Subtracting Fractions worksheet with 10 equations to solve, ideal for math practice.

To subtract fractions with different denominators, we need to find a common denominator. This means finding a number that both bottom numbers (denominators) can divide into evenly. Once the denominators are the same, we subtract the top numbers (numerators) and keep the bottom number the same. Finally, we simplify the fraction if possible.

Here is the step-by-step solution for each problem:

1. $\frac{4}{9} - \frac{2}{5}$
* The least common multiple for 9 and 5 is 45.
* Convert $\frac{4}{9}$: Multiply top and bottom by 5 $\rightarrow \frac{20}{45}$
* Convert $\frac{2}{5}$: Multiply top and bottom by 9 $\rightarrow \frac{18}{45}$
* Subtract: $\frac{20}{45} - \frac{18}{45} = \frac{2}{45}$

2. $\frac{3}{4} - \frac{1}{5}$
* The least common multiple for 4 and 5 is 20.
* Convert $\frac{3}{4}$: Multiply top and bottom by 5 $\rightarrow \frac{15}{20}$
* Convert $\frac{1}{5}$: Multiply top and bottom by 4 $\rightarrow \frac{4}{20}$
* Subtract: $\frac{15}{20} - \frac{4}{20} = \frac{11}{20}$

3. $\frac{3}{4} - \frac{2}{5}$
* The least common multiple for 4 and 5 is 20.
* Convert $\frac{3}{4}$: Multiply top and bottom by 5 $\rightarrow \frac{15}{20}$
* Convert $\frac{2}{5}$: Multiply top and bottom by 4 $\rightarrow \frac{8}{20}$
* Subtract: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$

4. $\frac{5}{9} - \frac{1}{3}$
* The least common multiple for 9 and 3 is 9.
* $\frac{5}{9}$ stays the same.
* Convert $\frac{1}{3}$: Multiply top and bottom by 3 $\rightarrow \frac{3}{9}$
* Subtract: $\frac{5}{9} - \frac{3}{9} = \frac{2}{9}$

5. $\frac{2}{3} - \frac{1}{5}$
* The least common multiple for 3 and 5 is 15.
* Convert $\frac{2}{3}$: Multiply top and bottom by 5 $\rightarrow \frac{10}{15}$
* Convert $\frac{1}{5}$: Multiply top and bottom by 3 $\rightarrow \frac{3}{15}$
* Subtract: $\frac{10}{15} - \frac{3}{15} = \frac{7}{15}$

6. $\frac{1}{2} - \frac{2}{7}$
* The least common multiple for 2 and 7 is 14.
* Convert $\frac{1}{2}$: Multiply top and bottom by 7 $\rightarrow \frac{7}{14}$
* Convert $\frac{2}{7}$: Multiply top and bottom by 2 $\rightarrow \frac{4}{14}$
* Subtract: $\frac{7}{14} - \frac{4}{14} = \frac{3}{14}$

7. $\frac{3}{4} - \frac{2}{6}$
* First, simplify $\frac{2}{6}$ to $\frac{1}{3}$ to make it easier. Now solve $\frac{3}{4} - \frac{1}{3}$.
* The least common multiple for 4 and 3 is 12.
* Convert $\frac{3}{4}$: Multiply top and bottom by 3 $\rightarrow \frac{9}{12}$
* Convert $\frac{1}{3}$: Multiply top and bottom by 4 $\rightarrow \frac{4}{12}$
* Subtract: $\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$

8. $\frac{2}{4} - \frac{3}{16}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$. Now solve $\frac{1}{2} - \frac{3}{16}$.
* The least common multiple for 2 and 16 is 16.
* Convert $\frac{1}{2}$: Multiply top and bottom by 8 $\rightarrow \frac{8}{16}$
* $\frac{3}{16}$ stays the same.
* Subtract: $\frac{8}{16} - \frac{3}{16} = \frac{5}{16}$

9. $\frac{6}{8} - \frac{1}{4}$
* First, simplify $\frac{6}{8}$ to $\frac{3}{4}$. Now solve $\frac{3}{4} - \frac{1}{4}$.
* The denominators are already the same.
* Subtract: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.

10. $\frac{1}{3} - \frac{1}{6}$
* The least common multiple for 3 and 6 is 6.
* Convert $\frac{1}{3}$: Multiply top and bottom by 2 $\rightarrow \frac{2}{6}$
* $\frac{1}{6}$ stays the same.
* Subtract: $\frac{2}{6} - \frac{1}{6} = \frac{1}{6}$

Final Answer:
1. $\frac{2}{45}$
2. $\frac{11}{20}$
3. $\frac{7}{20}$
4. $\frac{2}{9}$
5. $\frac{7}{15}$
6. $\frac{3}{14}$
7. $\frac{5}{12}$
8. $\frac{5}{16}$
9. $\frac{1}{2}$
10. $\frac{1}{6}$