## Engage NY Eureka Math 5th Grade Module 3 Lesson 9 Answer Key

### Eureka Math Grade 5 Module 3 Lesson 9 Sprint Answer Key

A
Add and Subtract Fractions with Like Units

Question 1.
$$\frac{1}{5}$$ + $$\frac{1}{5}$$ =
$$\frac{1}{5}$$ + $$\frac{1}{5}$$ = $$\frac{2}{5}$$

Question 2.
$$\frac{1}{10}$$ + $$\frac{5}{10}$$ =
$$\frac{1}{10}$$ + $$\frac{5}{10}$$ = $$\frac{6}{10}$$ = $$\frac{3}{5}$$

Question 3.
$$\frac{1}{10}$$ + $$\frac{7}{10}$$ =
$$\frac{1}{10}$$ + $$\frac{7}{10}$$ = $$\frac{8}{10}$$ = $$\frac{4}{5}$$

Question 4.
$$\frac{2}{5}$$ + $$\frac{2}{5}$$ =
$$\frac{2}{5}$$ + $$\frac{2}{5}$$ = $$\frac{4}{5}$$

Question 5.
$$\frac{5}{10}$$ – $$\frac{4}{10}$$ =
$$\frac{5}{10}$$ – $$\frac{4}{10}$$ = $$\frac{1}{10}$$

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

Question 7.
$$\frac{3}{10}$$ + $$\frac{3}{10}$$ =
$$\frac{3}{10}$$ + $$\frac{3}{10}$$ = $$\frac{6}{10}$$ = $$\frac{3}{5}$$

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

Question 9.
$$\frac{1}{4}$$ + $$\frac{1}{4}$$ =
$$\frac{1}{4}$$ + $$\frac{1}{4}$$ = $$\frac{2}{4}$$ = $$\frac{1}{2}$$

Question 10.
$$\frac{1}{4}$$ + $$\frac{2}{4}$$ =
$$\frac{1}{4}$$ + $$\frac{2}{4}$$ = $$\frac{3}{4}$$

Question 11.
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ =
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ = $$\frac{1}{12}$$

Question 12.
$$\frac{1}{4}$$ + $$\frac{3}{4}$$ =
$$\frac{1}{4}$$ + $$\frac{3}{4}$$ = $$\frac{4}{4}$$ = 1

Question 13.
$$\frac{1}{12}$$ + $$\frac{1}{12}$$ =
$$\frac{1}{12}$$ + $$\frac{1}{12}$$ = $$\frac{2}{12}$$ = $$\frac{1}{6}$$

Question 14.
$$\frac{1}{3}$$ + $$\frac{1}{3}$$ =
$$\frac{1}{3}$$ + $$\frac{1}{3}$$ = $$\frac{2}{3}$$

Question 15.
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ =
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ = $$\frac{1}{12}$$

Question 16.
$$\frac{5}{12}$$ + $$\frac{6}{12}$$ =
$$\frac{5}{12}$$ + $$\frac{6}{12}$$ = $$\frac{11}{12}$$

Question 17.
$$\frac{7}{12}$$ + $$\frac{4}{12}$$ =
$$\frac{7}{12}$$ + $$\frac{4}{12}$$ = $$\frac{11}{12}$$

Question 18.
$$\frac{4}{6}$$ – $$\frac{1}{6}$$ =
$$\frac{4}{6}$$ – $$\frac{1}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$

Question 19.
$$\frac{1}{6}$$ + $$\frac{2}{6}$$ =
$$\frac{1}{6}$$ + $$\frac{2}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$

Question 20.
$$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ =
$$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ = $$\frac{3}{6}$$ =  $$\frac{1}{2}$$

Question 21.
$$\frac{1}{3}$$ + $$\frac{1}{3}$$ + $$\frac{1}{3}$$ =
$$\frac{1}{3}$$ + $$\frac{1}{3}$$ + $$\frac{1}{3}$$ = $$\frac{3}{3}$$ = 1

