Adding and Subtracting Fractions worksheet with sections for practice problems and examples.

Let’s solve each problem step by step. We’ll start with Section A, then B, then C. Remember: to add or subtract fractions, we need a common denominator. Then simplify and convert to mixed numbers if needed.

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Section A

1) Already done in example:
$\frac{1}{8} + \frac{1}{2} = \frac{1}{8} + \frac{4}{8} = \frac{5}{8}$ → Answer: $\frac{5}{8}$

2) $\frac{1}{20} + \frac{1}{5}$
Common denominator of 20 and 5 is 20.
$\frac{1}{5} = \frac{4}{20}$
So: $\frac{1}{20} + \frac{4}{20} = \frac{5}{20} = \frac{1}{4}$ → Answer: $\frac{1}{4}$

3) $\frac{1}{7} - \frac{1}{14}$
Common denominator: 14
$\frac{1}{7} = \frac{2}{14}$
So: $\frac{2}{14} - \frac{1}{14} = \frac{1}{14}$ → Answer: $\frac{1}{14}$

4) $\frac{1}{5} - \frac{1}{15}$
Common denominator: 15
$\frac{1}{5} = \frac{3}{15}$
So: $\frac{3}{15} - \frac{1}{15} = \frac{2}{15}$ → Answer: $\frac{2}{15}$

5) $\frac{1}{40} + \frac{1}{2}$
Common denominator: 40
$\frac{1}{2} = \frac{20}{40}$
So: $\frac{1}{40} + \frac{20}{40} = \frac{21}{40}$ → Answer: $\frac{21}{40}$

6) $\frac{1}{2} - \frac{1}{3}$
Common denominator: 6
$\frac{1}{2} = \frac{3}{6}, \frac{1}{3} = \frac{2}{6}$
So: $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$ → Answer: $\frac{1}{6}$

7) $\frac{1}{5} + \frac{1}{4}$
Common denominator: 20
$\frac{1}{5} = \frac{4}{20}, \frac{1}{4} = \frac{5}{20}$
So: $\frac{4}{20} + \frac{5}{20} = \frac{9}{20}$ → Answer: $\frac{9}{20}$

8) $\frac{1}{7} - \frac{1}{11}$
Common denominator: 77
$\frac{1}{7} = \frac{11}{77}, \frac{1}{11} = \frac{7}{77}$
So: $\frac{11}{77} - \frac{7}{77} = \frac{4}{77}$ → Answer: $\frac{4}{77}$

9) $\frac{1}{15} + \frac{1}{2}$
Common denominator: 30
$\frac{1}{15} = \frac{2}{30}, \frac{1}{2} = \frac{15}{30}$
So: $\frac{2}{30} + \frac{15}{30} = \frac{17}{30}$ → Answer: $\frac{17}{30}$

10) $\frac{1}{12} + \frac{1}{5}$
Common denominator: 60
$\frac{1}{12} = \frac{5}{60}, \frac{1}{5} = \frac{12}{60}$
So: $\frac{5}{60} + \frac{12}{60} = \frac{17}{60}$ → Answer: $\frac{17}{60}$

11) $\frac{1}{5} + \frac{1}{8}$
Common denominator: 40
$\frac{1}{5} = \frac{8}{40}, \frac{1}{8} = \frac{5}{40}$
So: $\frac{8}{40} + \frac{5}{40} = \frac{13}{40}$ → Answer: $\frac{13}{40}$

12) $\frac{1}{9} - \frac{1}{10}$
Common denominator: 90
$\frac{1}{9} = \frac{10}{90}, \frac{1}{10} = \frac{9}{90}$
So: $\frac{10}{90} - \frac{9}{90} = \frac{1}{90}$ → Answer: $\frac{1}{90}$

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Section B

1) $\frac{1}{15} + \frac{2}{5}$
Common denominator: 15
$\frac{2}{5} = \frac{6}{15}$
So: $\frac{1}{15} + \frac{6}{15} = \frac{7}{15}$ → Answer: $\frac{7}{15}$

2) $\frac{2}{3} - \frac{1}{21}$
Common denominator: 21
$\frac{2}{3} = \frac{14}{21}$
So: $\frac{14}{21} - \frac{1}{21} = \frac{13}{21}$ → Answer: $\frac{13}{21}$

3) $\frac{1}{4} + \frac{5}{12}$
Common denominator: 12
$\frac{1}{4} = \frac{3}{12}$
So: $\frac{3}{12} + \frac{5}{12} = \frac{8}{12} = \frac{2}{3}$ → Answer: $\frac{2}{3}$

