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 .
