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

A
Subtract Fractions with Unlike Units

Question 1.
$$\frac{2}{4}$$ – $$\frac{1}{4}$$ =
$$\frac{2}{4}$$ – $$\frac{1}{4}$$ = $$\frac{1}{4}$$

Question 2.
$$\frac{1}{2}$$ – $$\frac{1}{4}$$ =
$$\frac{1}{2}$$ – $$\frac{1}{4}$$ = $$\frac{1}{4}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{1}{4}$$ = $$\frac{2}{4}$$ – $$\frac{1}{4}$$ = $$\frac{1}{4}$$

Question 3.
$$\frac{2}{6}$$ – $$\frac{1}{6}$$ =
$$\frac{2}{6}$$ – $$\frac{1}{6}$$ = $$\frac{1}{6}$$

Question 4.
$$\frac{1}{3}$$ – $$\frac{1}{6}$$ =
$$\frac{1}{3}$$ – $$\frac{1}{6}$$ = $$\frac{1}{6}$$
Explanation :
$$\frac{1}{3}$$ – $$\frac{1}{6}$$ =$$\frac{2}{6}$$ – $$\frac{1}{6}$$ = $$\frac{1}{6}$$

Question 5.
$$\frac{2}{8}$$ – $$\frac{1}{8}$$ =
$$\frac{2}{8}$$ – $$\frac{1}{8}$$ = $$\frac{1}{8}$$

Question 6.
$$\frac{1}{4}$$ – $$\frac{1}{8}$$ =
$$\frac{1}{4}$$ – $$\frac{1}{8}$$ =$$\frac{1}{8}$$
Explanation :
$$\frac{1}{4}$$ – $$\frac{1}{8}$$ = $$\frac{2}{8}$$ – $$\frac{1}{8}$$ = $$\frac{1}{8}$$

Question 7.
$$\frac{6}{8}$$ – $$\frac{1}{8}$$ =
$$\frac{6}{8}$$ – $$\frac{1}{8}$$ = $$\frac{5}{8}$$

Question 8.
$$\frac{3}{4}$$ – $$\frac{1}{8}$$ =
$$\frac{3}{4}$$ – $$\frac{1}{8}$$ = $$\frac{5}{8}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{1}{8}$$ = $$\frac{6}{8}$$ – $$\frac{1}{8}$$ = $$\frac{5}{8}$$

Question 9.
$$\frac{3}{4}$$ – $$\frac{3}{8}$$ =
$$\frac{3}{4}$$ – $$\frac{3}{8}$$ = $$\frac{3}{8}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{3}{8}$$ = $$\frac{6}{8}$$ – $$\frac{3}{8}$$ = $$\frac{3}{8}$$

Question 10.
$$\frac{5}{10}$$ – $$\frac{2}{10}$$ =
$$\frac{5}{10}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$

Question 11.
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ =
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ = $$\frac{5}{10}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$

Question 12.
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ =
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ = $$\frac{5}{10}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$

Question 13.
$$\frac{4}{10}$$ – $$\frac{1}{10}$$ =
$$\frac{4}{10}$$ – $$\frac{1}{10}$$ = $$\frac{3}{10}$$

Question 14.
$$\frac{2}{5}$$ – $$\frac{1}{10}$$ =
$$\frac{2}{5}$$ – $$\frac{1}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{2}{5}$$ – $$\frac{1}{10}$$ = $$\frac{4}{10}$$ – $$\frac{1}{10}$$ = $$\frac{3}{10}$$

Question 15.
$$\frac{2}{5}$$ – $$\frac{3}{10}$$ =
$$\frac{2}{5}$$ – $$\frac{3}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{2}{5}$$ – $$\frac{3}{10}$$ = $$\frac{4}{10}$$ – $$\frac{3}{10}$$ = $$\frac{1}{10}$$

Question 16.
$$\frac{6}{10}$$ – $$\frac{3}{10}$$ =
$$\frac{6}{10}$$ – $$\frac{3}{10}$$ =$$\frac{3}{10}$$

Question 17.
$$\frac{3}{5}$$ – $$\frac{3}{10}$$ =
$$\frac{3}{5}$$ – $$\frac{3}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{3}{5}$$ – $$\frac{3}{10}$$ = $$\frac{6}{10}$$ – $$\frac{3}{10}$$ = $$\frac{3}{10}$$

