Math worksheet for practicing addition and subtraction of fractions with unlike denominators.

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

1) $\frac{4}{3} + \frac{2}{5}$
* The common denominator for 3 and 5 is 15.
* Convert $\frac{4}{3}$: multiply top and bottom by 5 $\rightarrow \frac{20}{15}$.
* Convert $\frac{2}{5}$: multiply top and bottom by 3 $\rightarrow \frac{6}{15}$.
* Add them: $\frac{20}{15} + \frac{6}{15} = \frac{26}{15}$.
* This can be written as the mixed number $1 \frac{11}{15}$.

2) $\frac{7}{10} - \frac{2}{5}$
* The common denominator for 10 and 5 is 10.
* $\frac{7}{10}$ stays the same.
* Convert $\frac{2}{5}$: multiply top and bottom by 2 $\rightarrow \frac{4}{10}$.
* Subtract: $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$.

3) $\frac{5}{9} + \frac{2}{7}$
* The common denominator for 9 and 7 is 63 ($9 \times 7$).
* Convert $\frac{5}{9}$: multiply by 7 $\rightarrow \frac{35}{63}$.
* Convert $\frac{2}{7}$: multiply by 9 $\rightarrow \frac{18}{63}$.
* Add them: $\frac{35}{63} + \frac{18}{63} = \frac{53}{63}$.

4) $\frac{4}{8} - \frac{1}{4}$
* Notice that $\frac{4}{8}$ simplifies to $\frac{1}{2}$, but let's use 8 as the common denominator.
* $\frac{4}{8}$ stays the same.
* Convert $\frac{1}{4}$: multiply by 2 $\rightarrow \frac{2}{8}$.
* Subtract: $\frac{4}{8} - \frac{2}{8} = \frac{2}{8}$.
* Simplify the answer: $\frac{2}{8} = \frac{1}{4}$.

5) $\frac{3}{9} + \frac{1}{3}$
* The common denominator is 9.
* $\frac{3}{9}$ stays the same.
* Convert $\frac{1}{3}$: multiply by 3 $\rightarrow \frac{3}{9}$.
* Add them: $\frac{3}{9} + \frac{3}{9} = \frac{6}{9}$.
* Simplify the answer (divide by 3): $\frac{2}{3}$.

6) $\frac{2}{5} + \frac{1}{10}$
* The common denominator is 10.
* Convert $\frac{2}{5}$: multiply by 2 $\rightarrow \frac{4}{10}$.
* $\frac{1}{10}$ stays the same.
* Add them: $\frac{4}{10} + \frac{1}{10} = \frac{5}{10}$.
* Simplify the answer: $\frac{1}{2}$.

7) $\frac{4}{5} + \frac{9}{10}$
* The common denominator is 10.
* Convert $\frac{4}{5}$: multiply by 2 $\rightarrow \frac{8}{10}$.
* $\frac{9}{10}$ stays the same.
* Add them: $\frac{8}{10} + \frac{9}{10} = \frac{17}{10}$.
* Mixed number: $1 \frac{7}{10}$.

8) $\frac{4}{6} - \frac{1}{3}$
* The common denominator is 6.
* $\frac{4}{6}$ stays the same.
* Convert $\frac{1}{3}$: multiply by 2 $\rightarrow \frac{2}{6}$.
* Subtract: $\frac{4}{6} - \frac{2}{6} = \frac{2}{6}$.
* Simplify the answer: $\frac{1}{3}$.

9) $\frac{3}{12} + \frac{2}{4}$
* The common denominator is 12.
* $\frac{3}{12}$ stays the same.
* Convert $\frac{2}{4}$: multiply by 3 $\rightarrow \frac{6}{12}$.
* Add them: $\frac{3}{12} + \frac{6}{12} = \frac{9}{12}$.
* Simplify the answer (divide by 3): $\frac{3}{4}$.

10) $\frac{5}{12} - \frac{1}{6}$
* The common denominator is 12.
* $\frac{5}{12}$ stays the same.
* Convert $\frac{1}{6}$: multiply by 2 $\rightarrow \frac{2}{12}$.
* Subtract: $\frac{5}{12} - \frac{2}{12} = \frac{3}{12}$.
* Simplify the answer: $\frac{1}{4}$.

11) $\frac{2}{8} + \frac{3}{9}$
* First, simplify the fractions to make it easier: $\frac{2}{8} = \frac{1}{4}$ and $\frac{3}{9} = \frac{1}{3}$.
* Now solve $\frac{1}{4} + \frac{1}{3}$. Common denominator is 12.
* $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
* Add them: $\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$.

12) $\frac{1}{4} - \frac{1}{8}$
* The common denominator is 8.
* Convert $\frac{1}{4}$: multiply by 2 $\rightarrow \frac{2}{8}$.
* $\frac{1}{8}$ stays the same.
* Subtract: $\frac{2}{8} - \frac{1}{8} = \frac{1}{8}$.

13) $\frac{6}{7} + \frac{2}{6}$
* First simplify $\frac{2}{6}$ to $\frac{1}{3}$. So we have $\frac{6}{7} + \frac{1}{3}$.
* Common denominator for 7 and 3 is 21.
* Convert $\frac{6}{7}$: multiply by 3 $\rightarrow \frac{18}{21}$.
* Convert $\frac{1}{3}$: multiply by 7 $\rightarrow \frac{7}{21}$.
* Add them: $\frac{18}{21} + \frac{7}{21} = \frac{25}{21}$.
* Mixed number: $1 \frac{4}{21}$.

14) $\frac{1}{3} - \frac{1}{7}$
* Common denominator for 3 and 7 is 21.
* Convert $\frac{1}{3}$: multiply by 7 $\rightarrow \frac{7}{21}$.
* Convert $\frac{1}{7}$: multiply by 3 $\rightarrow \frac{3}{21}$.
* Subtract: $\frac{7}{21} - \frac{3}{21} = \frac{4}{21}$.

15) $\frac{7}{8} + \frac{4}{5}$
* Common denominator for 8 and 5 is 40.
* Convert $\frac{7}{8}$: multiply by 5 $\rightarrow \frac{35}{40}$.
* Convert $\frac{4}{5}$: multiply by 8 $\rightarrow \frac{32}{40}$.
* Add them: $\frac{35}{40} + \frac{32}{40} = \frac{67}{40}$.
* Mixed number: $1 \frac{27}{40}$.

Final Answer:
1) $\frac{26}{15}$ or $1 \frac{11}{15}$
2) $\frac{3}{10}$
3) $\frac{53}{63}$
4) $\frac{1}{4}$
5) $\frac{2}{3}$
6) $\frac{1}{2}$
7) $\frac{17}{10}$ or $1 \frac{7}{10}$
8) $\frac{1}{3}$
9) $\frac{3}{4}$
10) $\frac{1}{4}$
11) $\frac{7}{12}$
12) $\frac{1}{8}$
13) $\frac{25}{21}$ or $1 \frac{4}{21}$
14) $\frac{4}{21}$
15) $\frac{67}{40}$ or $1 \frac{27}{40}$