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 = \(\frac{1}{2}\) × 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 = \(\frac{5}{1}\) × 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 = \(\frac{2}{5}\) × 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 = \(\frac{3}{5}\) × 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 = \(\frac{4}{5}\) × 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 = \(\frac{3}{1}\) × 2
x = 3 × 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 = \(\frac{2}{3}\) × 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 = \(\frac{3}{1}\) × 3
x = 3 × 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 = \(\frac{2}{3}\) × 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 = \(\frac{1}{4}\) × 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 = \(\frac{3}{4}\) × 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 = \(\frac{4}{1}\) × 3
x = 4 × 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 = \(\frac{4}{3}\) × 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 = \(\frac{2}{4}\) × 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 = \(\frac{6}{2}\) × 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 = \(\frac{10}{2}\) × 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 = \(\frac{4}{10}\) × 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 = \(\frac{8}{10}\) × 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 = \(\frac{3}{9}\) × 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 = \(\frac{6}{9}\) × 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 = \(\frac{3}{12}\) × 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 = \(\frac{9}{12}\) × 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 = \(\frac{1}{3}\) × 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 = \(\frac{2}{3}\) × 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 = \(\frac{8}{12}\) × 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 = \(\frac{16}{12}\) × 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 = \(\frac{3}{5}\) × 25
x = 3 × 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 = \(\frac{5}{4}\) × 28
x = 5 × 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 = \(\frac{24}{18}\) × 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 = \(\frac{24}{30}\) × 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 = \(\frac{6}{5}\) × 35
x = 6 × 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 = \(\frac{56}{63}\) × 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 = \(\frac{72}{64}\) × 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 = \(\frac{5}{8}\) × 64
x = 5 × 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 = \(\frac{6}{5}\) × 45
x = 6 × 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 = \(\frac{45}{81}\) × 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 = \(\frac{7}{6}\) × 48
x = 7 × 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 = \(\frac{36}{81}\) × 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 = \(\frac{8}{56}\) × 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 = \(\frac{63}{35}\) × 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 = \(\frac{6}{1}\) × 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 = \(\frac{7}{3}\) × 36
x = 7 × 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 = \(\frac{60}{48}\) × 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 = \(\frac{72}{84}\) × 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 = \(\frac{5}{1}\) × 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 = \(\frac{2}{5}\) × 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 = \(\frac{3}{5}\) × 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 = \(\frac{4}{5}\) × 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 = \(\frac{3}{1}\) × 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 = \(\frac{1}{3}\) × 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 = \(\frac{3}{2}\) × 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 = \(\frac{1}{3}\) × 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 = \(\frac{3}{2}\) × 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 = \(\frac{4}{1}\) × 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 = \(\frac{4}{3}\) × 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 = \(\frac{1}{4}\) × 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 = \(\frac{3}{4}\) × 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 = \(\frac{4}{2}\) × 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 = \(\frac{2}{6}\) × 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 = \(\frac{2}{10}\) × 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 = \(\frac{10}{4}\) × 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 = \(\frac{10}{8}\) × 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 = \(\frac{9}{3}\) × 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 = \(\frac{9}{6}\) × 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 = \(\frac{1}{4}\) × 12
x = 3
Question 22.
\(\frac{9}{12}\) = \(\frac{3}{}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{}\)
Explanation :
\(\frac{6}{9}\) = \(\frac{2}{x}\)
x = \(\frac{9}{6}\) × 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 = \(\frac{3}{1}\) × 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 = \(\frac{3}{2}\) × 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 = \(\frac{12}{8}\) × 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 = \(\frac{12}{16}\) × 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 = \(\frac{5}{3}\) × 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 = \(\frac{4}{5}\) × 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 = \(\frac{18}{24}\) × 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 = \(\frac{30}{24}\) × 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 = \(\frac{5}{6}\) × 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 = \(\frac{63}{56}\) × 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 = \(\frac{64}{72}\) × 9
x = 8
Question 34.
\(\frac{5}{8}\) = \(\frac{40}{}\)
Answer:
\(\frac{5}{8}\) = \(\frac{40}{64}\)
Explanation :
\(\frac{5}{8}\) = \(\frac40}{x}\)
x = \(\frac{8}{5}\) × 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 = \(\frac{5}{6}\) × 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 = \(\frac{45}{81}\) × 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 = \(\frac{7}{6}\) × 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 = \(\frac{81}{36}\) × 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 = \(\frac{8}{56}\) × 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 = \(\frac{35}{63}\) × 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 = \(\frac{1}{6}\) × 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 = \(\frac{3}{7}\) × 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 = \(\frac{48}{60}\) × 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 = \(\frac{84}{72}\) × 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 × \(\frac{3}{4}\) + \(\frac{1}{4}\)
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 × \(\frac{3}{4}\) + \(\frac{1}{4}\)
\(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{1}{4}\) = \(\frac{7}{4}\)
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. \(\frac{6}{7}\) = \(\frac{2}{7}\) + \(\frac{2}{7}\) + \(\frac{2}{7}\) = 3×\(\frac{2}{7}\)
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 × \(\frac{3}{2}\)
c. \(\frac{12}{10}\) = \(\frac{6}{10}\) +\(\frac{6}{10}\)= 2×\(\frac{6}{10}\)
d. \(\frac{27}{5}\) = \(\frac{9}{5}\) + \(\frac{9}{5}\) + \(\frac{9}{5}\) = 3×\(\frac{9}{5}\)
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 × \(\frac{3}{9}\)
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 × \(\frac{3}{5}\) + \(\frac{1}{5}\)
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 again \(\frac{1}{4}\) 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 × \(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\) + \(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{7}{5}\) .
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 × \(\frac{3}{11}\) .
b. \(\frac{9}{4}\) = \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) = 3 × \(\frac{3}{4}\)
c. \(\frac{12}{8}\) =\(\frac{4}{8}\) + \(\frac{4}{8}\) + \(\frac{4}{8}\)= 3 × \(\frac{4}{8}\)
d. \(\frac{27}{10}\) = \(\frac{9}{10}\) + \(\frac{9}{10}\) + \(\frac{9}{10}\) = 3 × \(\frac{9}{10}\) .
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 + \(\frac{1}{2}\) = 3 + \(\frac{1}{2}\) .
c. \(\frac{25}{7}\) = \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{4}{7}\) = 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+ \(\frac{3}{9} \) = 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 tenths = \(\frac{9}{10}\) .
Total Length of board = 5 × \(\frac{9}{10}\) = \(\frac{45}{10}\).
\(\frac{45}{10}\) = \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{5}{10}\) = 1+ 1+ 1+ 1+ \(\frac{5}{10}\) = 4 + \(\frac{5}{10}\) .
