## Engage NY Eureka Math 5th Grade Module 3 Lesson 12 Answer Key

### Eureka Math Grade 5 Module 3 Lesson 12 Sprint Answer Key

A

Subtract Fractions with Unlike Units

Question 1.

\(\frac{2}{4}\) – \(\frac{1}{4}\) =

Answer:

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

Question 2.

\(\frac{1}{2}\) – \(\frac{1}{4}\) =

Answer:

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

Explanation :

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

Question 3.

\(\frac{2}{6}\) – \(\frac{1}{6}\) =

Answer:

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

Question 4.

\(\frac{1}{3}\) – \(\frac{1}{6}\) =

Answer:

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

Explanation :

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

Question 5.

\(\frac{2}{8}\) – \(\frac{1}{8}\) =

Answer:

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

Question 6.

\(\frac{1}{4}\) – \(\frac{1}{8}\) =

Answer:

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

Explanation :

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

Question 7.

\(\frac{6}{8}\) – \(\frac{1}{8}\) =

Answer:

\(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 8.

\(\frac{3}{4}\) – \(\frac{1}{8}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 9.

\(\frac{3}{4}\) – \(\frac{3}{8}\) =

Answer:

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

Explanation :

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

Question 10.

\(\frac{5}{10}\) – \(\frac{2}{10}\) =

Answer:

\(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 11.

\(\frac{1}{2}\) – \(\frac{2}{10}\) =

Answer:

\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Explanation :

\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 12.

\(\frac{1}{2}\) – \(\frac{2}{10}\) =

Answer:

\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Explanation :

\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 13.

\(\frac{4}{10}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 14.

\(\frac{2}{5}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Explanation :

\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 15.

\(\frac{2}{5}\) – \(\frac{3}{10}\) =

Answer:

\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{4}{10}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Question 16.

\(\frac{6}{10}\) – \(\frac{3}{10}\) =

Answer:

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

Question 17.

\(\frac{3}{5}\) – \(\frac{3}{10}\) =

Answer:

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

Explanation :

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

Question 18.

\(\frac{3}{5}\) – \(\frac{5}{10}\) =

Answer:

\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Question 19.

\(\frac{8}{10}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{8}{10}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)

Question 20.

\(\frac{4}{5}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{8}{10}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)

Question 21.

\(\frac{4}{5}\) – \(\frac{5}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)

Explanation :

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

Question 22.

\(\frac{4}{5}\) – \(\frac{5}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)

Explanation :

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

Question 23.

\(\frac{4}{5}\) – \(\frac{7}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{8}{10}\) – \(\frac{7}{10}\) = \(\frac{1}{10}\)

Question 24.

\(\frac{2}{12}\) – \(\frac{1}{12}\) =

Answer:

\(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 25.

\(\frac{1}{6}\) – \(\frac{1}{12}\) =

Answer:

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

Explanation :

\(\frac{1}{6}\) – \(\frac{1}{12}\) = \(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 26.

\(\frac{6}{12}\) – \(\frac{1}{12}\) =

Answer:

\(\frac{6}{12}\) – \(\frac{1}{12}\) = \(\frac{5}{12}\)

Question 27.

\(\frac{1}{2}\) – \(\frac{1}{12}\) =

Answer:

\(\frac{1}{2}\) – \(\frac{1}{12}\) = \(\frac{5}{12}\)

Explanation :

\(\frac{1}{2}\) – \(\frac{1}{12}\) = \(\frac{6}{12}\) – \(\frac{1}{12}\) = \(\frac{5}{12}\)

Question 28.

\(\frac{1}{2}\) – \(\frac{5}{12}\) =

Answer:

\(\frac{1}{2}\) – \(\frac{5}{12}\) = \(\frac{1}{12}\)

Explanation :

\(\frac{1}{2}\) – \(\frac{5}{12}\) = \(\frac{6}{12}\) – \(\frac{5}{12}\) = \(\frac{1}{12}\)

Question 29.

\(\frac{10}{12}\) – \(\frac{5}{12}\) =

Answer:

\(\frac{10}{12}\) – \(\frac{5}{12}\) = \(\frac{5}{12}\)

Question 30.

\(\frac{5}{6}\) – \(\frac{5}{12}\) =

Answer:

\(\frac{5}{6}\) – \(\frac{5}{12}\) = \(\frac{5}{12}\)

Explanation :

\(\frac{5}{6}\) – \(\frac{5}{12}\) = \(\frac{10}{12}\) – \(\frac{5}{12}\) = \(\frac{5}{12}\)

Question 31.

