Fraction addition and subtraction worksheet with unlike denominators.

Here are the step-by-step solutions for each problem. To add or subtract fractions with different denominators (bottom numbers), you first need to find a common denominator so the pieces are the same size.

1. $\frac{2}{3} + \frac{1}{2}$
* The common denominator for 3 and 2 is 6.
* Convert $\frac{2}{3}$: Multiply top and bottom by 2 to get $\frac{4}{6}$.
* Convert $\frac{1}{2}$: Multiply top and bottom by 3 to get $\frac{3}{6}$.
* Add them: $\frac{4}{6} + \frac{3}{6} = \frac{7}{6}$.
* This can also be written as $1 \frac{1}{6}$.

2. $\frac{2}{5} + \frac{1}{10}$
* The common denominator for 5 and 10 is 10.
* Convert $\frac{2}{5}$: Multiply top and bottom by 2 to get $\frac{4}{10}$.
* The second fraction is already $\frac{1}{10}$.
* Add them: $\frac{4}{10} + \frac{1}{10} = \frac{5}{10}$.
* Simplify the answer by dividing top and bottom by 5: $\frac{1}{2}$.

3. $\frac{1}{5} + \frac{2}{4}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$ to make it easier. Now the problem is $\frac{1}{5} + \frac{1}{2}$.
* The common denominator for 5 and 2 is 10.
* Convert $\frac{1}{5}$: Multiply by 2 to get $\frac{2}{10}$.
* Convert $\frac{1}{2}$: Multiply by 5 to get $\frac{5}{10}$.
* Add them: $\frac{2}{10} + \frac{5}{10} = \frac{7}{10}$.

4. $\frac{3}{5} + \frac{3}{8}$
* The common denominator for 5 and 8 is 40 ($5 \times 8$).
* Convert $\frac{3}{5}$: Multiply by 8 to get $\frac{24}{40}$.
* Convert $\frac{3}{8}$: Multiply by 5 to get $\frac{15}{40}$.
* Add them: $\frac{24}{40} + \frac{15}{40} = \frac{39}{40}$.

5. $\frac{2}{7} + \frac{1}{4}$
* The common denominator for 7 and 4 is 28 ($7 \times 4$).
* Convert $\frac{2}{7}$: Multiply by 4 to get $\frac{8}{28}$.
* Convert $\frac{1}{4}$: Multiply by 7 to get $\frac{7}{28}$.
* Add them: $\frac{8}{28} + \frac{7}{28} = \frac{15}{28}$.

6. $\frac{3}{5} - \frac{3}{10}$
* The common denominator for 5 and 10 is 10.
* Convert $\frac{3}{5}$: Multiply by 2 to get $\frac{6}{10}$.
* Subtract: $\frac{6}{10} - \frac{3}{10} = \frac{3}{10}$.

7. $\frac{4}{6} - \frac{1}{12}$
* First, simplify $\frac{4}{6}$ to $\frac{2}{3}$. Now the problem is $\frac{2}{3} - \frac{1}{12}$.
* The common denominator for 3 and 12 is 12.
* Convert $\frac{2}{3}$: Multiply by 4 to get $\frac{8}{12}$.
* Subtract: $\frac{8}{12} - \frac{1}{12} = \frac{7}{12}$.

8. $\frac{4}{6} - \frac{1}{2}$
* First, simplify $\frac{4}{6}$ to $\frac{2}{3}$. Now the problem is $\frac{2}{3} - \frac{1}{2}$.
* The common denominator for 3 and 2 is 6.
* Convert $\frac{2}{3}$: Multiply by 2 to get $\frac{4}{6}$.
* Convert $\frac{1}{2}$: Multiply by 3 to get $\frac{3}{6}$.
* Subtract: $\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$.

9. $\frac{3}{4} - \frac{1}{3}$
* The common denominator for 4 and 3 is 12.
* Convert $\frac{3}{4}$: Multiply by 3 to get $\frac{9}{12}$.
* Convert $\frac{1}{3}$: Multiply by 4 to get $\frac{4}{12}$.
* Subtract: $\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$.

10. $\frac{7}{8} - \frac{3}{4}$
* The common denominator for 8 and 4 is 8.
* The first fraction is already $\frac{7}{8}$.
* Convert $\frac{3}{4}$: Multiply by 2 to get $\frac{6}{8}$.
* Subtract: $\frac{7}{8} - \frac{6}{8} = \frac{1}{8}$.

Final Answer:
1. $\frac{7}{6}$ (or $1 \frac{1}{6}$)
2. $\frac{1}{2}$
3. $\frac{7}{10}$
4. $\frac{39}{40}$
5. $\frac{15}{28}$
6. $\frac{3}{10}$
7. $\frac{7}{12}$
8. $\frac{1}{6}$
9. $\frac{5}{12}$
10. $\frac{1}{8}$