Question 22.
$$\frac{1}{12}$$ + $$\frac{1}{12}$$ + $$\frac{1}{12}$$ =
$$\frac{1}{12}$$ + $$\frac{1}{12}$$ + $$\frac{1}{12}$$ = $$\frac{3}{12}$$ = $$\frac{1}{4}$$

Question 23.
$$\frac{1}{9}$$ + $$\frac{1}{9}$$ + $$\frac{1}{9}$$ =
$$\frac{1}{9}$$ + $$\frac{1}{9}$$ + $$\frac{1}{9}$$ = $$\frac{3}{9}$$ =  $$\frac{1}{3}$$

Question 24.
$$\frac{1}{9}$$ + $$\frac{3}{9}$$ + $$\frac{1}{9}$$ =
$$\frac{1}{9}$$ + $$\frac{3}{9}$$ + $$\frac{1}{9}$$ = $$\frac{5}{9}$$

Question 25.
$$\frac{4}{9}$$ – $$\frac{1}{9}$$ – $$\frac{3}{9}$$ =
$$\frac{4}{9}$$ – $$\frac{1}{9}$$ – $$\frac{3}{9}$$ = $$\frac{8}{9}$$

Question 26.
$$\frac{1}{4}$$ + $$\frac{2}{4}$$ + $$\frac{1}{4}$$ =
$$\frac{1}{4}$$ + $$\frac{2}{4}$$ + $$\frac{1}{4}$$ = $$\frac{4}{4}$$ = 1

Question 27.
$$\frac{1}{8}$$ + $$\frac{3}{8}$$ + $$\frac{2}{8}$$ =
$$\frac{1}{8}$$ + $$\frac{3}{8}$$ + $$\frac{2}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 28.
$$\frac{5}{12}$$ + $$\frac{1}{12}$$ + $$\frac{5}{12}$$ =
$$\frac{5}{12}$$ + $$\frac{1}{12}$$ + $$\frac{5}{12}$$ = $$\frac{11}{12}$$

Question 29.
$$\frac{2}{9}$$ + $$\frac{3}{9}$$ + $$\frac{2}{9}$$ =
$$\frac{2}{9}$$ + $$\frac{3}{9}$$ + $$\frac{2}{9}$$ = $$\frac{7}{9}$$

Question 30.
$$\frac{3}{10}$$ – $$\frac{3}{10}$$ + $$\frac{3}{10}$$ =
$$\frac{3}{10}$$ – $$\frac{3}{10}$$ + $$\frac{3}{10}$$ = $$\frac{9}{10}$$

Question 31.
$$\frac{3}{5}$$ – $$\frac{1}{5}$$ – $$\frac{1}{5}$$ =
$$\frac{3}{5}$$ – $$\frac{1}{5}$$ – $$\frac{1}{5}$$ = $$\frac{3}{5}$$ – $$\frac{2}{5}$$ = $$\frac{1}{5}$$

Question 32.
$$\frac{1}{6}$$ + $$\frac{2}{6}$$ =
$$\frac{1}{6}$$ + $$\frac{2}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$ =\

Question 33.
$$\frac{3}{12}$$ + $$\frac{4}{12}$$ =
$$\frac{3}{12}$$ + $$\frac{4}{12}$$ = $$\frac{7}{12}$$

Question 34.
$$\frac{3}{12}$$ + $$\frac{6}{12}$$ =
$$\frac{3}{12}$$ + $$\frac{6}{12}$$ = $$\frac{9}{12}$$ = $$\frac{3}{4}$$

Question 35.
$$\frac{4}{8}$$ + $$\frac{2}{8}$$ =
$$\frac{4}{8}$$ + $$\frac{2}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 36.
$$\frac{4}{12}$$ + $$\frac{1}{12}$$ =
$$\frac{4}{12}$$ + $$\frac{1}{12}$$ = $$\frac{5}{12}$$

Question 37.
$$\frac{1}{5}$$ + $$\frac{3}{5}$$ =
$$\frac{1}{5}$$ + $$\frac{3}{5}$$ = $$\frac{4}{5}$$

