Question 11.

\(\frac{3}{4}\) = \(\frac{}{8}\)

Answer:

\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation :

\(\frac{3}{4}\) = \(\frac{x}{8}\)

x = \(\frac{3}{4}\) Ã— 8

x = \(\frac{24}{4}\)

x = 6 .

Question 12.

\(\frac{1}{4}\) = \(\frac{3}{}\)

Answer:

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

Explanation :

\(\frac{1}{4}\) = \(\frac{3}{x}\)

x = \(\frac{4}{1}\) Ã— 3

x = 4 Ã— 3

x = 12 .

Question 13.

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

Answer:

\(\frac{3}{4}\) = \(\frac{9}{12}\)

Explanation :

\(\frac{3}{4}\) = \(\frac{9}{x}\)

x = \(\frac{4}{3}\) Ã— 9

x = \(\frac{36}{3}\)

x = 12 .

Question 14.

\(\frac{2}{4}\) = \(\frac{}{2}\)

Answer:

\(\frac{2}{4}\) = \(\frac{1}{2}\)

Explanation :

\(\frac{2}{4}\) = \(\frac{x}{2}\)

x = \(\frac{2}{4}\) Ã— 2

x = \(\frac{4}{4}\)

x = 1 .

Question 15.

\(\frac{2}{6}\) = \(\frac{1}{}\)

Answer:

\(\frac{2}{6}\) = \(\frac{1}{3}\)

Explanation :

\(\frac{2}{6}\) = \(\frac{1}{x}\)

x = \(\frac{6}{2}\) Ã— 1

x = \(\frac{6}{2}\)

x = 3 .

Question 16.

\(\frac{2}{10}\) = \(\frac{1}{}\)

Answer:

\(\frac{2}{10}\) = \(\frac{1}{5}\)

Explanation :

\(\frac{2}{10}\) = \(\frac{1}{x}\)

x = \(\frac{10}{2}\) Ã— 1

x = 5 .

Question 17.

\(\frac{4}{10}\) = \(\frac{}{5}\)

Answer:

\(\frac{4}{10}\) = \(\frac{2}{5}\)

Explanation :

\(\frac{4}{10}\) = \(\frac{x}{5}\)

x = \(\frac{4}{10}\) Ã— 5

x = \(\frac{20}{10}\)

x = 2 .

Question 18.

\(\frac{8}{10}\) = \(\frac{}{5}\)

Answer:

\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation :

\(\frac{8}{10}\) = \(\frac{x}{5}\)

x = \(\frac{8}{10}\) Ã— 5

x = \(\frac{40}{10}\)

x = 4 .

Question 19.

\(\frac{3}{9}\) = \(\frac{}{3}\)

Answer:

\(\frac{3}{9}\) = \(\frac{1}{3}\)

Explanation :

\(\frac{3}{9}\) = \(\frac{x}{3}\)

x = \(\frac{3}{9}\) Ã— 3

x = \(\frac{9}{9}\)

x = 1 .

Question 20.

\(\frac{6}{9}\) = \(\frac{}{3}\)

Answer:

\(\frac{6}{9}\) = \(\frac{2}{3}\)

Explanation :

\(\frac{6}{9}\) = \(\frac{x}{3}\)

x = \(\frac{6}{9}\) Ã— 3

x = \(\frac{18}{9}\)

x = 2 .

Question 21.

\(\frac{3}{12}\) = \(\frac{1}{}\)

Answer:

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

Explanation :

\(\frac{3}{12}\) = \(\frac{1}{x}\)

x = \(\frac{3}{12}\) Ã— 1

x = 4 .

Question 22.

\(\frac{9}{12}\) = \(\frac{}{4}\)

Answer:

\(\frac{9}{12}\) = \(\frac{3}{4}\)

Explanation :

\(\frac{9}{12}\) = \(\frac{x}{4}\)

x = \(\frac{9}{12}\) Ã— 4

x = \(\frac{36}{12}\)

x = 3 .

Question 23.

\(\frac{1}{3}\) = \(\frac{}{12}\)

Answer:

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

Explanation :

\(\frac{1}{3}\) = \(\frac{x}{12}\)

x = \(\frac{1}{3}\) Ã— 12

x = \(\frac{12}{3}\)

x = 4 .

