## 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.

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

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 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— \(\frac{3}{4}\) + \(\frac{1}{4}\)

Answer:

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. \(\frac{27}{5}\)

Answer:

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. \(\frac{24}{9}\)

Answer:

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.

Answer:

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. \(\frac{6}{3}\)+ \(\frac{2}{3}\)

Answer:

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. \(\frac{15}{4}\)

Answer:

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— \(\frac{3}{5}\) + \(\frac{1}{5}\)

Answer:

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. \(\frac{27}{10}\)

Answer:

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. \(\frac{21}{9}\)

Answer:

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.

Answer:

Explanation :

Number of boards = 5

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 + \(\frac{5}{10}\) .