\(\frac{1}{3}\) – \(\frac{3}{12}\) =

Answer:

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

Explanation :

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

Question 32.

\(\frac{2}{3}\) – \(\frac{1}{12}\) =

Answer:

\(\frac{2}{3}\) – \(\frac{1}{12}\) = \(\frac{7}{12}\)

Explanation :

\(\frac{2}{3}\) – \(\frac{1}{12}\) = \(\frac{8}{12}\) – \(\frac{1}{12}\) = \(\frac{7}{12}\)

Question 33.

\(\frac{2}{3}\) – \(\frac{3}{12}\) =

Answer:

\(\frac{2}{3}\) – \(\frac{3}{12}\) = \(\frac{5}{12}\)

Explanation :

\(\frac{2}{3}\) – \(\frac{3}{12}\) = \(\frac{8}{12}\) – \(\frac{3}{12}\) = \(\frac{5}{12}\)

Question 34.

\(\frac{2}{3}\) – \(\frac{7}{12}\) =

Answer:

\(\frac{2}{3}\) – \(\frac{7}{12}\) = \(\frac{1}{12}\)

Explanation :

\(\frac{2}{3}\) – \(\frac{7}{12}\) = \(\frac{8}{12}\) – \(\frac{7}{12}\) = \(\frac{1}{12}\)

Question 35.

\(\frac{1}{4}\) – \(\frac{2}{12}\) =

Answer:

\(\frac{1}{4}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Explanation :

\(\frac{1}{4}\) – \(\frac{2}{12}\) = \(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 36.

\(\frac{1}{5}\) – \(\frac{1}{15}\) =

Answer:

\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Explanation :

\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{3}{15}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Question 37.

\(\frac{1}{3}\) – \(\frac{1}{15}\) =

Answer:

\(\frac{1}{3}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Explanation :

\(\frac{1}{3}\) – \(\frac{1}{15}\) = \(\frac{5}{15}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Question 38.

\(\frac{2}{3}\) – \(\frac{3}{15}\) =

Answer:

\(\frac{2}{3}\) – \(\frac{3}{15}\) = \(\frac{7}{15}\)

Explanation :

\(\frac{2}{3}\) – \(\frac{3}{15}\) = \(\frac{10}{15}\) – \(\frac{3}{15}\) = \(\frac{7}{15}\)

Question 39.

\(\frac{2}{5}\) – \(\frac{4}{15}\) =

Answer:

\(\frac{2}{5}\) – \(\frac{4}{15}\) = \(\frac{2}{15}\)

Explanation :

\(\frac{2}{5}\) – \(\frac{4}{15}\) = \(\frac{6}{15}\) – \(\frac{4}{15}\) = \(\frac{2}{15}\)

Question 40.

\(\frac{3}{4}\) – \(\frac{2}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 41.

\(\frac{3}{4}\) – \(\frac{5}{16}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)

Question 42.

\(\frac{4}{5}\) – \(\frac{5}{15}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{5}{15}\) = \(\frac{7}{15}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{5}{15}\) = \(\frac{12}{15}\) – \(\frac{5}{15}\) = \(\frac{7}{15}\)

Question 43.

\(\frac{3}{4}\) – \(\frac{4}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 44.

\(\frac{3}{4}\) – \(\frac{7}{16}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)

B

Subtract Fractions with Unlike Units

Question 1.

\(\frac{2}{10}\) – \(\frac{1}{10}\) =

Answer:

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

Question 2.

\(\frac{1}{5}\) – \(\frac{1}{10}\) =

Answer:

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

Explanation :

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

Question 3.

\(\frac{2}{4}\) – \(\frac{1}{4}\) =

Answer:

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

Question 4.

\(\frac{1}{2}\) – \(\frac{1}{4}\) =

Answer:

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

Explanation :

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

Question 5.

\(\frac{5}{10}\) – \(\frac{2}{10}\) =

Answer:

\(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 6.

\(\frac{1}{2}\) – \(\frac{2}{10}\) =

Answer:

\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Explanation :

\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 7.

\(\frac{1}{2}\) – \(\frac{4}{10}\) =

Answer:

\(\frac{1}{2}\) – \(\frac{4}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{1}{2}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\) – \(\frac{4}{10}\) = \(\frac{1}{10}\)

Question 8.

