Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Let's solve each of these problems step by step. The key to adding or subtracting fractions with unlike denominators is to find a common denominator, usually the least common denominator (LCD), then convert each fraction so they have the same denominator, and finally add or subtract the numerators.

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🔷 Problem 1:

$\frac{4}{3} + \frac{2}{5}$

- LCD of 3 and 5 is 15
- Convert:
- $\frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15}$
- $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$
- Add: $\frac{20}{15} + \frac{6}{15} = \frac{26}{15}$
- Simplify: $\frac{26}{15} = 1\frac{11}{15}$

✔ Answer: $1\frac{11}{15}$

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🔷 Problem 2:

$\frac{7}{10} - \frac{2}{5}$

- LCD of 10 and 5 is 10
- Convert:
- $\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$
- Subtract: $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$

✔ Answer: $\frac{3}{10}$

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🔷 Problem 3:

$\frac{5}{9} + \frac{2}{7}$

- LCD of 9 and 7 is 63
- Convert:
- $\frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63}$
- $\frac{2}{7} = \frac{2 \times 9}{7 \times 9} = \frac{18}{63}$
- Add: $\frac{35}{63} + \frac{18}{63} = \frac{53}{63}$

✔ Answer: $\frac{53}{63}$

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🔷 Problem 4:

$\frac{4}{8} - \frac{1}{4}$

- Simplify $\frac{4}{8} = \frac{1}{2}$
- LCD of 2 and 4 is 4
- Convert:
- $\frac{1}{2} = \frac{2}{4}$
- Subtract: $\frac{2}{4} - \frac{1}{4} = \frac{1}{4}$

✔ Answer: $\frac{1}{4}$

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🔷 Problem 5:

$\frac{3}{9} + \frac{1}{3}$

- Simplify $\frac{3}{9} = \frac{1}{3}$
- So: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

✔ Answer: $\frac{2}{3}$

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🔷 Problem 6:

$\frac{2}{5} + \frac{1}{10}$

- LCD of 5 and 10 is 10
- Convert:
- $\frac{2}{5} = \frac{4}{10}$
- Add: $\frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$

✔ Answer: $\frac{1}{2}$

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🔷 Problem 7:

$\frac{4}{5} + \frac{9}{10}$

- LCD of 5 and 10 is 10
- Convert:
- $\frac{4}{5} = \frac{8}{10}$
- Add: $\frac{8}{10} + \frac{9}{10} = \frac{17}{10} = 1\frac{7}{10}$

✔ Answer: $1\frac{7}{10}$

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🔷 Problem 8:

$\frac{4}{6} - \frac{1}{3}$

- Simplify $\frac{4}{6} = \frac{2}{3}$
- $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$

✔ Answer: $\frac{1}{3}$

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🔷 Problem 9:

$\frac{3}{12} + \frac{2}{4}$

- Simplify:
- $\frac{3}{12} = \frac{1}{4}$
- $\frac{2}{4} = \frac{1}{2}$
- LCD of 4 and 2 is 4
- Convert: $\frac{1}{2} = \frac{2}{4}$
- Add: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$

✔ Answer: $\frac{3}{4}$

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🔷 Problem 10:

$\frac{5}{12} - \frac{1}{6}$

- LCD of 12 and 6 is 12
- Convert: $\frac{1}{6} = \frac{2}{12}$
- Subtract: $\frac{5}{12} - \frac{2}{12} = \frac{3}{12} = \frac{1}{4}$

✔ Answer: $\frac{1}{4}$

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🔷 Problem 11:

$\frac{2}{8} + \frac{3}{9}$

- Simplify:
- $\frac{2}{8} = \frac{1}{4}$
- $\frac{3}{9} = \frac{1}{3}$
- LCD of 4 and 3 is 12
- Convert:
- $\frac{1}{4} = \frac{3}{12}$
- $\frac{1}{3} = \frac{4}{12}$
- Add: $\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$

✔ Answer: $\frac{7}{12}$

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🔷 Problem 12:

$\frac{1}{4} - \frac{1}{8}$

- LCD of 4 and 8 is 8
- Convert: $\frac{1}{4} = \frac{2}{8}$
- Subtract: $\frac{2}{8} - \frac{1}{8} = \frac{1}{8}$

✔ Answer: $\frac{1}{8}$

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🔷 Problem 13:

$\frac{6}{7} + \frac{2}{6}$

- Simplify $\frac{2}{6} = \frac{1}{3}$
- LCD of 7 and 3 is 21
- Convert:
- $\frac{6}{7} = \frac{18}{21}$
- $\frac{1}{3} = \frac{7}{21}$
- Add: $\frac{18}{21} + \frac{7}{21} = \frac{25}{21} = 1\frac{4}{21}$

✔ Answer: $1\frac{4}{21}$

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🔷 Problem 14:

$\frac{1}{3} - \frac{1}{7}$

- LCD of 3 and 7 is 21
- Convert:
- $\frac{1}{3} = \frac{7}{21}$
- $\frac{1}{7} = \frac{3}{21}$
- Subtract: $\frac{7}{21} - \frac{3}{21} = \frac{4}{21}$

✔ Answer: $\frac{4}{21}$

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🔷 Problem 15:

$\frac{7}{8} + \frac{4}{5}$

- LCD of 8 and 5 is 40
- Convert:
- $\frac{7}{8} = \frac{35}{40}$
- $\frac{4}{5} = \frac{32}{40}$
- Add: $\frac{35}{40} + \frac{32}{40} = \frac{67}{40} = 1\frac{27}{40}$

✔ Answer: $1\frac{27}{40}$

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## ✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | $1\frac{11}{15}$ |
| 2 | $\frac{3}{10}$ |
| 3 | $\frac{53}{63}$ |
| 4 | $\frac{1}{4}$ |
| 5 | $\frac{2}{3}$ |
| 6 | $\frac{1}{2}$ |
| 7 | $1\frac{7}{10}$ |
| 8 | $\frac{1}{3}$ |
| 9 | $\frac{3}{4}$ |
|10 | $\frac{1}{4}$ |
|11 | $\frac{7}{12}$ |
|12 | $\frac{1}{8}$ |
|13 | $1\frac{4}{21}$ |
|14 | $\frac{4}{21}$ |
|15 | $1\frac{27}{40}$ |

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