Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

1) $\frac{1}{3} + \frac{2}{7}$
* Find a common denominator for 3 and 7, which is 21.
* Convert fractions: $\frac{1 \times 7}{3 \times 7} = \frac{7}{21}$ and $\frac{2 \times 3}{7 \times 3} = \frac{6}{21}$.
* Add numerators: $7 + 6 = 13$.
* Result: $\frac{13}{21}$

2) $\frac{1}{12} + \frac{1}{3}$
* The common denominator for 12 and 3 is 12.
* Convert $\frac{1}{3}$ to $\frac{4}{12}$.
* Add: $\frac{1}{12} + \frac{4}{12} = \frac{5}{12}$.

3) $\frac{1}{10} + \frac{2}{9}$
* Common denominator for 10 and 9 is 90.
* Convert: $\frac{9}{90} + \frac{20}{90}$.
* Add: $9 + 20 = 29$.
* Result: $\frac{29}{90}$

4) $\frac{3}{6} - \frac{2}{7}$
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$ first (optional, but easier). Let's stick to standard method: Common denominator for 6 and 7 is 42.
* Convert: $\frac{21}{42} - \frac{12}{42}$.
* Subtract: $21 - 12 = 9$.
* Result: $\frac{9}{42}$, which simplifies to $\frac{3}{14}$.

5) $\frac{2}{3} + \frac{3}{16}$
* Common denominator for 3 and 16 is 48.
* Convert: $\frac{32}{48} + \frac{9}{48}$.
* Add: $32 + 9 = 41$.
* Result: $\frac{41}{48}$

6) $\frac{1}{8} - \frac{1}{16}$
* Common denominator is 16.
* Convert $\frac{1}{8}$ to $\frac{2}{16}$.
* Subtract: $\frac{2}{16} - \frac{1}{16} = \frac{1}{16}$.

7) $\frac{1}{10} + \frac{6}{5}$
* Common denominator is 10.
* Convert $\frac{6}{5}$ to $\frac{12}{10}$.
* Add: $\frac{1}{10} + \frac{12}{10} = \frac{13}{10}$ (or $1 \frac{3}{10}$).

8) $\frac{9}{10} - \frac{1}{10}$
* Denominators are already the same.
* Subtract: $9 - 1 = 8$.
* Result: $\frac{8}{10}$, which simplifies to $\frac{4}{5}$.

9) $\frac{2}{3} - \frac{4}{9}$
* Common denominator is 9.
* Convert $\frac{2}{3}$ to $\frac{6}{9}$.
* Subtract: $\frac{6}{9} - \frac{4}{9} = \frac{2}{9}$.

10) $\frac{8}{12} - \frac{8}{16}$
* Simplify first: $\frac{8}{12} = \frac{2}{3}$ and $\frac{8}{16} = \frac{1}{2}$.
* New problem: $\frac{2}{3} - \frac{1}{2}$.
* Common denominator is 6.
* Convert: $\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$.

11) $\frac{2}{6} - \frac{1}{6}$
* Denominators are the same.
* Subtract: $2 - 1 = 1$.
* Result: $\frac{1}{6}$.

12) $\frac{1}{11} + \frac{1}{4}$
* Common denominator is 44.
* Convert: $\frac{4}{44} + \frac{11}{44}$.
* Add: $4 + 11 = 15$.
* Result: $\frac{15}{44}$

13) $\frac{3}{6} - \frac{1}{6}$
* Denominators are the same.
* Subtract: $3 - 1 = 2$.
* Result: $\frac{2}{6}$, which simplifies to $\frac{1}{3}$.

14) $\frac{2}{4} + \frac{2}{5}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* New problem: $\frac{1}{2} + \frac{2}{5}$.
* Common denominator is 10.
* Convert: $\frac{5}{10} + \frac{4}{10} = \frac{9}{10}$.

15) $\frac{2}{15} - \frac{1}{10}$
* Common denominator for 15 and 10 is 30.
* Convert: $\frac{4}{30} - \frac{3}{30}$.
* Subtract: $4 - 3 = 1$.
* Result: $\frac{1}{30}$

16) $\frac{1}{11} + \frac{5}{7}$
* Common denominator is 77.
* Convert: $\frac{7}{77} + \frac{55}{77}$.
* Add: $7 + 55 = 62$.
* Result: $\frac{62}{77}$

Final Answer:
1) 13/21
2) 5/12
3) 29/90
4) 3/14
5) 41/48
6) 1/16
7) 13/10
8) 4/5
9) 2/9
10) 1/6
11) 1/6
12) 15/44
13) 1/3
14) 9/10
15) 1/30
16) 62/77