Here are the solutions for the problems on the worksheet. I have filled in the missing numbers step-by-step for each question.
1) $\frac{1}{3} + \frac{2}{5}$
* Common denominator is 15.
* $\frac{1 \times 5}{3 \times 5} + \frac{2 \times 3}{5 \times 3} = \frac{5}{15} + \frac{6}{15}$
* Answer:
$\frac{11}{15}$
2) $\frac{1}{2} - \frac{1}{3}$
* Common denominator is 6.
* $\frac{1 \times 3}{2 \times 3} - \frac{1 \times 2}{3 \times 2} = \frac{3}{6} - \frac{2}{6}$
* Answer:
$\frac{1}{6}$
3) $\frac{1}{4} + \frac{1}{3}$
* Common denominator is 12.
* $\frac{1 \times 3}{12} + \frac{1 \times 4}{12} = \frac{3}{12} + \frac{4}{12}$
* Answer:
$\frac{7}{12}$
4) $\frac{1}{4} - \frac{1}{5}$
* Common denominator is 20.
* $\frac{1 \times 5}{20} - \frac{1 \times 4}{20} = \frac{5}{20} - \frac{4}{20}$
* Answer:
$\frac{1}{20}$
5) $\frac{2}{3} - \frac{1}{4}$
* Common denominator is 12.
* $\frac{2 \times 4}{12} - \frac{1 \times 3}{12} = \frac{8}{12} - \frac{3}{12}$
* Answer:
$\frac{5}{12}$
6) $\frac{2}{3} + \frac{2}{9}$
* Common denominator is 9.
* $\frac{2 \times 3}{9} + \frac{2}{9} = \frac{6}{9} + \frac{2}{9}$
* Answer:
$\frac{8}{9}$
7) $\frac{1}{3} + \frac{2}{5}$
* Common denominator is 15.
* $\frac{1 \times 5}{15} + \frac{2 \times 3}{15} = \frac{5}{15} + \frac{6}{15}$
* Answer:
$\frac{11}{15}$
8) $\frac{7}{8} - \frac{1}{2}$
* Common denominator is 8.
* $\frac{7}{8} - \frac{1 \times 4}{8} = \frac{7}{8} - \frac{4}{8}$
* Answer:
$\frac{3}{8}$
9) $\frac{4}{5} - \frac{1}{2}$
* Common denominator is 10.
* $\frac{4 \times 2}{10} - \frac{1 \times 5}{10} = \frac{8}{10} - \frac{5}{10}$
* Answer:
$\frac{3}{10}$
10) $\frac{1}{8} + \frac{2}{3}$
* Common denominator is 24.
* $\frac{1 \times 3}{24} + \frac{2 \times 8}{24} = \frac{3}{24} + \frac{16}{24}$
* Answer:
$\frac{19}{24}$
11) $\frac{9}{10} - \frac{4}{5}$
* Common denominator is 10.
* $\frac{9}{10} - \frac{4 \times 2}{10} = \frac{9}{10} - \frac{8}{10}$
* Answer:
$\frac{1}{10}$
12) $\frac{2}{7} + \frac{1}{4}$
* Common denominator is 28.
* $\frac{2 \times 4}{28} + \frac{1 \times 7}{28} = \frac{8}{28} + \frac{7}{28}$
* Answer:
$\frac{15}{28}$
13) $\frac{2}{3} - \frac{3}{5}$
* Common denominator is 15.
* $\frac{2 \times 5}{15} - \frac{3 \times 3}{15} = \frac{10}{15} - \frac{9}{15}$
* Answer:
$\frac{1}{15}$
14) $\frac{1}{5} + \frac{2}{7}$
* Common denominator is 35.
* $\frac{1 \times 7}{35} + \frac{2 \times 5}{35} = \frac{7}{35} + \frac{10}{35}$
* Answer:
$\frac{17}{35}$
15) $\frac{1}{6} + \frac{5}{12}$
* Common denominator is 12.
* $\frac{1 \times 2}{12} + \frac{5}{12} = \frac{2}{12} + \frac{5}{12}$
* Answer:
$\frac{7}{12}$
16) $\frac{4}{5} - \frac{1}{9}$
* Common denominator is 45.
* $\frac{4 \times 9}{45} - \frac{1 \times 5}{45} = \frac{36}{45} - \frac{5}{45}$
* Answer:
$\frac{31}{45}$
17) $\frac{3}{4} + \frac{1}{5}$
* Common denominator is 20.
* $\frac{3 \times 5}{20} + \frac{1 \times 4}{20} = \frac{15}{20} + \frac{4}{20}$
* Answer:
$\frac{19}{20}$
18) $\frac{5}{8} - \frac{2}{5}$
* Common denominator is 40.
* $\frac{5 \times 5}{40} - \frac{2 \times 8}{40} = \frac{25}{40} - \frac{16}{40}$
* Answer:
$\frac{9}{40}$
Final Answer:
1) 11/15
2) 1/6
3) 7/12
4) 1/20
5) 5/12
6) 8/9
7) 11/15
8) 3/8
9) 3/10
10) 19/24
11) 1/10
12) 15/28
13) 1/15
14) 17/35
15) 7/12
16) 31/45
17) 19/20
18) 9/40
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting fractions worksheet 5th grade.