Question 18.
$$\frac{3}{5}$$ – $$\frac{5}{10}$$ =
$$\frac{3}{5}$$ – $$\frac{5}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{3}{5}$$ – $$\frac{5}{10}$$ = $$\frac{6}{10}$$ – $$\frac{5}{10}$$ = $$\frac{1}{10}$$

Question 19.
$$\frac{8}{10}$$ – $$\frac{1}{10}$$ =
$$\frac{8}{10}$$ – $$\frac{1}{10}$$ =  $$\frac{7}{10}$$

Question 20.
$$\frac{4}{5}$$ – $$\frac{1}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{1}{10}$$ = $$\frac{7}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{1}{10}$$ = $$\frac{8}{10}$$ – $$\frac{1}{10}$$ =  $$\frac{7}{10}$$

Question 21.
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{8}{10}$$ – $$\frac{5}{10}$$ =  $$\frac{4}{10}$$

Question 22.
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{8}{10}$$ – $$\frac{5}{10}$$ =  $$\frac{4}{10}$$

Question 23.
$$\frac{4}{5}$$ – $$\frac{7}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{7}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{7}{10}$$ = $$\frac{8}{10}$$ – $$\frac{7}{10}$$ =  $$\frac{1}{10}$$

Question 24.
$$\frac{2}{12}$$ – $$\frac{1}{12}$$ =
$$\frac{2}{12}$$ – $$\frac{1}{12}$$ = $$\frac{1}{12}$$

Question 25.
$$\frac{1}{6}$$ – $$\frac{1}{12}$$ =
$$\frac{1}{6}$$ – $$\frac{1}{12}$$ =$$\frac{1}{12}$$
Explanation :
$$\frac{1}{6}$$ – $$\frac{1}{12}$$ = $$\frac{2}{12}$$ – $$\frac{1}{12}$$ = $$\frac{1}{12}$$

Question 26.
$$\frac{6}{12}$$ – $$\frac{1}{12}$$ =
$$\frac{6}{12}$$ – $$\frac{1}{12}$$ = $$\frac{5}{12}$$

Question 27.
$$\frac{1}{2}$$ – $$\frac{1}{12}$$ =
$$\frac{1}{2}$$ – $$\frac{1}{12}$$ =  $$\frac{5}{12}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{1}{12}$$ = $$\frac{6}{12}$$ – $$\frac{1}{12}$$ = $$\frac{5}{12}$$

Question 28.
$$\frac{1}{2}$$ – $$\frac{5}{12}$$ =
$$\frac{1}{2}$$ – $$\frac{5}{12}$$ =  $$\frac{1}{12}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{5}{12}$$ = $$\frac{6}{12}$$ – $$\frac{5}{12}$$ = $$\frac{1}{12}$$

Question 29.
$$\frac{10}{12}$$ – $$\frac{5}{12}$$ =
$$\frac{10}{12}$$ – $$\frac{5}{12}$$ = $$\frac{5}{12}$$

Question 30.
$$\frac{5}{6}$$ – $$\frac{5}{12}$$ =
$$\frac{5}{6}$$ – $$\frac{5}{12}$$ = $$\frac{5}{12}$$
Explanation :
$$\frac{5}{6}$$ – $$\frac{5}{12}$$ = $$\frac{10}{12}$$ – $$\frac{5}{12}$$ = $$\frac{5}{12}$$

Question 31.
$$\frac{1}{3}$$ – $$\frac{3}{12}$$ =
$$\frac{1}{3}$$ – $$\frac{3}{12}$$ = $$\frac{1}{12}$$
Explanation :
$$\frac{1}{3}$$ – $$\frac{3}{12}$$ = $$\frac{4}{12}$$ – $$\frac{3}{12}$$ = $$\frac{1}{12}$$

Question 32.
$$\frac{2}{3}$$ – $$\frac{1}{12}$$ =
$$\frac{2}{3}$$ – $$\frac{1}{12}$$ = $$\frac{7}{12}$$
Explanation :
$$\frac{2}{3}$$ – $$\frac{1}{12}$$ = $$\frac{8}{12}$$ – $$\frac{1}{12}$$ = $$\frac{7}{12}$$