Question 38.
$$\frac{2}{5}$$ + $$\frac{2}{5}$$ =
$$\frac{2}{5}$$ + $$\frac{2}{5}$$ = $$\frac{4}{5}$$

Question 39.
$$\frac{1}{6}$$ + $$\frac{2}{6}$$ =
$$\frac{1}{6}$$ + $$\frac{2}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$

Question 40.
$$\frac{5}{12}$$ – $$\frac{3}{12}$$ =
$$\frac{5}{12}$$ – $$\frac{3}{12}$$ = $$\frac{2}{12}$$ = $$\frac{1}{6}$$

Question 41.
$$\frac{7}{15}$$ – $$\frac{2}{15}$$ =
$$\frac{7}{15}$$ – $$\frac{2}{15}$$ = $$\frac{5}{15}$$ = $$\frac{1}{3}$$

Question 42.
$$\frac{7}{15}$$ – $$\frac{3}{15}$$ =
$$\frac{7}{15}$$ – $$\frac{3}{15}$$ = $$\frac{4}{15}$$

Question 43.
$$\frac{11}{15}$$ – $$\frac{2}{15}$$ =
$$\frac{11}{15}$$ – $$\frac{2}{15}$$ = $$\frac{9}{15}$$

Question 44.
$$\frac{2}{15}$$ + $$\frac{4}{15}$$ =
$$\frac{2}{15}$$ + $$\frac{4}{15}$$ = $$\frac{6}{15}$$ = $$\frac{2}{5}$$

B
Add and Subtract Fractions with Like Units

Question 1.
$$\frac{1}{2}$$ + $$\frac{1}{2}$$ =
$$\frac{1}{2}$$ + $$\frac{1}{2}$$ = $$\frac{2}{2}$$ = 1

Question 2.
$$\frac{2}{8}$$ + $$\frac{1}{8}$$ =
$$\frac{2}{8}$$ + $$\frac{1}{8}$$ = $$\frac{3}{8}$$

Question 3.
$$\frac{2}{8}$$ + $$\frac{3}{8}$$ =
$$\frac{2}{8}$$ + $$\frac{3}{8}$$ = $$\frac{5}{8}$$

Question 4.
$$\frac{2}{12}$$ – $$\frac{1}{12}$$ =
$$\frac{2}{12}$$ – $$\frac{1}{12}$$ = $$\frac{1}{12}$$

Question 5.
$$\frac{5}{12}$$ + $$\frac{2}{12}$$ =
$$\frac{5}{12}$$ + $$\frac{2}{12}$$ = $$\frac{7}{12}$$

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

Question 7.
$$\frac{4}{8}$$ – $$\frac{3}{8}$$ =
$$\frac{4}{8}$$ – $$\frac{3}{8}$$ = $$\frac{1}{8}$$

Question 8.
$$\frac{1}{8}$$ + $$\frac{5}{8}$$ =
$$\frac{1}{8}$$ + $$\frac{5}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 9.
$$\frac{3}{4}$$ – $$\frac{1}{4}$$ =
$$\frac{3}{4}$$ – $$\frac{1}{4}$$ = $$\frac{2}{4}$$ = $$\frac{1}{2}$$

Question 10.
$$\frac{3}{6}$$ – $$\frac{3}{6}$$ =
$$\frac{3}{6}$$ – $$\frac{3}{6}$$ = 0

Question 11.
$$\frac{3}{9}$$ + $$\frac{3}{9}$$ =
$$\frac{3}{9}$$ + $$\frac{3}{9}$$ = $$\frac{6}{9}$$ = $$\frac{2}{3}$$

Question 12.
$$\frac{2}{3}$$ + $$\frac{1}{3}$$ =
$$\frac{2}{3}$$ + $$\frac{1}{3}$$ = $$\frac{3}{3}$$ = 1

Question 13.
$$\frac{6}{9}$$ – $$\frac{4}{9}$$ =
$$\frac{6}{9}$$ – $$\frac{4}{9}$$ = $$\frac{2}{9}$$