Question 24.

\(\frac{2}{3}\) = \(\frac{}{12}\)

Answer:

\(\frac{2}{3}\) = \(\frac{8}{12}\)

Explanation :

\(\frac{2}{3}\) = \(\frac{x}{12}\)

x = \(\frac{2}{3}\) Ã— 12

x = \(\frac{24}{3}\)

x = 8 .

Question 25.

\(\frac{8}{12}\) = \(\frac{}{3}\)

Answer:

\(\frac{8}{12}\) = \(\frac{2}{3}\)

Explanation :

\(\frac{8}{12}\) = \(\frac{x}{3}\)

x = \(\frac{8}{12}\) Ã— 3

x = \(\frac{24}{12}\)

x = 2 .

Question 26.

\(\frac{12}{16}\) = \(\frac{3}{}\)

Answer:

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

Explanation :

\(\frac{12}{16}\) = \(\frac{3}{x}\)

x = \(\frac{16}{12}\) Ã— 3

x = 4 .

Question 27.

\(\frac{3}{5}\) = \(\frac{}{25}\)

Answer:

\(\frac{3}{5}\) = \(\frac{15}{25}\)

Explanation :

\(\frac{3}{5}\) = \(\frac{x}{25}\)

x = \(\frac{3}{5}\) Ã— 25

x = 3 Ã— 5

x = 15 .

Question 28.

\(\frac{4}{5}\) = \(\frac{28}{}\)

Answer:

\(\frac{4}{5}\) = \(\frac{28}{35}\)

Explanation :

\(\frac{4}{5}\) = \(\frac{28}{x}\)

x = \(\frac{5}{4}\) Ã— 28

x = 5 Ã— 7

x = 35 .

Question 29.

\(\frac{18}{24}\) = \(\frac{3}{}\)

Answer:

\(\frac{18}{24}\) = \(\frac{3}{4}\)

Explanation :

\(\frac{18}{24}\) = \(\frac{3}{x}\)

x = \(\frac{24}{18}\) Ã— 3

x = \(\frac{24}{6}\)

x = 4 .

Question 30.

\(\frac{24}{30}\) = \(\frac{}{5}\)

Answer:

\(\frac{24}{30}\) = \(\frac{4}{5}\)

Explanation :

\(\frac{24}{30}\) = \(\frac{x}{5}\)

x = \(\frac{24}{30}\) Ã— 5

x = \(\frac{24}{6}\)

x = 4 .

Question 31.

\(\frac{5}{6}\) = \(\frac{35}{}\)

Answer:

\(\frac{5}{6}\) = \(\frac{35}{42}\)

Explanation :

\(\frac{5}{6}\) = \(\frac{35}{x}\)

x = \(\frac{6}{5}\) Ã— 35

x = 6 Ã— 7

x = 42 .

Question 32.

\(\frac{56}{63}\) = \(\frac{}{9}\)

Answer:

\(\frac{56}{63}\) = \(\frac{8}{9}\)

Explanation :

\(\frac{56}{63}\) = \(\frac{x}{9}\)

x = \(\frac{56}{63}\) Ã— 9

x = \(\frac{56}{7}\)

x = 8 .

Question 33.

\(\frac{64}{72}\) = \(\frac{8}{}\)

Answer:

\(\frac{64}{72}\) = \(\frac{8}{9}\)

Explanation :

\(\frac{64}{72}\) = \(\frac{8}{x}\)

x = \(\frac{72}{64}\) Ã— 8

x = \(\frac{72}{8}\)

x = 9 .

Question 34.

\(\frac{5}{8}\) = \(\frac{}{64}\)

Answer:

\(\frac{5}{8}\) = \(\frac{40}{64}\)

Explanation :

\(\frac{5}{8}\) = \(\frac{x}{64}\)

x = \(\frac{5}{8}\) Ã— 64

x = 5 Ã— 8

x = 40 .

Question 35.

\(\frac{5}{6}\) = \(\frac{45}{}\)

Answer:

\(\frac{5}{6}\) = \(\frac{45}{54}\)

Explanation :

\(\frac{5}{6}\) = \(\frac{45}{x}\)

x = \(\frac{6}{5}\) Ã— 45

x = 6 Ã— 9

x = 54 .

Question 36.