Question 33.
$$\frac{2}{3}$$ – $$\frac{3}{12}$$ =
$$\frac{2}{3}$$ – $$\frac{3}{12}$$ = $$\frac{5}{12}$$
Explanation :
$$\frac{2}{3}$$ – $$\frac{3}{12}$$ = $$\frac{8}{12}$$ – $$\frac{3}{12}$$ = $$\frac{5}{12}$$

Question 34.
$$\frac{2}{3}$$ – $$\frac{7}{12}$$ =
$$\frac{2}{3}$$ – $$\frac{7}{12}$$ = $$\frac{1}{12}$$
Explanation :
$$\frac{2}{3}$$ – $$\frac{7}{12}$$ = $$\frac{8}{12}$$ – $$\frac{7}{12}$$ = $$\frac{1}{12}$$

Question 35.
$$\frac{1}{4}$$ – $$\frac{2}{12}$$ =
$$\frac{1}{4}$$ – $$\frac{2}{12}$$ =  $$\frac{1}{12}$$
Explanation :
$$\frac{1}{4}$$ – $$\frac{2}{12}$$ = $$\frac{3}{12}$$ – $$\frac{2}{12}$$ = $$\frac{1}{12}$$

Question 36.
$$\frac{1}{5}$$ – $$\frac{1}{15}$$ =
$$\frac{1}{5}$$ – $$\frac{1}{15}$$ = $$\frac{2}{15}$$
Explanation :
$$\frac{1}{5}$$ – $$\frac{1}{15}$$ = $$\frac{3}{15}$$ – $$\frac{1}{15}$$ = $$\frac{2}{15}$$

Question 37.
$$\frac{1}{3}$$ – $$\frac{1}{15}$$ =
$$\frac{1}{3}$$ – $$\frac{1}{15}$$ =  $$\frac{4}{15}$$
Explanation :
$$\frac{1}{3}$$ – $$\frac{1}{15}$$ = $$\frac{5}{15}$$ – $$\frac{1}{15}$$ = $$\frac{4}{15}$$

Question 38.
$$\frac{2}{3}$$ – $$\frac{3}{15}$$ =
$$\frac{2}{3}$$ – $$\frac{3}{15}$$ =  $$\frac{7}{15}$$
Explanation :
$$\frac{2}{3}$$ – $$\frac{3}{15}$$ = $$\frac{10}{15}$$ – $$\frac{3}{15}$$ = $$\frac{7}{15}$$

Question 39.
$$\frac{2}{5}$$ – $$\frac{4}{15}$$ =
$$\frac{2}{5}$$ – $$\frac{4}{15}$$ = $$\frac{2}{15}$$
Explanation :
$$\frac{2}{5}$$ – $$\frac{4}{15}$$ = $$\frac{6}{15}$$ – $$\frac{4}{15}$$ = $$\frac{2}{15}$$

Question 40.
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ =  $$\frac{7}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ = $$\frac{9}{12}$$ – $$\frac{2}{12}$$ = $$\frac{7}{12}$$

Question 41.
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ =
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ = $$\frac{7}{16}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ = $$\frac{12}{16}$$ – $$\frac{5}{16}$$ = $$\frac{7}{16}$$

Question 42.
$$\frac{4}{5}$$ – $$\frac{5}{15}$$ =
$$\frac{4}{5}$$ – $$\frac{5}{15}$$ = $$\frac{7}{15}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{5}{15}$$ = $$\frac{12}{15}$$ – $$\frac{5}{15}$$ = $$\frac{7}{15}$$

Question 43.
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ =  $$\frac{5}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ = $$\frac{9}{12}$$ – $$\frac{4}{12}$$ = $$\frac{5}{12}$$

Question 44.
$$\frac{3}{4}$$ – $$\frac{7}{16}$$ =
$$\frac{3}{4}$$ – $$\frac{7}{16}$$ = $$\frac{5}{16}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ = $$\frac{12}{16}$$ – $$\frac{7}{16}$$ = $$\frac{5}{16}$$

B
Subtract Fractions with Unlike Units

Question 1.
$$\frac{2}{10}$$ – $$\frac{1}{10}$$ =
$$\frac{2}{10}$$ – $$\frac{1}{10}$$ = $$\frac{1}{10}$$