Question 14.
$$\frac{5}{9}$$ – $$\frac{3}{9}$$ =
$$\frac{5}{9}$$ – $$\frac{3}{9}$$ = $$\frac{2}{9}$$

Question 15.
$$\frac{2}{9}$$ + $$\frac{2}{9}$$ =
$$\frac{2}{9}$$ + $$\frac{2}{9}$$ = $$\frac{4}{9}$$

Question 16.
$$\frac{1}{12}$$ + $$\frac{3}{12}$$ =
$$\frac{1}{12}$$ + $$\frac{3}{12}$$ = $$\frac{4}{12}$$ = $$\frac{1}{4}$$

Question 17.
$$\frac{5}{12}$$ – $$\frac{4}{12}$$ =
$$\frac{5}{12}$$ – $$\frac{4}{12}$$ = $$\frac{1}{12}$$

Question 18.
$$\frac{9}{12}$$ – $$\frac{6}{12}$$ =
$$\frac{9}{12}$$ – $$\frac{6}{12}$$ = $$\frac{3}{12}$$ = $$\frac{1}{4}$$

Question 19.
$$\frac{6}{10}$$ – $$\frac{4}{10}$$ =
$$\frac{6}{10}$$ – $$\frac{4}{10}$$ = $$\frac{2}{10}$$ = $$\frac{1}{5}$$

Question 20.
$$\frac{2}{8}$$ + $$\frac{2}{8}$$ + $$\frac{2}{8}$$ =
$$\frac{2}{8}$$ + $$\frac{2}{8}$$ + $$\frac{2}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 21.
$$\frac{1}{10}$$ + $$\frac{1}{10}$$ + $$\frac{1}{10}$$ =
$$\frac{1}{10}$$ + $$\frac{1}{10}$$ + $$\frac{1}{10}$$ = $$\frac{3}{10}$$ +

Question 22.
$$\frac{7}{12}$$ – $$\frac{2}{10}$$ – $$\frac{4}{10}$$ =
$$\frac{7}{12}$$ – $$\frac{2}{10}$$ – $$\frac{4}{10}$$ = $$\frac{7}{12}$$ – $$\frac{6}{10}$$ = $$\frac{1}{10}$$

Question 23.
$$\frac{1}{12}$$ + $$\frac{6}{12}$$ + $$\frac{2}{12}$$ =
$$\frac{1}{12}$$ + $$\frac{6}{12}$$ + $$\frac{2}{12}$$ = $$\frac{9}{12}$$ = $$\frac{3}{4}$$

Question 24.
$$\frac{4}{12}$$ + $$\frac{3}{12}$$ + $$\frac{3}{12}$$ =
$$\frac{4}{12}$$ + $$\frac{3}{12}$$ + $$\frac{3}{12}$$ = $$\frac{10}{12}$$ = $$\frac{5}{6}$$

Question 25.
$$\frac{8}{12}$$ – $$\frac{4}{12}$$ – $$\frac{4}{12}$$ =
$$\frac{8}{12}$$ – $$\frac{4}{12}$$ – $$\frac{4}{12}$$ = $$\frac{8}{12}$$ – $$\frac{8}{12}$$ = 0

Question 26.
$$\frac{1}{10}$$ + $$\frac{2}{10}$$ + $$\frac{4}{10}$$ =
$$\frac{1}{10}$$ + $$\frac{2}{10}$$ + $$\frac{4}{10}$$ = $$\frac{7}{10}$$

Question 27.
$$\frac{1}{10}$$ + $$\frac{1}{10}$$ + $$\frac{6}{10}$$ =
$$\frac{1}{10}$$ + $$\frac{1}{10}$$ + $$\frac{6}{10}$$ = $$\frac{8}{10}$$ = $$\frac{4}{5}$$

Question 28.
$$\frac{4}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ =
$$\frac{4}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ = $$\frac{6}{6}$$ = 1

Question 29.
$$\frac{2}{12}$$ + $$\frac{3}{12}$$ + $$\frac{4}{12}$$ =
$$\frac{2}{12}$$ + $$\frac{3}{12}$$ + $$\frac{4}{12}$$ = $$\frac{9}{12}$$ = $$\frac{3}{4}$$