\(\frac{4}{10}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 9.

\(\frac{2}{5}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Explanation :

\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 10.

\(\frac{2}{5}\) – \(\frac{3}{10}\) =

Answer:

\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{4}{10}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Question 11.

\(\frac{6}{10}\) – \(\frac{3}{10}\) =

Answer:

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

Question 12.

\(\frac{3}{5}\) – \(\frac{3}{10}\) =

Answer:

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

Explanation :

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

Question 13.

\(\frac{3}{5}\) – \(\frac{5}{10}\) =

Answer:

\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Question 14.

\(\frac{8}{10}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{8}{10}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)

Question 15.

\(\frac{4}{5}\) – \(\frac{1}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{8}{10}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)

Question 16.

\(\frac{4}{5}\) – \(\frac{5}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)

Explanation :

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

Question 17.

\(\frac{4}{5}\) – \(\frac{5}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)

Explanation :

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

Question 18.

\(\frac{4}{5}\) – \(\frac{7}{10}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{1}{10}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{8}{10}\) – \(\frac{7}{10}\) = \(\frac{1}{10}\)

Question 19.

\(\frac{2}{8}\) – \(\frac{1}{8}\) =

Answer:

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

Question 20.

\(\frac{1}{4}\) – \(\frac{1}{8}\) =

Answer:

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

Explanation :

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

Question 21.

\(\frac{6}{8}\) – \(\frac{1}{8}\) =

Answer:

\(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 22.

\(\frac{3}{4}\) – \(\frac{1}{8}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 23.

\(\frac{3}{4}\) – \(\frac{3}{8}\) =

Answer:

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

Explanation :

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

Question 24.

\(\frac{5}{15}\) – \(\frac{1}{15}\) =

Answer:

\(\frac{5}{15}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Question 25.

\(\frac{1}{3}\) – \(\frac{1}{15}\) =

Answer:

\(\frac{1}{3}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Explanation :

\(\frac{1}{3}\) – \(\frac{1}{15}\) = \(\frac{5}{15}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Question 26.

\(\frac{3}{15}\) – \(\frac{1}{15}\) =

Answer:

\(\frac{3}{15}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Question 27.

\(\frac{1}{5}\) – \(\frac{1}{15}\) =

Answer:

\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Explanation :

\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{3}{15}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Question 28.

\(\frac{1}{5}\) – \(\frac{2}{15}\) =

Answer:

\(\frac{1}{5}\) – \(\frac{2}{15}\) = \(\frac{1}{15}\)

Explanation :

\(\frac{1}{5}\) – \(\frac{2}{15}\) = \(\frac{3}{15}\) – \(\frac{2}{15}\) = \(\frac{1}{15}\)

Question 29.

\(\frac{12}{15}\) – \(\frac{4}{15}\) =

Answer:

\(\frac{12}{15}\) – \(\frac{4}{15}\) = \(\frac{8}{15}\)

Question 30.

\(\frac{4}{5}\) – \(\frac{4}{15}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{2}{15}\) = \(\frac{2}{3}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{2}{15}\) = \(\frac{12}{15}\) – \(\frac{2}{15}\) = \(\frac{10}{15}\)= \(\frac{2}{3}\)

Question 31.

\(\frac{1}{4}\) – \(\frac{2}{12}\) =

Answer:

\(\frac{1}{4}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Explanation :

\(\frac{1}{4}\) – \(\frac{2}{12}\) = \(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 32.

\(\frac{3}{4}\) – \(\frac{2}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 33.

\(\frac{3}{4}\) – \(\frac{4}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 34.

\(\frac{3}{4}\) – \(\frac{8}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{8}{12}\) = \(\frac{1}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{8}{12}\) = \(\frac{9}{12}\) – \(\frac{8}{12}\) = \(\frac{1}{12}\)

Question 35.

\(\frac{1}{3}\) – \(\frac{3}{12}\) =

Answer:

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

Explanation :

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

Question 36.

\(\frac{1}{6}\) – \(\frac{1}{12}\) =

Answer:

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

Explanation :

\(\frac{1}{6}\) – \(\frac{1}{12}\) = \(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 37.

\(\frac{1}{3}\) – \(\frac{3}{15}\) =

Answer:

\(\frac{1}{3}\) – \(\frac{3}{15}\) = \(\frac{2}{15}\)

Explanation :

\(\frac{1}{3}\) – \(\frac{3}{15}\) = \(\frac{5}{15}\) – \(\frac{3}{15}\) = \(\frac{2}{15}\)

Question 38.