Question 2.
$$\frac{1}{5}$$ – $$\frac{1}{10}$$ =
$$\frac{1}{5}$$ – $$\frac{1}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{1}{5}$$ – $$\frac{1}{10}$$ = $$\frac{2}{10}$$ – $$\frac{1}{10}$$ = $$\frac{1}{10}$$

Question 3.
$$\frac{2}{4}$$ – $$\frac{1}{4}$$ =
$$\frac{2}{4}$$ – $$\frac{1}{4}$$ = $$\frac{1}{4}$$

Question 4.
$$\frac{1}{2}$$ – $$\frac{1}{4}$$ =
$$\frac{1}{2}$$ – $$\frac{1}{4}$$ = $$\frac{1}{4}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{1}{4}$$ = $$\frac{2}{4}$$ – $$\frac{1}{4}$$ = $$\frac{1}{4}$$

Question 5.
$$\frac{5}{10}$$ – $$\frac{2}{10}$$ =
$$\frac{5}{10}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$

Question 6.
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ =
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{2}{10}$$ = $$\frac{5}{10}$$ – $$\frac{2}{10}$$ = $$\frac{3}{10}$$

Question 7.
$$\frac{1}{2}$$ – $$\frac{4}{10}$$ =
$$\frac{1}{2}$$ – $$\frac{4}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{1}{2}$$ – $$\frac{4}{10}$$ = $$\frac{5}{10}$$ – $$\frac{4}{10}$$ = $$\frac{1}{10}$$

Question 8.
$$\frac{4}{10}$$ – $$\frac{1}{10}$$ =
$$\frac{4}{10}$$ – $$\frac{1}{10}$$ = $$\frac{3}{10}$$

Question 9.
$$\frac{2}{5}$$ – $$\frac{1}{10}$$ =
$$\frac{2}{5}$$ – $$\frac{1}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{2}{5}$$ – $$\frac{1}{10}$$ = $$\frac{4}{10}$$ – $$\frac{1}{10}$$ = $$\frac{3}{10}$$

Question 10.
$$\frac{2}{5}$$ – $$\frac{3}{10}$$ =
$$\frac{2}{5}$$ – $$\frac{3}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{2}{5}$$ – $$\frac{3}{10}$$ = $$\frac{4}{10}$$ – $$\frac{3}{10}$$ = $$\frac{1}{10}$$

Question 11.
$$\frac{6}{10}$$ – $$\frac{3}{10}$$ =
$$\frac{6}{10}$$ – $$\frac{3}{10}$$ =$$\frac{3}{10}$$

Question 12.
$$\frac{3}{5}$$ – $$\frac{3}{10}$$ =
$$\frac{3}{5}$$ – $$\frac{3}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{3}{5}$$ – $$\frac{3}{10}$$ = $$\frac{6}{10}$$ – $$\frac{3}{10}$$ = $$\frac{3}{10}$$

Question 13.
$$\frac{3}{5}$$ – $$\frac{5}{10}$$ =
$$\frac{3}{5}$$ – $$\frac{5}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{3}{5}$$ – $$\frac{5}{10}$$ = $$\frac{6}{10}$$ – $$\frac{5}{10}$$ = $$\frac{1}{10}$$

Question 14.
$$\frac{8}{10}$$ – $$\frac{1}{10}$$ =
$$\frac{8}{10}$$ – $$\frac{1}{10}$$ =  $$\frac{7}{10}$$

Question 15.
$$\frac{4}{5}$$ – $$\frac{1}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{1}{10}$$ = $$\frac{7}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{1}{10}$$ = $$\frac{8}{10}$$ – $$\frac{1}{10}$$ =  $$\frac{7}{10}$$

Question 16.
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{8}{10}$$ – $$\frac{5}{10}$$ =  $$\frac{4}{10}$$

Question 17.
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{3}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{5}{10}$$ = $$\frac{8}{10}$$ – $$\frac{5}{10}$$ =  $$\frac{4}{10}$$

Question 18.
$$\frac{4}{5}$$ – $$\frac{7}{10}$$ =
$$\frac{4}{5}$$ – $$\frac{7}{10}$$ = $$\frac{1}{10}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{7}{10}$$ = $$\frac{8}{10}$$ – $$\frac{7}{10}$$ =  $$\frac{1}{10}$$

