Adding and Subtracting Unlike Denominators worksheet - Free Printable

Let's solve each of these fraction addition problems step by step. The key to adding fractions is to have a common denominator. If the denominators are different, we find the least common denominator (LCD), convert each fraction, and then add.

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1. $\frac{1}{3} + \frac{2}{6}$

- Simplify $\frac{2}{6} = \frac{1}{3}$
- Now: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

✔ Answer: $\boxed{\frac{2}{3}}$

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2. $\frac{3}{12} + \frac{4}{24}$

- Simplify both:
- $\frac{3}{12} = \frac{1}{4}$
- $\frac{4}{24} = \frac{1}{6}$
- LCD of 4 and 6 is 12
- Convert:
- $\frac{1}{4} = \frac{3}{12}$
- $\frac{1}{6} = \frac{2}{12}$
- Add: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

✔ Answer: $\boxed{\frac{5}{12}}$

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3. $\frac{1}{2} + \frac{4}{8}$

- Simplify $\frac{4}{8} = \frac{1}{2}$
- So: $\frac{1}{2} + \frac{1}{2} = 1$

✔ Answer: $\boxed{1}$

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4. $\frac{1}{7} + \frac{2}{21}$

- LCD of 7 and 21 is 21
- Convert $\frac{1}{7} = \frac{3}{21}$
- $\frac{3}{21} + \frac{2}{21} = \frac{5}{21}$

✔ Answer: $\boxed{\frac{5}{21}}$

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5. $\frac{2}{5} + \frac{3}{10}$

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

✔ Answer: $\boxed{\frac{7}{10}}$

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6. $\frac{1}{4} + \frac{3}{8}$

- LCD of 4 and 8 is 8
- Convert $\frac{1}{4} = \frac{2}{8}$
- $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$

✔ Answer: $\boxed{\frac{5}{8}}$

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7. $\frac{1}{2} + \frac{2}{6}$

- Simplify $\frac{2}{6} = \frac{1}{3}$
- LCD of 2 and 3 is 6
- Convert:
- $\frac{1}{2} = \frac{3}{6}$
- $\frac{1}{3} = \frac{2}{6}$
- $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

✔ Answer: $\boxed{\frac{5}{6}}$

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8. $\frac{2}{9} + \frac{3}{18}$

- Simplify $\frac{3}{18} = \frac{1}{6}$
- LCD of 9 and 6 is 18
- Convert:
- $\frac{2}{9} = \frac{4}{18}$
- $\frac{1}{6} = \frac{3}{18}$
- $\frac{4}{18} + \frac{3}{18} = \frac{7}{18}$

✔ Answer: $\boxed{\frac{7}{18}}$

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9. $\frac{2}{10} + \frac{5}{20}$

- Simplify:
- $\frac{2}{10} = \frac{1}{5}$
- $\frac{5}{20} = \frac{1}{4}$
- LCD of 5 and 4 is 20
- Convert:
- $\frac{1}{5} = \frac{4}{20}$
- $\frac{1}{4} = \frac{5}{20}$
- $\frac{4}{20} + \frac{5}{20} = \frac{9}{20}$

✔ Answer: $\boxed{\frac{9}{20}}$

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10. $\frac{1}{4} + \frac{2}{24}$

- Simplify $\frac{2}{24} = \frac{1}{12}$
- LCD of 4 and 12 is 12
- Convert $\frac{1}{4} = \frac{3}{12}$
- $\frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$

✔ Answer: $\boxed{\frac{1}{3}}$

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✔ Final Answers:

1. $\frac{2}{3}$
2. $\frac{5}{12}$
3. $1$
4. $\frac{5}{21}$
5. $\frac{7}{10}$
6. $\frac{5}{8}$
7. $\frac{5}{6}$
8. $\frac{7}{18}$
9. $\frac{9}{20}$
10. $\frac{1}{3}$

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