\(\frac{2}{3}\) – \(\frac{2}{15}\) =

Answer:

\(\frac{2}{3}\) – \(\frac{2}{15}\) = \(\frac{8}{15}\)

Explanation :

\(\frac{2}{3}\) – \(\frac{2}{15}\) = \(\frac{10}{15}\) – \(\frac{2}{15}\) = \(\frac{8}{15}\)

Question 39.

\(\frac{2}{5}\) – \(\frac{2}{15}\) =

Answer:

\(\frac{2}{5}\) – \(\frac{2}{15}\) = \(\frac{4}{15}\)

Explanation :

\(\frac{2}{5}\) – \(\frac{2}{15}\) = \(\frac{6}{15}\) – \(\frac{2}{15}\) = \(\frac{4}{15}\)

Question 40.

\(\frac{3}{4}\) – \(\frac{4}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 41.

\(\frac{3}{4}\) – \(\frac{7}{16}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)

Question 42.

\(\frac{4}{5}\) – \(\frac{4}{15}\) =

Answer:

\(\frac{4}{5}\) – \(\frac{4}{15}\) = \(\frac{8}{15}\)

Explanation :

\(\frac{4}{5}\) – \(\frac{4}{15}\) = \(\frac{12}{15}\) – \(\frac{4}{15}\) = \(\frac{8}{15}\)

Question 43.

\(\frac{3}{4}\) – \(\frac{2}{12}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 44.

\(\frac{3}{4}\) – \(\frac{5}{16}\) =

Answer:

\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)

Explanation :

\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)

### Eureka Math Grade 5 Module 3 Lesson 12 Problem Set Answer Key

Question 1.

Subtract.

a. 3\(\frac{1}{5}\) – 2\(\frac{1}{4}\) =

b. 4\(\frac{2}{5}\) – 3\(\frac{3}{4}\) =

c. 7\(\frac{1}{5}\) – 4\(\frac{1}{5}\) =

d. 7\(\frac{2}{5}\) – 5\(\frac{2}{3}\) =

e. 4\(\frac{2}{7}\) – 3\(\frac{1}{3}\) =

f. 9\(\frac{2}{3}\) – 2\(\frac{6}{7}\) =

g. 17\(\frac{2}{3}\) – 5\(\frac{5}{6}\) =

h. 18\(\frac{1}{3}\) – 3\(\frac{3}{8}\) =

Answer:

a. 3\(\frac{1}{5}\) – 2\(\frac{1}{4}\) = \(\frac{19}{20}\)

Explanation :

3\(\frac{1}{5}\) – 2\(\frac{1}{4}\) = \(\frac{16}{5}\) – \(\frac{9}{4}\)

lcm of 5 and 4 is 20 .

\(\frac{64}{20}\) – \(\frac{45}{20}\) = \(\frac{19}{20}\)

b. 4\(\frac{2}{5}\) – 3\(\frac{3}{4}\) = \(\frac{13}{20}\)

Explanation :

4\(\frac{2}{5}\) – 3\(\frac{3}{4}\) = \(\frac{22}{5}\) – \(\frac{15}{4}\)

lcm of 5 and 4 is 20 .

\(\frac{88}{20}\) – \(\frac{75}{20}\) = \(\frac{13}{20}\)

c. 7\(\frac{1}{5}\) – 4\(\frac{1}{5}\) =

Explanation :

7\(\frac{1}{5}\) – 4\(\frac{1}{5}\) = \(\frac{36}{5}\) – \(\frac{21}{5}\) = \(\frac{15}{5}\) = 3 .

d. 7\(\frac{2}{5}\) – 5\(\frac{2}{3}\) = 1\(\frac{11}{15}\) .

Explanation :

7\(\frac{2}{5}\) – 5\(\frac{2}{3}\) = \(\frac{37}{5}\) – \(\frac{17}{3}\)

lcm of 5 and 3 is 15 .

\(\frac{111}{15}\) – \(\frac{85}{15}\) = \(\frac{26}{15}\) = 1\(\frac{11}{15}\) .

e. 4\(\frac{2}{7}\) – 3\(\frac{1}{3}\) = \(\frac{20}{21}\)

Explanation :

4\(\frac{2}{7}\) – 3\(\frac{1}{3}\) = \(\frac{30}{7}\) – \(\frac{10}{3}\)

lcm of 7 and 3 is 21.