Question 19.
$$\frac{2}{8}$$ – $$\frac{1}{8}$$ =
$$\frac{2}{8}$$ – $$\frac{1}{8}$$ = $$\frac{1}{8}$$

Question 20.
$$\frac{1}{4}$$ – $$\frac{1}{8}$$ =
$$\frac{1}{4}$$ – $$\frac{1}{8}$$ =$$\frac{1}{8}$$
Explanation :
$$\frac{1}{4}$$ – $$\frac{1}{8}$$ = $$\frac{2}{8}$$ – $$\frac{1}{8}$$ = $$\frac{1}{8}$$

Question 21.
$$\frac{6}{8}$$ – $$\frac{1}{8}$$ =
$$\frac{6}{8}$$ – $$\frac{1}{8}$$ = $$\frac{5}{8}$$

Question 22.
$$\frac{3}{4}$$ – $$\frac{1}{8}$$ =
$$\frac{3}{4}$$ – $$\frac{1}{8}$$ = $$\frac{5}{8}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{1}{8}$$ = $$\frac{6}{8}$$ – $$\frac{1}{8}$$ = $$\frac{5}{8}$$

Question 23.
$$\frac{3}{4}$$ – $$\frac{3}{8}$$ =
$$\frac{3}{4}$$ – $$\frac{3}{8}$$ = $$\frac{3}{8}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{3}{8}$$ = $$\frac{6}{8}$$ – $$\frac{3}{8}$$ = $$\frac{3}{8}$$

Question 24.
$$\frac{5}{15}$$ – $$\frac{1}{15}$$ =
$$\frac{5}{15}$$ – $$\frac{1}{15}$$ = $$\frac{4}{15}$$

Question 25.
$$\frac{1}{3}$$ – $$\frac{1}{15}$$ =
$$\frac{1}{3}$$ – $$\frac{1}{15}$$ =  $$\frac{4}{15}$$
Explanation :
$$\frac{1}{3}$$ – $$\frac{1}{15}$$ = $$\frac{5}{15}$$ – $$\frac{1}{15}$$ = $$\frac{4}{15}$$

Question 26.
$$\frac{3}{15}$$ – $$\frac{1}{15}$$ =
$$\frac{3}{15}$$ – $$\frac{1}{15}$$ = $$\frac{2}{15}$$

Question 27.
$$\frac{1}{5}$$ – $$\frac{1}{15}$$ =
$$\frac{1}{5}$$ – $$\frac{1}{15}$$ = $$\frac{2}{15}$$
Explanation :
$$\frac{1}{5}$$ – $$\frac{1}{15}$$ = $$\frac{3}{15}$$ – $$\frac{1}{15}$$ = $$\frac{2}{15}$$

Question 28.
$$\frac{1}{5}$$ – $$\frac{2}{15}$$ =
$$\frac{1}{5}$$ – $$\frac{2}{15}$$ = $$\frac{1}{15}$$
Explanation :
$$\frac{1}{5}$$ – $$\frac{2}{15}$$ = $$\frac{3}{15}$$ – $$\frac{2}{15}$$ = $$\frac{1}{15}$$

Question 29.
$$\frac{12}{15}$$ – $$\frac{4}{15}$$ =
$$\frac{12}{15}$$ – $$\frac{4}{15}$$ = $$\frac{8}{15}$$

Question 30.
$$\frac{4}{5}$$ – $$\frac{4}{15}$$ =
$$\frac{4}{5}$$ – $$\frac{2}{15}$$ = $$\frac{2}{3}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{2}{15}$$ = $$\frac{12}{15}$$ – $$\frac{2}{15}$$ = $$\frac{10}{15}$$= $$\frac{2}{3}$$

Question 31.
$$\frac{1}{4}$$ – $$\frac{2}{12}$$ =
$$\frac{1}{4}$$ – $$\frac{2}{12}$$ =  $$\frac{1}{12}$$
Explanation :
$$\frac{1}{4}$$ – $$\frac{2}{12}$$ = $$\frac{3}{12}$$ – $$\frac{2}{12}$$ = $$\frac{1}{12}$$

