Subtracting Fractions Different Denominator Worksheet - Have Fun ... - Free Printable

Here are the step-by-step solutions for each subtraction problem. Remember, to subtract fractions, you must first make the bottom numbers (denominators) the same by finding a common denominator.

1. $\frac{6}{8} - \frac{2}{3}$
* Find the least common denominator for 8 and 3, which is 24.
* Convert $\frac{6}{8}$: Multiply top and bottom by 3 $\rightarrow$ $\frac{18}{24}$.
* Convert $\frac{2}{3}$: Multiply top and bottom by 8 $\rightarrow$ $\frac{16}{24}$.
* Subtract: $\frac{18}{24} - \frac{16}{24} = \frac{2}{24}$.
* Simplify: Divide top and bottom by 2 $\rightarrow$ $\frac{1}{12}$.

2. $\frac{7}{10} - \frac{4}{8}$
* Find the least common denominator for 10 and 8, which is 40.
* Convert $\frac{7}{10}$: Multiply top and bottom by 4 $\rightarrow$ $\frac{28}{40}$.
* Convert $\frac{4}{8}$: Multiply top and bottom by 5 $\rightarrow$ $\frac{20}{40}$.
* Subtract: $\frac{28}{40} - \frac{20}{40} = \frac{8}{40}$.
* Simplify: Divide top and bottom by 8 $\rightarrow$ $\frac{1}{5}$.

3. $\frac{6}{7} - \frac{7}{4}$
* Find the least common denominator for 7 and 4, which is 28.
* Convert $\frac{6}{7}$: Multiply top and bottom by 4 $\rightarrow$ $\frac{24}{28}$.
* Convert $\frac{7}{4}$: Multiply top and bottom by 7 $\rightarrow$ $\frac{49}{28}$.
* Subtract: $\frac{24}{28} - \frac{49}{28} = -\frac{25}{28}$.
* Answer: $-\frac{25}{28}$

4. $\frac{8}{14} - \frac{2}{8}$
* First, simplify the fractions if possible. $\frac{8}{14}$ becomes $\frac{4}{7}$ and $\frac{2}{8}$ becomes $\frac{1}{4}$.
* Find the least common denominator for 7 and 4, which is 28.
* Convert $\frac{4}{7}$: Multiply top and bottom by 4 $\rightarrow$ $\frac{16}{28}$.
* Convert $\frac{1}{4}$: Multiply top and bottom by 7 $\rightarrow$ $\frac{7}{28}$.
* Subtract: $\frac{16}{28} - \frac{7}{28} =$ $\frac{9}{28}$.

5. $\frac{6}{12} - \frac{3}{6}$
* Notice that $\frac{6}{12}$ is equal to $\frac{1}{2}$ and $\frac{3}{6}$ is also equal to $\frac{1}{2}$.
* Subtract: $\frac{1}{2} - \frac{1}{2} =$ $0$.
* *(Alternatively using LCD 12: $\frac{6}{12} - \frac{6}{12} = 0$)*

6. $\frac{4}{7} - \frac{2}{6}$
* Find the least common denominator for 7 and 6, which is 42.
* Convert $\frac{4}{7}$: Multiply top and bottom by 6 $\rightarrow$ $\frac{24}{42}$.
* Convert $\frac{2}{6}$: Multiply top and bottom by 7 $\rightarrow$ $\frac{14}{42}$.
* Subtract: $\frac{24}{42} - \frac{14}{42} = \frac{10}{42}$.
* Simplify: Divide top and bottom by 2 $\rightarrow$ $\frac{5}{21}$.

7. $\frac{8}{13} - \frac{7}{13}$
* The denominators are already the same (13).
* Subtract the numerators: $8 - 7 = 1$.
* Answer: $\frac{1}{13}$.

8. $\frac{5}{10} - \frac{6}{15}$
* Simplify first: $\frac{5}{10} = \frac{1}{2}$ and $\frac{6}{15} = \frac{2}{5}$.
* Find the least common denominator for 2 and 5, which is 10.
* Convert $\frac{1}{2}$: Multiply top and bottom by 5 $\rightarrow$ $\frac{5}{10}$.
* Convert $\frac{2}{5}$: Multiply top and bottom by 2 $\rightarrow$ $\frac{4}{10}$.
* Subtract: $\frac{5}{10} - \frac{4}{10} =$ $\frac{1}{10}$.

9. $\frac{9}{17} - \frac{3}{12}$
* Simplify $\frac{3}{12}$ to $\frac{1}{4}$.
* Find the least common denominator for 17 and 4, which is 68.
* Convert $\frac{9}{17}$: Multiply top and bottom by 4 $\rightarrow$ $\frac{36}{68}$.
* Convert $\frac{1}{4}$: Multiply top and bottom by 17 $\rightarrow$ $\frac{17}{68}$.
* Subtract: $\frac{36}{68} - \frac{17}{68} =$ $\frac{19}{68}$.

10. $\frac{4}{10} - \frac{1}{30}$
* The common denominator is 30.
* Convert $\frac{4}{10}$: Multiply top and bottom by 3 $\rightarrow$ $\frac{12}{30}$.
* Keep $\frac{1}{30}$ as is.
* Subtract: $\frac{12}{30} - \frac{1}{30} =$ $\frac{11}{30}$.

Final Answer:
1. $\frac{1}{12}$
2. $\frac{1}{5}$
3. $-\frac{25}{28}$
4. $\frac{9}{28}$
5. $0$
6. $\frac{5}{21}$
7. $\frac{1}{13}$
8. $\frac{1}{10}$
9. $\frac{19}{68}$
10. $\frac{11}{30}$