Fraction addition worksheet with unlike denominators for practice.

Let's solve each of these fraction addition problems step by step. The key concept is adding fractions with unlike denominators, which requires finding a common denominator (preferably the least common denominator, or LCD), converting each fraction to an equivalent one with that denominator, and then adding the numerators.

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Step-by-step Solution:

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

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

✔ Answer: $\boxed{\frac{9}{10}}$

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2) $\frac{4}{9} + \frac{3}{12}$

- Simplify $\frac{3}{12} = \frac{1}{4}$
- LCD of 9 and 4 is 36
- $\frac{4}{9} = \frac{16}{36}$, $\frac{1}{4} = \frac{9}{36}$
- $\frac{16}{36} + \frac{9}{36} = \frac{25}{36}$

✔ Answer: $\boxed{\frac{25}{36}}$

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3) $\frac{1}{4} + \frac{3}{5}$

- LCD of 4 and 5 is 20
- $\frac{1}{4} = \frac{5}{20}$, $\frac{3}{5} = \frac{12}{20}$
- $\frac{5}{20} + \frac{12}{20} = \frac{17}{20}$

✔ Answer: $\boxed{\frac{17}{20}}$

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4) $\frac{2}{5} + \frac{1}{3}$

- LCD of 5 and 3 is 15
- $\frac{2}{5} = \frac{6}{15}$, $\frac{1}{3} = \frac{5}{15}$
- $\frac{6}{15} + \frac{5}{15} = \frac{11}{15}$

✔ Answer: $\boxed{\frac{11}{15}}$

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

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

✔ Answer: $\boxed{\frac{7}{10}}$

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6) $\frac{5}{14} + \frac{3}{7}$

- LCD of 14 and 7 is 14
- $\frac{3}{7} = \frac{6}{14}$
- $\frac{5}{14} + \frac{6}{14} = \frac{11}{14}$

✔ Answer: $\boxed{\frac{11}{14}}$

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7) $\frac{5}{9} + \frac{1}{3}$

- LCD of 9 and 3 is 9
- $\frac{1}{3} = \frac{3}{9}$
- $\frac{5}{9} + \frac{3}{9} = \frac{8}{9}$

✔ Answer: $\boxed{\frac{8}{9}}$

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8) $\frac{1}{6} + \frac{2}{9}$

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

✔ Answer: $\boxed{\frac{7}{18}}$

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9) $\frac{5}{15} + \frac{3}{5}$

- Simplify $\frac{5}{15} = \frac{1}{3}$
- LCD of 3 and 5 is 15
- $\frac{1}{3} = \frac{5}{15}$, $\frac{3}{5} = \frac{9}{15}$
- $\frac{5}{15} + \frac{9}{15} = \frac{14}{15}$

✔ Answer: $\boxed{\frac{14}{15}}$

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10) $\frac{3}{9} + \frac{1}{5}$

- Simplify $\frac{3}{9} = \frac{1}{3}$
- LCD of 3 and 5 is 15
- $\frac{1}{3} = \frac{5}{15}$, $\frac{1}{5} = \frac{3}{15}$
- $\frac{5}{15} + \frac{3}{15} = \frac{8}{15}$

✔ Answer: $\boxed{\frac{8}{15}}$

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11) $\frac{4}{10} + \frac{7}{20}$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- LCD of 5 and 20 is 20
- $\frac{2}{5} = \frac{8}{20}$
- $\frac{8}{20} + \frac{7}{20} = \frac{15}{20} = \frac{3}{4}$

✔ Answer: $\boxed{\frac{3}{4}}$

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12) $\frac{3}{10} + \frac{2}{15}$

- LCD of 10 and 15 is 30
- $\frac{3}{10} = \frac{9}{30}$, $\frac{2}{15} = \frac{4}{30}$
- $\frac{9}{30} + \frac{4}{30} = \frac{13}{30}$

✔ Answer: $\boxed{\frac{13}{30}}$

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13) $\frac{6}{15} + \frac{3}{20}$

- Simplify $\frac{6}{15} = \frac{2}{5}$
- LCD of 5 and 20 is 20
- $\frac{2}{5} = \frac{8}{20}$
- $\frac{8}{20} + \frac{3}{20} = \frac{11}{20}$

✔ Answer: $\boxed{\frac{11}{20}}$

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14) $\frac{1}{4} + \frac{4}{10}$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- LCD of 4 and 5 is 20
- $\frac{1}{4} = \frac{5}{20}$, $\frac{2}{5} = \frac{8}{20}$
- $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$

✔ Answer: $\boxed{\frac{13}{20}}$

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15) $\frac{3}{15} + \frac{7}{12}$

- Simplify $\frac{3}{15} = \frac{1}{5}$
- LCD of 5 and 12 is 60
- $\frac{1}{5} = \frac{12}{60}$, $\frac{7}{12} = \frac{35}{60}$
- $\frac{12}{60} + \frac{35}{60} = \frac{47}{60}$

✔ Answer: $\boxed{\frac{47}{60}}$

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16) $\frac{4}{15} + \frac{3}{25}$

- LCD of 15 and 25 is 75
- $\frac{4}{15} = \frac{20}{75}$, $\frac{3}{25} = \frac{9}{75}$
- $\frac{20}{75} + \frac{9}{75} = \frac{29}{75}$

✔ Answer: $\boxed{\frac{29}{75}}$

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17) $\frac{4}{10} + \frac{7}{15}$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- LCD of 5 and 15 is 15
- $\frac{2}{5} = \frac{6}{15}$
- $\frac{6}{15} + \frac{7}{15} = \frac{13}{15}$

✔ Answer: $\boxed{\frac{13}{15}}$

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18) $\frac{3}{10} + \frac{2}{15}$

- This is the same as problem #12!
- LCD of 10 and 15 is 30
- $\frac{3}{10} = \frac{9}{30}$, $\frac{2}{15} = \frac{4}{30}$
- $\frac{9}{30} + \frac{4}{30} = \frac{13}{30}$

✔ Answer: $\boxed{\frac{13}{30}}$

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✔ Final Answers:

| Problem | Answer |
|--------|---------------|
| 1) | $\frac{9}{10}$ |
| 2) | $\frac{25}{36}$ |
| 3) | $\frac{17}{20}$ |
| 4) | $\frac{11}{15}$ |
| 5) | $\frac{7}{10}$ |
| 6) | $\frac{11}{14}$ |
| 7) | $\frac{8}{9}$ |
| 8) | $\frac{7}{18}$ |
| 9) | $\frac{14}{15}$ |
| 10) | $\frac{8}{15}$ |
| 11) | $\frac{3}{4}$ |
| 12) | $\frac{13}{30}$ |
| 13) | $\frac{11}{20}$ |
| 14) | $\frac{13}{20}$ |
| 15) | $\frac{47}{60}$ |
| 16) | $\frac{29}{75}$ |
| 17) | $\frac{13}{15}$ |
| 18) | $\frac{13}{30}$ |

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