Question 30.
$$\frac{2}{10}$$ + $$\frac{4}{10}$$ + $$\frac{4}{10}$$ =
$$\frac{2}{10}$$ + $$\frac{4}{10}$$ + $$\frac{4}{10}$$ = $$\frac{10}{10}$$ = 1

Question 31.
$$\frac{3}{10}$$ + $$\frac{1}{10}$$ + $$\frac{2}{10}$$ =
$$\frac{3}{10}$$ + $$\frac{1}{10}$$ + $$\frac{2}{10}$$ = $$\frac{6}{10}$$ = $$\frac{3}{5}$$

Question 32.
$$\frac{4}{6}$$ – $$\frac{2}{6}$$ =
$$\frac{4}{6}$$ – $$\frac{2}{6}$$ = $$\frac{2}{6}$$ = $$\frac{1}{3}$$

Question 33.
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ =
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ = $$\frac{1}{12}$$

Question 34.
$$\frac{2}{3}$$ + $$\frac{1}{3}$$ =
$$\frac{2}{3}$$ + $$\frac{1}{3}$$ = $$\frac{3}{3}$$ = 1

Question 35.
$$\frac{2}{4}$$ + $$\frac{1}{4}$$ =
$$\frac{2}{4}$$ + $$\frac{1}{4}$$ = $$\frac{3}{4}$$

Question 36.
$$\frac{3}{12}$$ + $$\frac{2}{12}$$ =
$$\frac{3}{12}$$ + $$\frac{2}{12}$$ = $$\frac{5}{12}$$

Question 37.
$$\frac{1}{5}$$ + $$\frac{2}{5}$$ =
$$\frac{1}{5}$$ + $$\frac{2}{5}$$ = $$\frac{3}{5}$$

Question 38.
$$\frac{4}{5}$$ – $$\frac{4}{5}$$ =
$$\frac{4}{5}$$ – $$\frac{4}{5}$$ = 0

Question 39.
$$\frac{5}{12}$$ – $$\frac{1}{12}$$ =
$$\frac{5}{12}$$ – $$\frac{1}{12}$$ = $$\frac{4}{12}$$ = $$\frac{1}{3}$$

Question 40.
$$\frac{6}{8}$$ + $$\frac{2}{8}$$ =
$$\frac{6}{8}$$ + $$\frac{2}{8}$$ = $$\frac{8}{8}$$ = 1

Question 41.
$$\frac{2}{8}$$ + $$\frac{2}{8}$$ + $$\frac{2}{8}$$ =
$$\frac{2}{8}$$ + $$\frac{2}{8}$$ + $$\frac{2}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 42.
$$\frac{9}{10}$$ – $$\frac{7}{10}$$ – $$\frac{1}{10}$$ =
$$\frac{9}{10}$$ – $$\frac{7}{10}$$ – $$\frac{1}{10}$$ = $$\frac{9}{10}$$ – $$\frac{8}{10}$$ = $$\frac{1}{10}$$ =

Question 43.
$$\frac{2}{10}$$ + $$\frac{5}{10}$$ + $$\frac{2}{10}$$ =
$$\frac{2}{10}$$ + $$\frac{5}{10}$$ + $$\frac{2}{10}$$ = $$\frac{9}{10}$$

Question 44.
$$\frac{9}{12}$$ – $$\frac{1}{12}$$ – $$\frac{4}{12}$$ =
$$\frac{9}{12}$$ – $$\frac{1}{12}$$ – $$\frac{4}{12}$$ = $$\frac{9}{12}$$ – $$\frac{5}{12}$$ = $$\frac{4}{12}$$ = $$\frac{1}{3}$$  .

