Fractions Worksheets -Worksheets Library - Free Printable

Here are the step-by-step solutions for each fraction subtraction problem.

1. $\frac{1}{2} - \frac{1}{11}$
* Find a common denominator for 2 and 11, which is 22.
* Convert $\frac{1}{2}$ to $\frac{11}{22}$.
* Convert $\frac{1}{11}$ to $\frac{2}{22}$.
* Subtract: $\frac{11}{22} - \frac{2}{22} = \frac{9}{22}$.

2. $\frac{4}{6} - \frac{2}{6}$
* The denominators are already the same (6).
* Subtract the numerators: $4 - 2 = 2$.
* Result: $\frac{2}{6}$.
* Simplify by dividing top and bottom by 2: $\frac{1}{3}$.

3. $\frac{1}{3} - \frac{1}{4}$
* Find a common denominator for 3 and 4, which is 12.
* Convert $\frac{1}{3}$ to $\frac{4}{12}$.
* Convert $\frac{1}{4}$ to $\frac{3}{12}$.
* Subtract: $\frac{4}{12} - \frac{3}{12} = \frac{1}{12}$.

4. $\frac{2}{3} - \frac{3}{8}$
* Find a common denominator for 3 and 8, which is 24.
* Convert $\frac{2}{3}$ to $\frac{16}{24}$ ($2 \times 8 = 16$, $3 \times 8 = 24$).
* Convert $\frac{3}{8}$ to $\frac{9}{24}$ ($3 \times 3 = 9$, $8 \times 3 = 24$).
* Subtract: $\frac{16}{24} - \frac{9}{24} = \frac{7}{24}$.

5. $\frac{2}{3} - \frac{1}{4}$
* Find a common denominator for 3 and 4, which is 12.
* Convert $\frac{2}{3}$ to $\frac{8}{12}$.
* Convert $\frac{1}{4}$ to $\frac{3}{12}$.
* Subtract: $\frac{8}{12} - \frac{3}{12} = \frac{5}{12}$.

6. $\frac{4}{6} - \frac{4}{8}$
* First, simplify the fractions if possible. $\frac{4}{6}$ becomes $\frac{2}{3}$. $\frac{4}{8}$ becomes $\frac{1}{2}$.
* New problem: $\frac{2}{3} - \frac{1}{2}$.
* Common denominator for 3 and 2 is 6.
* Convert $\frac{2}{3}$ to $\frac{4}{6}$.
* Convert $\frac{1}{2}$ to $\frac{3}{6}$.
* Subtract: $\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$.

7. $\frac{2}{8} - \frac{1}{8}$
* The denominators are the same (8).
* Subtract the numerators: $2 - 1 = 1$.
* Result: $\frac{1}{8}$.

8. $\frac{2}{4} - \frac{2}{7}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* New problem: $\frac{1}{2} - \frac{2}{7}$.
* Common denominator for 2 and 7 is 14.
* Convert $\frac{1}{2}$ to $\frac{7}{14}$.
* Convert $\frac{2}{7}$ to $\frac{4}{14}$.
* Subtract: $\frac{7}{14} - \frac{4}{14} = \frac{3}{14}$.

9. $\frac{7}{9} - \frac{13}{21}$
* Find the least common denominator for 9 and 21. Multiples of 9: 9, 18, 27, 36, 45, 54, 63... Multiples of 21: 21, 42, 63... The LCD is 63.
* Convert $\frac{7}{9}$: Multiply top and bottom by 7 $\rightarrow \frac{49}{63}$.
* Convert $\frac{13}{21}$: Multiply top and bottom by 3 $\rightarrow \frac{39}{63}$.
* Subtract: $\frac{49}{63} - \frac{39}{63} = \frac{10}{63}$.

10. $\frac{9}{15} - \frac{1}{2}$
* First, simplify $\frac{9}{15}$ by dividing top and bottom by 3 $\rightarrow \frac{3}{5}$.
* New problem: $\frac{3}{5} - \frac{1}{2}$.
* Common denominator for 5 and 2 is 10.
* Convert $\frac{3}{5}$ to $\frac{6}{10}$.
* Convert $\frac{1}{2}$ to $\frac{5}{10}$.
* Subtract: $\frac{6}{10} - \frac{5}{10} = \frac{1}{10}$.

Final Answer:
1. $\frac{9}{22}$
2. $\frac{1}{3}$
3. $\frac{1}{12}$
4. $\frac{7}{24}$
5. $\frac{5}{12}$
6. $\frac{1}{6}$
7. $\frac{1}{8}$
8. $\frac{3}{14}$
9. $\frac{10}{63}$
10. $\frac{1}{10}$