\(\frac{45}{81}\) = \(\frac{}{9}\)

Answer:

\(\frac{45}{81}\) = \(\frac{5}{9}\)

Explanation :

\(\frac{45}{81}\) = \(\frac{x}{9}\)

x = \(\frac{45}{81}\) Ã— 9

x = \(\frac{45}{9}\)

x = 5 .

Question 37.

\(\frac{6}{7}\) = \(\frac{48}{}\)

Answer:

\(\frac{6}{7}\) = \(\frac{48}{56}\)

Explanation :

\(\frac{6}{7}\) = \(\frac{48}{x}\)

x = \(\frac{7}{6}\) Ã— 48

x = 7 Ã— 8

x = 56 .

Question 38.

\(\frac{36}{81}\) = \(\frac{}{9}\)

Answer:

\(\frac{36}{81}\) = \(\frac{4}{9}\)

Explanation :

\(\frac{36}{81}\) = \(\frac{x}{9}\)

x = \(\frac{36}{81}\) Ã— 9

x = \(\frac{36}{9}\)

x = 4 .

Question 39.

\(\frac{8}{56}\) = \(\frac{1}{}\)

Answer:

\(\frac{8}{56}\) = \(\frac{1}{7}\)

Explanation :

\(\frac{8}{56}\) = \(\frac{1}{x}\)

x = \(\frac{8}{56}\) Ã— 1

x = 7 .

Question 40.

\(\frac{35}{63}\) = \(\frac{5}{}\)

Answer:

\(\frac{35}{63}\) = \(\frac{5}{9}\)

Explanation :

\(\frac{35}{63}\) = \(\frac{5}{x}\)

x = \(\frac{63}{35}\) Ã— 5

x = \(\frac{63}{7}\)

x = 9 .

Question 41.

\(\frac{1}{6}\) = \(\frac{12}{}\)

Answer:

\(\frac{1}{6}\) = \(\frac{12}{72}\)

Explanation :

\(\frac{1}{6}\) = \(\frac{12}{x}\)

x = \(\frac{6}{1}\) Ã— 12

x = 72 .

Question 42.

\(\frac{3}{7}\) = \(\frac{36}{}\)

Answer:

\(\frac{3}{7}\) = \(\frac{36}{84}\)

Explanation :

\(\frac{3}{7}\) = \(\frac{36}{x}\)

x = \(\frac{7}{3}\) Ã— 36

x = 7 Ã— 12

x = 84 .

Question 43.

\(\frac{48}{60}\) = \(\frac{4}{}\)

Answer:

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

Explanation :

\(\frac{48}{60}\) = \(\frac{4}{x}\)

x = \(\frac{60}{48}\) Ã— 4

x = \(\frac{60}{12}\)

x = 5 .

Question 44.

\(\frac{72}{84}\) = \(\frac{}{7}\)

Answer:

\(\frac{72}{84}\) = \(\frac{6}{7}\)

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.

\(\frac{1}{5}\) = \(\frac{2}{}\)

Answer:

\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation :

\(\frac{1}{5}\) = \(\frac{2}{x}\)

x = \(\frac{5}{1}\) Ã— 2

x = 10 .

Question 2.

\(\frac{2}{5}\) = \(\frac{}{10}\)

Answer:

\(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation :

\(\frac{2}{5}\) = \(\frac{x}{10}\)

x = \(\frac{2}{5}\) Ã— 10

x = 4 .

Question 3.

\(\frac{3}{5}\) = \(\frac{}{10}\)

Answer:

\(\frac{3}{5}\) = \(\frac{6}{10}\)

Explanation :

\(\frac{3}{5}\) = \(\frac{x}{10}\)

x = \(\frac{3}{5}\) Ã— 10

x = 6 .

Question 4.

\(\frac{4}{5}\) = \(\frac{}{10}\)

Answer:

\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation :

\(\frac{4}{5}\) = \(\frac{x}{10}\)

x = \(\frac{4}{5}\) Ã— 10

x = 8 .

Question 5.

\(\frac{1}{3}\) = \(\frac{2}{}\)

Answer:

\(\frac{1}{3}\) = \(\frac{2}{6}\)

Explanation :

\(\frac{1}{3}\) = \(\frac{2}{x}\)

x = \(\frac{3}{1}\) Ã— 2

x = 6

Question 6.