\(\frac{90}{21}\) – \(\frac{70}{21}\) = \(\frac{20}{21}\)

f. 9\(\frac{2}{3}\) – 2\(\frac{6}{7}\) = 6\(\frac{17}{21}\)

Explanation :

9\(\frac{2}{3}\) – 2\(\frac{6}{7}\) = \(\frac{29}{3}\) – \(\frac{20}{7}\)

lcm of 3 and 7 is 21.

\(\frac{203}{21}\) – \(\frac{60}{21}\) = \(\frac{143}{21}\) = 6\(\frac{17}{21}\)

g. 17\(\frac{2}{3}\) – 5\(\frac{5}{6}\) = 11\(\frac{5}{6}\)

Explanation :

17\(\frac{2}{3}\) – 5\(\frac{5}{6}\) = \(\frac{53}{3}\) – \(\frac{35}{6}\)

lcm of 3 and 6 is 6 .

\(\frac{106}{6}\) – \(\frac{35}{6}\) = \(\frac{71}{6}\) = 11\(\frac{5}{6}\)

h. 18\(\frac{1}{3}\) – 3\(\frac{3}{8}\) = 14\(\frac{23}{24}\)

Explanation :

18\(\frac{1}{3}\) – 3\(\frac{3}{8}\) = \(\frac{55}{3}\) – \(\frac{27}{8}\)

lcm of 3 and 8 is 24 .

\(\frac{440}{24}\) – \(\frac{81}{24}\) = \(\frac{359}{24}\) = 14\(\frac{23}{24}\)

Question 2.

Toby wrote the following:

7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{2}{4}\) = 4\(\frac{1}{2}\)

Is Toby’s calculation correct? Draw a number line to support your answer.

Answer:

Tody’s calculation is wrong .

7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 3\(\frac{1}{2}\) .

Explanation :

7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = \(\frac{29}{4}\) – \(\frac{15}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\) .

Question 3.

Mr. Neville Iceguy mixed up 12\(\frac{3}{5}\) gallons of chili for a party. If 7\(\frac{3}{4}\)gallons of chili was mild, and the rest was extra spicy, how much extra spicy chili did Mr. Iceguy make?

Answer:

Fraction of chili mixed up for a party = 12\(\frac{3}{5}\) gallons = \(\frac{63}{5}\) gallons

Fraction of chilli is mild = 7\(\frac{3}{4}\)gallons = \(\frac{31}{4}\)gallons

Fraction of chilli is extra spicy = x

\(\frac{63}{5}\) = \(\frac{31}{4}\) + x

x = \(\frac{63}{5}\) – \(\frac{31}{4}\)

lcm of 5 and 4 is 20 .

x = \(\frac{252}{20}\) – \(\frac{155}{20}\) = \(\frac{97}{20}\) = 4\(\frac{17}{20}\)

Therefore, Fraction of chilli is extra spicy = x = 4\(\frac{17}{20}\) gallons .

Question 4.

Jazmyne decided to spend 6\(\frac{1}{2}\) hours studying over the weekend. She spent 1\(\frac{1}{4}\) hours studying on Friday evening and 2\(\frac{2}{3}\) hours on Saturday. How much longer does she need to spend studying on Sunday in order to reach her goal?

Answer:

Total Fraction of time should spend on Studying = 6\(\frac{1}{2}\) hours = \(\frac{13}{2}\) hours

Fraction of Time spent on Friday for studying = 1\(\frac{1}{4}\) hours = \(\frac{5}{4}\) hours

Fraction of Time spent on Saturday for studying = 2\(\frac{2}{3}\) hours = \(\frac{8}{3}\) hours

Fraction of Time should spend on Sunday for studying = x

\(\frac{13}{2}\) = \(\frac{5}{4}\) + \(\frac{8}{3}\) + x

lcm of 2 , 4 , and 3 is 12 .

x = \(\frac{13}{2}\) – \(\frac{5}{4}\) – \(\frac{8}{3}\)

x = \(\frac{78}{12}\) – \(\frac{15}{12}\) – \(\frac{32}{12}\)

x = \(\frac{78}{12}\) – \(\frac{47}{12}\)

x = \(\frac{31}{12}\)

x = 2\(\frac{7}{12}\)

Therefore, Fraction of Time should spend on Sunday for studying = x = 2\(\frac{7}{12}\) hours .