### Eureka Math Grade 5 Module 3 Lesson 9 Problem Set Answer Key

Question 1.
First make like units, and then add.
a. $$\frac{3}{4}$$ + $$\frac{1}{7}$$ =
b. $$\frac{1}{4}$$ + $$\frac{9}{8}$$ =
c. $$\frac{3}{8}$$ + $$\frac{3}{7}$$ =
d. $$\frac{4}{9}$$ + $$\frac{4}{7}$$ =
e. $$\frac{1}{5}$$ + $$\frac{2}{3}$$ =
f. $$\frac{3}{4}$$ + $$\frac{5}{6}$$ =
g. $$\frac{2}{3}$$ + $$\frac{1}{11}$$ =
h. $$\frac{3}{4}$$ + 1$$\frac{1}{10}$$ =
a.
$$\frac{3}{4}$$ + $$\frac{1}{7}$$
lcm of 4 and 7 is 28
=$$\frac{21}{28}$$ + $$\frac{4}{28}$$ = $$\frac{25}{28}$$
b.
$$\frac{1}{4}$$ + $$\frac{9}{8}$$
lcm of 4 and 8 is 8
$$\frac{2}{8}$$ + $$\frac{9}{8}$$ =$$\frac{11}{8}$$ = 1$$\frac{3}{8}$$
c.
$$\frac{3}{8}$$ + $$\frac{3}{7}$$
lcm of 8 and 7 is 56
$$\frac{21}{56}$$ + $$\frac{24}{56}$$ = $$\frac{45}{56}$$
d.
$$\frac{4}{9}$$ + $$\frac{4}{7}$$
lcm of 9 and 7 is 63
$$\frac{28}{63}$$ + $$\frac{36}{63}$$ = $$\frac{64}{63}$$ = 1$$\frac{1}{63}$$
e.
$$\frac{1}{5}$$ + $$\frac{2}{3}$$
lcm of 5 and 3 is 15 .
$$\frac{3}{15}$$ + $$\frac{10}{15}$$ = $$\frac{13}{15}$$
f.
$$\frac{3}{4}$$ + $$\frac{5}{6}$$
lcm of 4 and 6 is 12.
$$\frac{9}{12}$$ + $$\frac{10}{12}$$ = $$\frac{19}{12}$$ =1 $$\frac{7}{12}$$
g.
$$\frac{2}{3}$$ + $$\frac{1}{11}$$
lcm of 3 and 11 is 33
$$\frac{22}{33}$$ + $$\frac{3}{33}$$ = $$\frac{25}{33}$$
h.
$$\frac{3}{4}$$ + 1$$\frac{1}{10}$$ = $$\frac{3}{4}$$ + $$\frac{11}{10}$$
lcm of 4 and 10 is 20.
$$\frac{15}{20}$$ + $$\frac{22}{10}$$ = $$\frac{37}{20}$$ = 1$$\frac{17}{20}$$

Question 2.
Whitney says that to add fractions with different denominators, you always have to multiply the denominators to find the common unit; for example:
$$\frac{1}{4}+\frac{1}{6}=\frac{6}{24}+\frac{4}{24}$$
Show Whitney how she could have chosen a denominator smaller than 24, and solve the problem.
multiples of 4 and 6 are
4 : 4, 8, 12, 16, 20, 24
6: 6, 12, 18, 24, 30 .
12 and 24 are the common multiplies of 4 and 6. smaller than 24 we get 12 multiple .
($$\frac{1 × 3}{4 × 3}$$) + ($$\frac{1 × 2}{6 × 2}$$) = $$\frac{3}{12}$$ + $$\frac{2}{12}$$ = $$\frac{5}{12}$$

Question 3.
Jackie brought $$\frac{3}{4}$$ of a gallon of iced tea to the party. Bill brought $$\frac{7}{8}$$ of a gallon of iced tea to the same party. How much iced tea did Jackie and Bill bring to the party?
Fraction of iced tea brought by Jackie = $$\frac{3}{4}$$
Fraction of iced tea brought by Bill = $$\frac{7}{8}$$
Total Fraction of iced tea brought to party = $$\frac{3}{4}$$ + $$\frac{7}{8}$$  = $$\frac{6}{8}$$ + $$\frac{7}{8}$$ = $$\frac{13}{8}$$ = 1$$\frac{5}{8}$$
Therefore, Total Fraction of iced tea brought to party = $$\frac{13}{8}$$ = 1$$\frac{5}{8}$$ .