\(\frac{1}{3}\) = \(\frac{}{6}\)

Answer:

\(\frac{1}{3}\) = \(\frac{2}{6}\)

Explanation :

\(\frac{1}{3}\) = \(\frac{x}{6}\)

x = \(\frac{1}{3}\) Ã— 6

x = 2

Question 7.

\(\frac{2}{3}\) = \(\frac{4}{}\)

Answer:

\(\frac{2}{3}\) = \(\frac{4}{12}\)

Explanation :

\(\frac{2}{3}\) = \(\frac{4}{x}\)

x = \(\frac{3}{2}\) Ã— 4

x = 6

Question 8.

\(\frac{1}{3}\) = \(\frac{}{9}\)

Answer:

\(\frac{1}{3}\) = \(\frac{3}{9}\)

Explanation :

\(\frac{1}{3}\) = \(\frac{x}{9}\)

x = \(\frac{1}{3}\) Ã— 9

x = 3

Question 9.

\(\frac{2}{3}\) = \(\frac{6}{}\)

Answer:

\(\frac{2}{3}\) = \(\frac{6}{9}\)

Explanation :

\(\frac{2}{3}\) = \(\frac{6}{x}\)

x = \(\frac{3}{2}\) Ã— 6

x = 9

Question 10.

\(\frac{1}{4}\) = \(\frac{2}{}\)

Answer:

\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation :

\(\frac{1}{4}\) = \(\frac{2}{x}\)

x = \(\frac{4}{1}\) Ã— 2

x = 8

Question 11.

\(\frac{3}{4}\) = \(\frac{6}{}\)

Answer:

\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation :

\(\frac{3}{4}\) = \(\frac{6}{x}\)

x = \(\frac{4}{3}\) Ã— 6

x = 8

Question 12.

\(\frac{1}{4}\) = \(\frac{}{12}\)

Answer:

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

Explanation :

\(\frac{1}{4}\) = \(\frac{x}{12}\)

x = \(\frac{1}{4}\) Ã— 12

x = 3

Question 13.

\(\frac{3}{4}\) = \(\frac{}{12}\)

Answer:

\(\frac{3}{4}\) = \(\frac{9}{12}\)

Explanation :

\(\frac{3}{4}\) = \(\frac{x}{12}\)

x = \(\frac{3}{4}\) Ã— 12

x = 9

Question 14.

\(\frac{2}{4}\) = \(\frac{1}{}\)

Answer:

\(\frac{2}{4}\) = \(\frac{1}{2}\)

Explanation :

\(\frac{2}{4}\) = \(\frac{1}{x}\)

x = \(\frac{4}{2}\) Ã— 1

x = 2

Question 15.

\(\frac{2}{6}\) = \(\frac{}{3}\)

Answer:

\(\frac{2}{6}\) = \(\frac{4}{12}\)

Explanation :

\(\frac{2}{6}\) = \(\frac{x}{12}\)

x = \(\frac{2}{6}\) Ã— 12

x = 4

Question 16.

\(\frac{2}{10}\) = \(\frac{}{5}\)

Answer:

\(\frac{2}{10}\) = \(\frac{1}{5}\)

Explanation :

\(\frac{2}{10}\) = \(\frac{x}{5}\)

x = \(\frac{2}{10}\) Ã— 5

x = 1

Question 17.

\(\frac{4}{10}\) = \(\frac{2}{}\)

Answer:

\(\frac{4}{10}\) = \(\frac{2}{5}\)

Explanation :

\(\frac{4}{10}\) = \(\frac{2}{x}\)

x = \(\frac{10}{4}\) Ã— 2

x = 5

Question 18.

\(\frac{8}{10}\) = \(\frac{4}{}\)

Answer:

\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation :

\(\frac{8}{10}\) = \(\frac{4}{x}\)

x = \(\frac{10}{8}\) Ã— 4

x = 5

Question 19.

\(\frac{3}{9}\) = \(\frac{1}{}\)

Answer:

\(\frac{3}{9}\) = \(\frac{1}{3}\)

Explanation :

\(\frac{3}{9}\) = \(\frac{1}{x}\)

x = \(\frac{9}{3}\) Ã— 1

x = 3

Question 20.