### Eureka Math Grade 5 Module 3 Lesson 12 Exit Ticket Answer Key

Subtract.

Question 1.

5\(\frac{1}{2}\) – 1\(\frac{1}{3}\) =

Answer:

5\(\frac{1}{2}\) – 1\(\frac{1}{3}\) = 4\(\frac{1}{6}\) .

Explanation :

5\(\frac{1}{2}\) – 1\(\frac{1}{3}\) = \(\frac{11}{2}\) – \(\frac{4}{3}\)

lcm of 2 and 3 is 6

\(\frac{33}{6}\) – \(\frac{8}{6}\) = \(\frac{25}{6}\) = 4\(\frac{1}{6}\) .

Question 2.

8\(\frac{3}{4}\) – 5\(\frac{5}{6}\) =

Answer:

8\(\frac{3}{4}\) – 5\(\frac{5}{6}\) = 2\(\frac{11}{12}\)

Explanation :

8\(\frac{3}{4}\) – 5\(\frac{5}{6}\) = \(\frac{35}{4}\) – \(\frac{35}{6}\)

lcm of 4 and 6 is 12 .

\(\frac{105}{12}\) – \(\frac{70}{12}\) = \(\frac{35}{12}\) = 2\(\frac{11}{12}\)

### Eureka Math Grade 5 Module 3 Lesson 12 Homework Answer Key

Question 1.

Subtract.

a. 3\(\frac{1}{4}\) – 2\(\frac{1}{3}\) =

b. 3\(\frac{2}{3}\) – 2\(\frac{3}{4}\) =

c. 6\(\frac{1}{5}\) – 4\(\frac{1}{4}\) =

d. 6\(\frac{3}{5}\) – 4\(\frac{3}{4}\) =

e. 5\(\frac{2}{7}\) – 4\(\frac{1}{3}\) =

f. 8\(\frac{2}{3}\) – 3\(\frac{5}{7}\) =

g. 18\(\frac{3}{4}\) – 5\(\frac{7}{8}\) =

h. 17\(\frac{1}{5}\) – 2\(\frac{5}{8}\) =

Answer:

a. 3\(\frac{1}{4}\) – 2\(\frac{1}{3}\) = \(\frac{11}{12}\)

Explanation :

3\(\frac{1}{4}\) – 2\(\frac{1}{3}\) = \(\frac{13}{4}\) – \(\frac{7}{3}\)

lcm of 4 and 3 is 12

\(\frac{39}{12}\) – \(\frac{28}{12}\) = \(\frac{11}{12}\)

b. 3\(\frac{2}{3}\) – 2\(\frac{3}{4}\) = \(\frac{11}{12}\)

Explanation :

3\(\frac{2}{3}\) – 2\(\frac{3}{4}\) = \(\frac{11}{3}\) – \(\frac{11}{4}\)

lcm of 3 and 4 is 12

\(\frac{44}{12}\) – \(\frac{33}{12}\) = \(\frac{11}{12}\)

c. 6\(\frac{1}{5}\) – 4\(\frac{1}{4}\) = 3\(\frac{13}{20}\)

Explanation :

6\(\frac{1}{5}\) – 4\(\frac{1}{4}\) = \(\frac{31}{5}\) – \(\frac{17}{4}\)

lcm of 4 and 5 is 20 .

\(\frac{124}{20}\) – \(\frac{51}{20}\) = \(\frac{73}{20}\) = 3\(\frac{13}{20}\) .

d. 6\(\frac{3}{5}\) – 4\(\frac{3}{4}\) = 1\(\frac{17}{20}\)

Explanation :

6\(\frac{3}{5}\) – 4\(\frac{3}{4}\) = \(\frac{33}{5}\) – \(\frac{19}{4}\)

lcm of 4 and 5 is 20 .

\(\frac{132}{20}\) – \(\frac{95}{20}\) = \(\frac{37}{20}\) = 1\(\frac{17}{20}\)

e. 5\(\frac{2}{7}\) – 4\(\frac{1}{3}\) = \(\frac{20}{21}\)

Explanation :

5\(\frac{2}{7}\) – 4\(\frac{1}{3}\) = \(\frac{37}{7}\) – \(\frac{13}{3}\)

lcm of 3 and 7 is 21.