Question 4.
Madame Curie made some radium in her lab. She used $$\frac{2}{5}$$ kg of the radium in an experiment and had 1$$\frac{1}{4}$$ kg left. How much radium did she have at first? (Extension: If she performed the experiment twice, how much radium would she have left?)
Fraction of Quantity of Radium used by Experiment = $$\frac{2}{5}$$ kg
Fraction of Quantity of Radium left = 1$$\frac{1}{4}$$ kg = $$\frac{5}{4}$$ kg
Quantity of Radium made by Madam Curie = $$\frac{2}{5}$$ + $$\frac{5}{4}[/latex lcm of 5 and 4 is 20 . [latex]\frac{8}{20}$$  + $$\frac{25}{20}$$ = $$\frac{33}{20}$$ =1$$\frac{13}{20}$$ .
Therefore if the experiment is done once the Total Quantity = $$\frac{33}{20}$$ =1$$\frac{13}{20}$$
If the Experiment if done twiced .
Total Quantity – Quantity Used for Experiment twice = left Quantity .
$$\frac{33}{20}$$ – 2 × $$\frac{2}{5}$$ = $$\frac{33}{20}$$ –  $$\frac{4}{5}$$ = $$\frac{33}{20}$$ – $$\frac{16}{20}$$ = $$\frac{17}{20}$$
Therefore if the experiment is done once the Total Quantity = $$\frac{17}{20}$$

### Eureka Math Grade 5 Module 3 Lesson 9 Exit Ticket Answer Key

Make like units, and then add.
a. $$\frac{1}{6}$$ + $$\frac{3}{4}$$ =
b. 1$$\frac{1}{2}$$ + $$\frac{2}{5}$$ =
a.
$$\frac{1}{6}$$ + $$\frac{3}{4}$$
lcm of 6 and 4 is 12
$$\frac{2}{12}$$ + $$\frac{9}{12}$$ = $$\frac{11}{12}$$
b.
1$$\frac{1}{2}$$ + $$\frac{2}{5}$$ = $$\frac{3}{2}$$ + $$\frac{2}{5}$$
lcm of 2 and 5 is 10.
$$\frac{15}{10}$$ + $$\frac{4}{10}$$ =$$\frac{19}{10}$$ = 1$$\frac{9}{10}$$