\(\frac{6}{9}\) = \(\frac{2}{}\)

Answer:

\(\frac{6}{9}\) = \(\frac{2}{3}\)

Explanation :

\(\frac{6}{9}\) = \(\frac{2}{x}\)

x = \(\frac{9}{6}\) Ã— 2

x = 3

Question 21.

\(\frac{1}{4}\) = \(\frac{}{12}\)

Answer:

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

Explanation :

\(\frac{1}{4}\) = \(\frac{x}{12}\)

x = \(\frac{1}{4}\) Ã— 12

x = 3

Question 22.

\(\frac{9}{12}\) = \(\frac{3}{}\)

Answer:

\(\frac{9}{12}\) = \(\frac{3}{}\)

Explanation :

\(\frac{6}{9}\) = \(\frac{2}{x}\)

x = \(\frac{9}{6}\) Ã— 2

x = 3

Question 23.

\(\frac{1}{3}\) = \(\frac{4}{}\)

Answer:

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

Explanation :

\(\frac{1}{3}\) = \(\frac{4}{x}\)

x = \(\frac{3}{1}\) Ã— 4

x = 12

Question 24.

\(\frac{2}{3}\) = \(\frac{8}{}\)

Answer:

\(\frac{2}{3}\) = \(\frac{8}{12}\)

Explanation :

\(\frac{2}{3}\) = \(\frac{8}{x}\)

x = \(\frac{3}{2}\) Ã— 8

x = 12

Question 25.

\(\frac{8}{12}\) = \(\frac{2}{}\)

Answer:

\(\frac{8}{12}\) = \(\frac{2}{3}\)

Explanation :

\(\frac{8}{12}\) = \(\frac{2}{x}\)

x = \(\frac{12}{8}\) Ã— 2

x = 3

Question 26.

\(\frac{12}{16}\) = \(\frac{}{4}\)

Answer:

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

Explanation :

\(\frac{12}{16}\) = \(\frac{x}{4}\)

x = \(\frac{12}{16}\) Ã— 4

x = 3

Question 27.

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

Answer:

\(\frac{3}{5}\) = \(\frac{15}{25}\)

Explanation :

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

x = \(\frac{5}{3}\) Ã— 15

x = 25

Question 28.

\(\frac{4}{5}\) = \(\frac{}{35}\)

Answer:

\(\frac{4}{5}\) = \(\frac{28}{35}\)

Explanation :

\(\frac{4}{5}\) = \(\frac{x}{35}\)

x = \(\frac{4}{5}\) Ã— 35

x = 28

Question 29.

\(\frac{18}{24}\) = \(\frac{}{4}\)

Answer:

\(\frac{18}{24}\) = \(\frac{3}{4}\)

Explanation :

\(\frac{18}{24}\) = \(\frac{x}{4}\)

x = \(\frac{18}{24}\) Ã— 4

x = 3

Question 30.

\(\frac{24}{30}\) = \(\frac{4}{}\)

Answer:

\(\frac{24}{30}\) = \(\frac{4}{5}\)

Explanation :

\(\frac{24}{30}\) = \(\frac{4}{x}\)

x = \(\frac{30}{24}\) Ã— 4

x = 5

Question 31.

\(\frac{5}{6}\) = \(\frac{}{42}\)

Answer:

\(\frac{5}{6}\) = \(\frac{35}{42}\)

Explanation :

\(\frac{5}{6}\) = \(\frac{x}{42}\)

x = \(\frac{5}{6}\) Ã— 42

x = 35

Question 32.

\(\frac{56}{63}\) = \(\frac{8}{}\)

Answer:

\(\frac{56}{63}\) = \(\frac{8}{9}\)

Explanation :

\(\frac{56}{63}\) = \(\frac{8}{x}\)

x = \(\frac{63}{56}\) Ã— 8

x = 9

Question 33.

\(\frac{64}{72}\) = \(\frac{}{9}\)

Answer:

\(\frac{64}{72}\) = \(\frac{8}{9}\)

Explanation :

\(\frac{64}{72}\) = \(\frac{x}{9}\)

x = \(\frac{64}{72}\) Ã— 9

x = 8

Question 34.

