Subtracting Fractions Worksheet with 10 Problems for Practice

To solve the given problems involving subtracting fractions, we need to follow these steps:

1. Find a Common Denominator: If the denominators of the fractions are different, we need to find a common denominator so that we can subtract the numerators directly.
2. Adjust the Fractions: Rewrite each fraction with the common denominator.
3. Subtract the Numerators: Subtract the numerators while keeping the common denominator.
4. Simplify the Result: Simplify the resulting fraction if possible.

Let's solve each problem step by step.

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Problem 1: $\frac{3}{4} - \frac{2}{9}$

- Step 1: Find the least common denominator (LCD) of 4 and 9. The LCD is 36.
- Step 2: Rewrite each fraction with the denominator 36:
$$
\frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36}, \quad \frac{2}{9} = \frac{2 \times 4}{9 \times 4} = \frac{8}{36}
$$
- Step 3: Subtract the numerators:
$$
\frac{27}{36} - \frac{8}{36} = \frac{27 - 8}{36} = \frac{19}{36}
$$
- Step 4: The fraction $\frac{19}{36}$ is already in simplest form.
- Answer: $\boxed{\frac{19}{36}}$

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Problem 2: $\frac{5}{8} - \frac{1}{2}$

- Step 1: Find the LCD of 8 and 2. The LCD is 8.
- Step 2: Rewrite each fraction with the denominator 8:
$$
\frac{5}{8} = \frac{5}{8}, \quad \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
$$
- Step 3: Subtract the numerators:
$$
\frac{5}{8} - \frac{4}{8} = \frac{5 - 4}{8} = \frac{1}{8}
$$
- Step 4: The fraction $\frac{1}{8}$ is already in simplest form.
- Answer: $\boxed{\frac{1}{8}}$

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Problem 3: $\frac{1}{6} - \frac{1}{7}$

- Step 1: Find the LCD of 6 and 7. The LCD is 42.
- Step 2: Rewrite each fraction with the denominator 42:
$$
\frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42}, \quad \frac{1}{7} = \frac{1 \times 6}{7 \times 6} = \frac{6}{42}
$$
- Step 3: Subtract the numerators:
$$
\frac{7}{42} - \frac{6}{42} = \frac{7 - 6}{42} = \frac{1}{42}
$$
- Step 4: The fraction $\frac{1}{42}$ is already in simplest form.
- Answer: $\boxed{\frac{1}{42}}$

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Problem 4: $\frac{7}{8} - \frac{1}{4}$

- Step 1: Find the LCD of 8 and 4. The LCD is 8.
- Step 2: Rewrite each fraction with the denominator 8:
$$
\frac{7}{8} = \frac{7}{8}, \quad \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
$$
- Step 3: Subtract the numerators:
$$
\frac{7}{8} - \frac{2}{8} = \frac{7 - 2}{8} = \frac{5}{8}
$$
- Step 4: The fraction $\frac{5}{8}$ is already in simplest form.
- Answer: $\boxed{\frac{5}{8}}$

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Problem 5: $\frac{6}{10} - \frac{2}{5}$

- Step 1: Find the LCD of 10 and 5. The LCD is 10.
- Step 2: Rewrite each fraction with the denominator 10:
$$
\frac{6}{10} = \frac{6}{10}, \quad \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
$$
- Step 3: Subtract the numerators:
$$
\frac{6}{10} - \frac{4}{10} = \frac{6 - 4}{10} = \frac{2}{10}
$$
- Step 4: Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
- Answer: $\boxed{\frac{1}{5}}$

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Problem 6: $\frac{9}{10} - \frac{1}{3}$

- Step 1: Find the LCD of 10 and 3. The LCD is 30.
- Step 2: Rewrite each fraction with the denominator 30:
$$
\frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30}, \quad \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}
$$
- Step 3: Subtract the numerators:
$$
\frac{27}{30} - \frac{10}{30} = \frac{27 - 10}{30} = \frac{17}{30}
$$
- Step 4: The fraction $\frac{17}{30}$ is already in simplest form.
- Answer: $\boxed{\frac{17}{30}}$

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Problem 7: $\frac{6}{7} - \frac{3}{14}$

- Step 1: Find the LCD of 7 and 14. The LCD is 14.
- Step 2: Rewrite each fraction with the denominator 14:
$$
\frac{6}{7} = \frac{6 \times 2}{7 \times 2} = \frac{12}{14}, \quad \frac{3}{14} = \frac{3}{14}
$$
- Step 3: Subtract the numerators:
$$
\frac{12}{14} - \frac{3}{14} = \frac{12 - 3}{14} = \frac{9}{14}
$$
- Step 4: The fraction $\frac{9}{14}$ is already in simplest form.
- Answer: $\boxed{\frac{9}{14}}$

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Problem 8: $\frac{16}{30} - \frac{9}{20}$

- Step 1: Find the LCD of 30 and 20. The LCD is 60.
- Step 2: Rewrite each fraction with the denominator 60:
$$
\frac{16}{30} = \frac{16 \times 2}{30 \times 2} = \frac{32}{60}, \quad \frac{9}{20} = \frac{9 \times 3}{20 \times 3} = \frac{27}{60}
$$
- Step 3: Subtract the numerators:
$$
\frac{32}{60} - \frac{27}{60} = \frac{32 - 27}{60} = \frac{5}{60}
$$
- Step 4: Simplify $\frac{5}{60}$ to $\frac{1}{12}$.
- Answer: $\boxed{\frac{1}{12}}$

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Problem 9: $\frac{1}{6} - \frac{3}{20}$

- Step 1: Find the LCD of 6 and 20. The LCD is 60.
- Step 2: Rewrite each fraction with the denominator 60:
$$
\frac{1}{6} = \frac{1 \times 10}{6 \times 10} = \frac{10}{60}, \quad \frac{3}{20} = \frac{3 \times 3}{20 \times 3} = \frac{9}{60}
$$
- Step 3: Subtract the numerators:
$$
\frac{10}{60} - \frac{9}{60} = \frac{10 - 9}{60} = \frac{1}{60}
$$
- Step 4: The fraction $\frac{1}{60}$ is already in simplest form.
- Answer: $\boxed{\frac{1}{60}}$

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Problem 10: $\frac{8}{9} - \frac{13}{21}$

- Step 1: Find the LCD of 9 and 21. The LCD is 63.
- Step 2: Rewrite each fraction with the denominator 63:
$$
\frac{8}{9} = \frac{8 \times 7}{9 \times 7} = \frac{56}{63}, \quad \frac{13}{21} = \frac{13 \times 3}{21 \times 3} = \frac{39}{63}
$$
- Step 3: Subtract the numerators:
$$
\frac{56}{63} - \frac{39}{63} = \frac{56 - 39}{63} = \frac{17}{63}
$$
- Step 4: The fraction $\frac{17}{63}$ is already in simplest form.
- Answer: $\boxed{\frac{17}{63}}$

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Final Answers:

1. $\boxed{\frac{19}{36}}$
2. $\boxed{\frac{1}{8}}$
3. $\boxed{\frac{1}{42}}$
4. $\boxed{\frac{5}{8}}$
5. $\boxed{\frac{1}{5}}$
6. $\boxed{\frac{17}{30}}$
7. $\boxed{\frac{9}{14}}$
8. $\boxed{\frac{1}{12}}$
9. $\boxed{\frac{1}{60}}$
10. $\boxed{\frac{17}{63}}$