4) $\frac{1}{2} - \frac{7}{16}$
Common denominator: 16
$\frac{1}{2} = \frac{8}{16}$
So: $\frac{8}{16} - \frac{7}{16} = \frac{1}{16}$ → Answer: $\frac{1}{16}$

5) $\frac{3}{5} + \frac{1}{2}$
Common denominator: 10
$\frac{3}{5} = \frac{6}{10}, \frac{1}{2} = \frac{5}{10}$
So: $\frac{6}{10} + \frac{5}{10} = \frac{11}{10} = 1\frac{1}{10}$ → Answer: $1\frac{1}{10}$

6) $\frac{1}{6} + \frac{9}{10}$
Common denominator: 30
$\frac{1}{6} = \frac{5}{30}, \frac{9}{10} = \frac{27}{30}$
So: $\frac{5}{30} + \frac{27}{30} = \frac{32}{30} = \frac{16}{15} = 1\frac{1}{15}$ → Answer: $1\frac{1}{15}$

7) $\frac{3}{7} - \frac{2}{5}$
Common denominator: 35
$\frac{3}{7} = \frac{15}{35}, \frac{2}{5} = \frac{14}{35}$
So: $\frac{15}{35} - \frac{14}{35} = \frac{1}{35}$ → Answer: $\frac{1}{35}$

8) $\frac{7}{11} + \frac{2}{3}$
Common denominator: 33
$\frac{7}{11} = \frac{21}{33}, \frac{2}{3} = \frac{22}{33}$
So: $\frac{21}{33} + \frac{22}{33} = \frac{43}{33} = 1\frac{10}{33}$ → Answer: $1\frac{10}{33}$

9) $\frac{4}{5} - \frac{5}{8}$
Common denominator: 40
$\frac{4}{5} = \frac{32}{40}, \frac{5}{8} = \frac{25}{40}$
So: $\frac{32}{40} - \frac{25}{40} = \frac{7}{40}$ → Answer: $\frac{7}{40}$

10) $\frac{3}{10} + \frac{6}{7}$
Common denominator: 70
$\frac{3}{10} = \frac{21}{70}, \frac{6}{7} = \frac{60}{70}$
So: $\frac{21}{70} + \frac{60}{70} = \frac{81}{70} = 1\frac{11}{70}$ → Answer: $1\frac{11}{70}$

11) $\frac{7}{9} + \frac{3}{8}$
Common denominator: 72
$\frac{7}{9} = \frac{56}{72}, \frac{3}{8} = \frac{27}{72}$
So: $\frac{56}{72} + \frac{27}{72} = \frac{83}{72} = 1\frac{11}{72}$ → Answer: $1\frac{11}{72}$

12) $\frac{3}{4} - \frac{6}{15}$
First simplify $\frac{6}{15} = \frac{2}{5}$
Now: $\frac{3}{4} - \frac{2}{5}$
Common denominator: 20
$\frac{3}{4} = \frac{15}{20}, \frac{2}{5} = \frac{8}{20}$
So: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$ → Answer: $\frac{7}{20}$

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Section C

1) $3 + \frac{56}{9}$
Convert 3 to ninths: $3 = \frac{27}{9}$
So: $\frac{27}{9} + \frac{56}{9} = \frac{83}{9} = 9\frac{2}{9}$ → Answer: $9\frac{2}{9}$

2) $7\frac{2}{3} + 5$
Add whole numbers: $7 + 5 = 12$, keep fraction: $\frac{2}{3}$
So: $12\frac{2}{3}$ → Answer: $12\frac{2}{3}$

3) $1\frac{1}{3} + 2\frac{1}{5}$
Convert to improper fractions:
$1\frac{1}{3} = \frac{4}{3}, 2\frac{1}{5} = \frac{11}{5}$
Common denominator: 15
$\frac{4}{3} = \frac{20}{15}, \frac{11}{5} = \frac{33}{15}$
Sum: $\frac{53}{15} = 3\frac{8}{15}$ → Answer: $3\frac{8}{15}$

4) $2\frac{1}{4} + 3\frac{1}{2}$
Convert: $2\frac{1}{4} = \frac{9}{4}, 3\frac{1}{2} = \frac{7}{2} = \frac{14}{4}$
Sum: $\frac{9}{4} + \frac{14}{4} = \frac{23}{4} = 5\frac{3}{4}$ → Answer: $5\frac{3}{4}$