### Eureka Math Grade 5 Module 3 Lesson 9 Homework Answer Key

Question 1.
Make like units, and then add.
a. $$\frac{3}{5}$$ + $$\frac{1}{3}$$ =
b. $$\frac{3}{5}$$ + $$\frac{1}{11}$$ =
c. $$\frac{2}{9}$$ + $$\frac{5}{6}$$ =
d. $$\frac{2}{5}$$ + $$\frac{1}{4}$$ + $$\frac{1}{10}$$ =
e. $$\frac{1}{3}$$ + $$\frac{7}{5}$$ =
f. $$\frac{5}{8}$$ + $$\frac{7}{12}$$ =
g. 1$$\frac{1}{3}$$ + $$\frac{3}{4}$$ =
h. $$\frac{5}{6}$$ + 1$$\frac{1}{4}$$ =
a.
$$\frac{3}{5}$$ + $$\frac{1}{3}$$
lcm of 5 and 3 is 15
$$\frac{9}{15}$$ + $$\frac{5}{15}$$ = $$\frac{14}{15}$$
b.
$$\frac{3}{5}$$ + $$\frac{1}{11}$$
lcm of 5 and 11 is 55
$$\frac{33}{55}$$ + $$\frac{5}{55}$$ = $$\frac{38}{55}$$
c.
$$\frac{2}{9}$$ + $$\frac{5}{6}$$
lcm of 9 and 6 is 18 .
$$\frac{4}{18}$$ + $$\frac{15}{18}$$ = $$\frac{19}{18}$$ = 1 $$\frac{1}{18}$$
d.
$$\frac{2}{5}$$ + $$\frac{1}{4}$$ + $$\frac{1}{10}$$
lcm of 5 , 4 and 10 is 20 .
$$\frac{8}{20}$$ + $$\frac{5}{20}$$ + $$\frac{2}{20}$$ = $$\frac{15}{20}$$= $$\frac{3}{4}$$
e.
$$\frac{1}{3}$$ + $$\frac{7}{5}$$
lcm of 3 and 5 is 15 .
$$\frac{5}{15}$$ + $$\frac{21}{15}$$ =$$\frac{26}{3}$$ =1$$\frac{11}{15}$$
f.
$$\frac{5}{8}$$ + $$\frac{7}{12}$$
lcm of 8 and 12 is 24.
$$\frac{15}{24}$$ + $$\frac{14}{24}$$ = $$\frac{29}{24}$$ = 1$$\frac{5}{24}$$
g.
1$$\frac{1}{3}$$ + $$\frac{3}{4}$$ = $$\frac{4}{3}$$ + $$\frac{3}{4}$$
lcm of 3 and 4  is 12
$$\frac{16}{12}$$ + $$\frac{9}{12}$$ = $$\frac{25}{12}$$ = 2 $$\frac{1}{12}$$
h.
$$\frac{5}{6}$$ + 1$$\frac{1}{4}$$ =$$\frac{5}{6}$$ + $$\frac{5}{4}$$
lcm of 4 and 6 is 12 .
$$\frac{10}{12}$$ + $$\frac{15}{12}$$ = $$\frac{25}{12}$$ = 2$$\frac{1}{12}$$

Question 2.
On Monday, Ka practiced guitar for $$\frac{2}{3}$$ of one hour. When she finished, she practiced piano for $$\frac{3}{4}$$ of one hour. How much time did Ka spend practicing instruments on Monday?
Fraction of Time spent in playing guitar of one hour = $$\frac{2}{3}$$
Fraction of Time spent in playing guitar when finished = $$\frac{3}{4}$$
Total Time taken for practicing = $$\frac{2}{3}$$ + $$\frac{3}{4}$$ = $$\frac{8}{12}$$ + $$\frac{9}{12}$$ = $$\frac{17}{12}$$ = 1$$\frac{5}{12}$$ hour .
Therefore, Total Time taken in practicing = $$\frac{17}{12}$$ = 1$$\frac{5}{12}$$ hour

Question 3.
Ms. How bought a bag of rice for dinner. She used $$\frac{3}{5}$$ kg of the rice and still had 2$$\frac{1}{4}$$ kg left. How heavy was the bag of rice that Ms. How bought?
Fraction of Quantity of rice used = $$\frac{3}{5}$$ kg
Fraction of Quantity of rice left = 2$$\frac{1}{4}$$ kg
Total Quantity of rice = $$\frac{3}{5}$$  + 2$$\frac{1}{4}$$  = $$\frac{3}{5}$$ + $$\frac{9}{4}$$
= $$\frac{12}{20}$$ + $$\frac{45}{20}$$ =$$\frac{57}{20}$$ = 2$$\frac{17}{20}$$
Therefore, Total Quantity of rice = $$\frac{57}{20}$$ = 2$$\frac{17}{20}$$ .

Question 4.
Joe spends $$\frac{2}{5}$$ of his money on a jacket and $$\frac{3}{8}$$ of his money on a shirt. He spends the rest on a pair of pants. What fraction of his money does he use to buy the pants?
Money spent on jacket = $$\frac{2}{5}$$
Money spent on a shirt = $$\frac{3}{8}$$
1 = $$\frac{2}{5}$$ + $$\frac{3}{8}$$  + x
$$\frac{40}{40}$$  = $$\frac{16}{40}$$ + $$\frac{10}{40}$$ +x
$$\frac{40}{40}$$  = $$\frac{26}{40}$$ + x
x = $$\frac{40}{40}$$  – $$\frac{13}{40}$$
x = $$\frac{27}{40}$$