Question 32.
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ =  $$\frac{7}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ = $$\frac{9}{12}$$ – $$\frac{2}{12}$$ = $$\frac{7}{12}$$

Question 33.
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ =  $$\frac{5}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ = $$\frac{9}{12}$$ – $$\frac{4}{12}$$ = $$\frac{5}{12}$$

Question 34.
$$\frac{3}{4}$$ – $$\frac{8}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{8}{12}$$ =  $$\frac{1}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{8}{12}$$ = $$\frac{9}{12}$$ – $$\frac{8}{12}$$ = $$\frac{1}{12}$$

Question 35.
$$\frac{1}{3}$$ – $$\frac{3}{12}$$ =
$$\frac{1}{3}$$ – $$\frac{3}{12}$$ = $$\frac{1}{12}$$
Explanation :
$$\frac{1}{3}$$ – $$\frac{3}{12}$$ = $$\frac{4}{12}$$ – $$\frac{3}{12}$$ = $$\frac{1}{12}$$

Question 36.
$$\frac{1}{6}$$ – $$\frac{1}{12}$$ =
$$\frac{1}{6}$$ – $$\frac{1}{12}$$ =$$\frac{1}{12}$$
Explanation :
$$\frac{1}{6}$$ – $$\frac{1}{12}$$ = $$\frac{2}{12}$$ – $$\frac{1}{12}$$ = $$\frac{1}{12}$$

Question 37.
$$\frac{1}{3}$$ – $$\frac{3}{15}$$ =
$$\frac{1}{3}$$ – $$\frac{3}{15}$$ =  $$\frac{2}{15}$$
Explanation :
$$\frac{1}{3}$$ – $$\frac{3}{15}$$ = $$\frac{5}{15}$$ – $$\frac{3}{15}$$ = $$\frac{2}{15}$$

Question 38.
$$\frac{2}{3}$$ – $$\frac{2}{15}$$ =
$$\frac{2}{3}$$ – $$\frac{2}{15}$$ =  $$\frac{8}{15}$$
Explanation :
$$\frac{2}{3}$$ – $$\frac{2}{15}$$ = $$\frac{10}{15}$$ – $$\frac{2}{15}$$ = $$\frac{8}{15}$$

Question 39.
$$\frac{2}{5}$$ – $$\frac{2}{15}$$ =
$$\frac{2}{5}$$ – $$\frac{2}{15}$$ = $$\frac{4}{15}$$
Explanation :
$$\frac{2}{5}$$ – $$\frac{2}{15}$$ = $$\frac{6}{15}$$ – $$\frac{2}{15}$$ = $$\frac{4}{15}$$

Question 40.
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ =  $$\frac{5}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{4}{12}$$ = $$\frac{9}{12}$$ – $$\frac{4}{12}$$ = $$\frac{5}{12}$$

Question 41.
$$\frac{3}{4}$$ – $$\frac{7}{16}$$ =
$$\frac{3}{4}$$ – $$\frac{7}{16}$$ = $$\frac{5}{16}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ = $$\frac{12}{16}$$ – $$\frac{7}{16}$$ = $$\frac{5}{16}$$

Question 42.
$$\frac{4}{5}$$ – $$\frac{4}{15}$$ =
$$\frac{4}{5}$$ – $$\frac{4}{15}$$ = $$\frac{8}{15}$$
Explanation :
$$\frac{4}{5}$$ – $$\frac{4}{15}$$ = $$\frac{12}{15}$$ – $$\frac{4}{15}$$ = $$\frac{8}{15}$$

Question 43.
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ =
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ =  $$\frac{7}{12}$$
Explanation :
$$\frac{3}{4}$$ – $$\frac{2}{12}$$ = $$\frac{9}{12}$$ – $$\frac{2}{12}$$ = $$\frac{7}{12}$$

Question 44.
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ =
$$\frac{3}{4}$$ – $$\frac{5}{16}$$ = $$\frac{7}{16}$$
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$$\frac{3}{8}$$ =
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.
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?
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?
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$$\frac{1}{3}$$ =
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$$\frac{5}{6}$$ =
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$$\frac{11}{12}$$

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$$\frac{5}{8}$$ =
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.
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?
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?
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 .

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