\(\frac{5}{8}\) = \(\frac{40}{}\)

Answer:

\(\frac{5}{8}\) = \(\frac{40}{64}\)

Explanation :

\(\frac{5}{8}\) = \(\frac40}{x}\)

x = \(\frac{8}{5}\) Ã— 40

x = 64

Question 35.

\(\frac{5}{6}\) = \(\frac{}{54}\)

Answer:

\(\frac{5}{6}\) = \(\frac{45}{54}\)

Explanation :

\(\frac{5}{6}\) = \(\frac{x}{54}\)

x = \(\frac{5}{6}\) Ã— 54

x = 45

Question 36.

\(\frac{45}{81}\) = \(\frac{5}{}\)

Answer:

\(\frac{45}{81}\) = \(\frac{5}{9}\)

Explanation :

\(\frac{45}{81}\) = \(\frac{x}{9}\)

x = \(\frac{45}{81}\) Ã— 9

x = 9

Question 37.

\(\frac{6}{7}\) = \(\frac{}{56}\)

Answer:

\(\frac{6}{7}\) = \(\frac{48}{56}\)

Explanation :

\(\frac{6}{7}\) = \(\frac{x}{56}\)

x = \(\frac{7}{6}\) Ã— 56

x = 48

Question 38.

\(\frac{36}{81}\) = \(\frac{4}{}\)

Answer:

\(\frac{36}{81}\) = \(\frac{4}{9}\)

Explanation :

\(\frac{36}{81}\) = \(\frac{4}{x}\)

x = \(\frac{81}{36}\)Â Ã— 4

x = 9

Question 39.

\(\frac{8}{56}\) = \(\frac{}{7}\)

Answer:

\(\frac{8}{56}\) = \(\frac{1}{7}\)

Explanation :

\(\frac{8}{56}\) = \(\frac{x}{7}\)

x = \(\frac{8}{56}\) Ã— 7

x = 1

Question 40.

\(\frac{35}{63}\) = \(\frac{}{9}\)

Answer:

\(\frac{35}{63}\) = \(\frac{5}{9}\)

Explanation :

\(\frac{35}{63}\) = \(\frac{x}{9}\)

x = \(\frac{35}{63}\) Ã— 9

x = 5

Question 41.

\(\frac{1}{6}\) = \(\frac{}{72}\)

Answer:

\(\frac{1}{6}\) = \(\frac{12}{72}\)

Explanation :

\(\frac{1}{6}\) = \(\frac{x}{72}\)

x = \(\frac{1}{6}\) Ã— 72

x = 12

Question 42.

\(\frac{3}{7}\) = \(\frac{}{84}\)

Answer:

\(\frac{3}{7}\) = \(\frac{36}{84}\)

Explanation :

\(\frac{3}{7}\) = \(\frac{x}{84}\)

x = \(\frac{3}{7}\) Ã— 84

x = 36

Question 43.

\(\frac{48}{60}\) = \(\frac{}{5}\)

Answer:

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

Explanation :

\(\frac{48}{60}\) = \(\frac{x}{5}\)

x = \(\frac{48}{60}\) Ã— 5

x = 4

Question 44.

\(\frac{72}{84}\) = \(\frac{6}{}\)

Answer:

\(\frac{72}{84}\) = \(\frac{6}{7}\)

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. \(\frac{2}{3}\) + \(\frac{2}{7}\) =

Answer:

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

Write fraction of shaded parts and add them .

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

Write fraction of shaded parts and add them .

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

Write fraction of shaded parts and add them .

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

Write fraction of shaded parts and add them .

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

Write fraction of shaded parts and add them .

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

Write fraction of shaded parts and add them .

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?

Answer:

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?

Answer :

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?

Answer:

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.

\(\frac{1}{2}\) + \(\frac{1}{5}\) =

Answer:

\(\frac{1}{2}\) + \(\frac{1}{5}\) = \(\frac{5}{10}\) + \(\frac{2}{10}\) = \(\frac{7}{10}\)

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.)

Answer:

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 .

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

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. \(\frac{3}{5}\) + \(\frac{3}{7}\) =

Answer:

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?

Answer:

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?)

Answer:

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?

Answer :

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 – \(\frac{17}{30}\) = \(\frac{30 }{30}\) – \(\frac{17}{30}\) = \(\frac{13}{30}\) .