5) $8\frac{1}{3} + 4\frac{2}{5}$
Convert: $8\frac{1}{3} = \frac{25}{3}, 4\frac{2}{5} = \frac{22}{5}$
Common denominator: 15
$\frac{25}{3} = \frac{125}{15}, \frac{22}{5} = \frac{66}{15}$
Sum: $\frac{191}{15} = 12\frac{11}{15}$ → Answer: $12\frac{11}{15}$

6) $5\frac{8}{11} + 3\frac{7}{9}$
Convert: $5\frac{8}{11} = \frac{63}{11}, 3\frac{7}{9} = \frac{34}{9}$
Common denominator: 99
$\frac{63}{11} = \frac{567}{99}, \frac{34}{9} = \frac{374}{99}$
Sum: $\frac{941}{99} = 9\frac{50}{99}$ → Answer: $9\frac{50}{99}$

7) $\frac{17}{8} - 1$
$1 = \frac{8}{8}$
So: $\frac{17}{8} - \frac{8}{8} = \frac{9}{8} = 1\frac{1}{8}$ → Answer: $1\frac{1}{8}$

8) $\frac{21}{9} - 2$
Simplify $\frac{21}{9} = \frac{7}{3}$
$2 = \frac{6}{3}$
So: $\frac{7}{3} - \frac{6}{3} = \frac{1}{3}$ → Answer: $\frac{1}{3}$

9) $5 - 2\frac{3}{5}$
Convert 5 to fifths: $5 = \frac{25}{5}$
Convert $2\frac{3}{5} = \frac{13}{5}$
So: $\frac{25}{5} - \frac{13}{5} = \frac{12}{5} = 2\frac{2}{5}$ → Answer: $2\frac{2}{5}$

10) $3\frac{1}{10} - 1\frac{2}{3}$
Convert: $3\frac{1}{10} = \frac{31}{10}, 1\frac{2}{3} = \frac{5}{3}$
Common denominator: 30
$\frac{31}{10} = \frac{93}{30}, \frac{5}{3} = \frac{50}{30}$
Difference: $\frac{43}{30} = 1\frac{13}{30}$ → Answer: $1\frac{13}{30}$

11) $9\frac{5}{8} - 4\frac{6}{7}$
Convert: $9\frac{5}{8} = \frac{77}{8}, 4\frac{6}{7} = \frac{34}{7}$
Common denominator: 56
$\frac{77}{8} = \frac{539}{56}, \frac{34}{7} = \frac{272}{56}$
Difference: $\frac{267}{56} = 4\frac{43}{56}$ → Answer: $4\frac{43}{56}$

12) $4\frac{2}{11} - 2\frac{8}{9}$
Convert: $4\frac{2}{11} = \frac{46}{11}, 2\frac{8}{9} = \frac{26}{9}$
Common denominator: 99
$\frac{46}{11} = \frac{414}{99}, \frac{26}{9} = \frac{286}{99}$
Difference: $\frac{128}{99} = 1\frac{29}{99}$ → Answer: $1\frac{29}{99}$

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Final Answer:

Section A
1) $\frac{5}{8}$
2) $\frac{1}{4}$
3) $\frac{1}{14}$
4) $\frac{2}{15}$
5) $\frac{21}{40}$
6) $\frac{1}{6}$
7) $\frac{9}{20}$
8) $\frac{4}{77}$
9) $\frac{17}{30}$
10) $\frac{17}{60}$
11) $\frac{13}{40}$
12) $\frac{1}{90}$

Section B
1) $\frac{7}{15}$
2) $\frac{13}{21}$
3) $\frac{2}{3}$
4) $\frac{1}{16}$
5) $1\frac{1}{10}$
6) $1\frac{1}{15}$
7) $\frac{1}{35}$
8) $1\frac{10}{33}$
9) $\frac{7}{40}$
10) $1\frac{11}{70}$
11) $1\frac{11}{72}$
12) $\frac{7}{20}$

Section C
1) $9\frac{2}{9}$
2) $12\frac{2}{3}$
3) $3\frac{8}{15}$
4) $5\frac{3}{4}$
5) $12\frac{11}{15}$
6) $9\frac{50}{99}$
7) $1\frac{1}{8}$
8) $\frac{1}{3}$
9) $2\frac{2}{5}$
10) $1\frac{13}{30}$
11) $4\frac{43}{56}$
12) $1\frac{29}{99}$