\(\frac{111}{21}\) – \(\frac{91}{21}\) = \(\frac{20}{21}\)

f. 8\(\frac{2}{3}\) – 3\(\frac{5}{7}\) = 4\(\frac{20}{21}\)

Explanation :

8\(\frac{2}{3}\) – 3\(\frac{5}{7}\) = \(\frac{26}{3}\) – \(\frac{26}{7}\)

lcm of 3 and 7 is 21.

\(\frac{182}{21}\) – \(\frac{78}{21}\) = \(\frac{104}{21}\) = 4\(\frac{20}{21}\)

g. 18\(\frac{3}{4}\) – 5\(\frac{7}{8}\) = 11\(\frac{9}{8}\)

Explanation :

18\(\frac{3}{4}\) – 5\(\frac{7}{8}\) = \(\frac{75}{4}\) – \(\frac{47}{8}\)

lcm of 4 and 8 is 8 .

\(\frac{130}{8}\) – \(\frac{47}{8}\) = \(\frac{97}{8}\) = 11\(\frac{9}{8}\)

h. 17\(\frac{1}{5}\) – 2\(\frac{5}{8}\) = 14\(\frac{23}{40}\)

Explanation :

17\(\frac{1}{5}\) – 2\(\frac{5}{8}\) = \(\frac{86}{5}\) – \(\frac{21}{8}\)

lcm of 5 and 8 is 40 .

\(\frac{688}{40}\) – \(\frac{105}{40}\) = \(\frac{583}{40}\) = 14\(\frac{23}{40}\)

Question 2.

Tony wrote the following:

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

Is Tony’s statement correct? Draw a number line to support your answer.

Answer:

Yes Tony’s statement is correct .

7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{1}{4}\) – \(\frac{3}{4}\) = 3\(\frac{1}{2}\) .

Explanation :

7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = \(\frac{29}{4}\) – \(\frac{15}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\) .

4\(\frac{1}{4}\) – \(\frac{3}{4}\) = \(\frac{17}{4}\) – \(\frac{3}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\) .

Therefore , 7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{1}{4}\) – \(\frac{3}{4}\) = 3\(\frac{1}{2}\) .

Question 3.

Ms. Sanger blended 8\(\frac{3}{4}\) gallons of iced tea with some lemonade for a picnic. If there were 13\(\frac{2}{5}\) gallons of the beverage, how many gallons of lemonade did she use?

Answer:

Fraction of gallons of iced tea with some lemonade for a picnic = 8\(\frac{3}{4}\) = \(\frac{35}{4}\) gallons .

Fraction of gallons of the beverage = 13\(\frac{2}{5}\) = \(\frac{67}{5}\) .

Fraction of gallons of the lemonade = x

\(\frac{67}{5}\) = \(\frac{35}{4}\) – x

x = \(\frac{67}{5}\) – \(\frac{35}{4}\)

lcm of 4 and 5 is 20 .

x = \(\frac{268}{20}\) – \(\frac{175}{20}\)

x = \(\frac{93}{20}\) = 4\(\frac{13}{20}\)

Therefore, Fraction of gallons of the lemonade = x = 4\(\frac{13}{20}\) gallons .

Question 4.

A carpenter has 10\(\frac{1}{2}\) feet of wooden plank. He cuts off 4\(\frac{1}{4}\) feet to replace the slat of a deck and 3\(\frac{2}{3}\) feet to repair a bannister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?

Answer:

Total Fraction of wooden plank = 10\(\frac{1}{2}\) feet = \(\frac{21}{2}\) feet

Fraction of wooden plank cut off = 4\(\frac{1}{4}\) feet = \(\frac{17}{4}\) feet

Fraction of wooden plank used to repair a bannister = 3\(\frac{2}{3}\) feet = \(\frac{11}{3}\) feet

Fraction of wooden plank used for stair = x feet

10\(\frac{1}{2}\) = \(\frac{17}{4}\) + \(\frac{11}{3}\) + x

\(\frac{21}{2}\) = \(\frac{17}{4}\) + \(\frac{11}{3}\) + x

lcm of 2 , 4 and 3 is 12 .

\(\frac{126}{12}\) = \(\frac{51}{4}\) + \(\frac{44}{3}\) + x

x = \(\frac{126}{12}\) – \(\frac{95}{4}\)

x = \(\frac{31}{4}\) = 7\(\frac{3}{4}\) .

Therefore, Fraction of wooden plank used for stair = 7\(\frac{3}{4}\) feet .