Adding Fractions Worksheets - Free Printable

Let's solve each of the addition problems in Adding Fractions Sheet 3. We'll go through them one by one, showing the steps for adding fractions, especially when they have different denominators.

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1. $ \frac{2}{5} + \frac{1}{4} $

Find a common denominator: LCM of 5 and 4 is 20.

$$
\frac{2}{5} = \frac{8}{20},\quad \frac{1}{4} = \frac{5}{20}
$$

$$
\frac{8}{20} + \frac{5}{20} = \frac{13}{20}
$$

✔ Answer: $ \frac{13}{20} $

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

LCM of 3 and 6 is 6.

$$
\frac{1}{3} = \frac{2}{6},\quad \frac{1}{6} = \frac{1}{6}
$$

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

✔ Answer: $ \frac{1}{2} $

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3. $ \frac{3}{7} + \frac{1}{2} $

LCM of 7 and 2 is 14.

$$
\frac{3}{7} = \frac{6}{14},\quad \frac{1}{2} = \frac{7}{14}
$$

$$
\frac{6}{14} + \frac{7}{14} = \frac{13}{14}
$$

✔ Answer: $ \frac{13}{14} $

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4. $ \frac{1}{5} + \frac{10}{15} $

Simplify $ \frac{10}{15} = \frac{2}{3} $

Now: $ \frac{1}{5} + \frac{2}{3} $

LCM of 5 and 3 is 15.

$$
\frac{1}{5} = \frac{3}{15},\quad \frac{2}{3} = \frac{10}{15}
$$

$$
\frac{3}{15} + \frac{10}{15} = \frac{13}{15}
$$

✔ Answer: $ \frac{13}{15} $

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5. $ \frac{2}{9} + \frac{1}{3} $

LCM of 9 and 3 is 9.

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

$$
\frac{2}{9} + \frac{3}{9} = \frac{5}{9}
$$

✔ Answer: $ \frac{5}{9} $

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

LCM of 8 and 4 is 8.

$$
\frac{1}{4} = \frac{2}{8}
$$

$$
\frac{1}{8} + \frac{2}{8} = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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

LCM of 8 and 4 is 8.

$$
\frac{1}{4} = \frac{2}{8}
$$

$$
\frac{3}{8} + \frac{2}{8} = \frac{5}{8}
$$

✔ Answer: $ \frac{5}{8} $

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8. $ \frac{1}{6} + \frac{1}{12} $

LCM of 6 and 12 is 12.

$$
\frac{1}{6} = \frac{2}{12}
$$

$$
\frac{2}{12} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4}
$$

✔ Answer: $ \frac{1}{4} $

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

Same as #2:

$$
\frac{1}{3} = \frac{2}{6},\quad \frac{1}{6} = \frac{1}{6}
\Rightarrow \frac{3}{6} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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10. $ \frac{1}{4} + \frac{1}{8} $

LCM of 4 and 8 is 8.

$$
\frac{1}{4} = \frac{2}{8}
\Rightarrow \frac{2}{8} + \frac{1}{8} = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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11. $ \frac{1}{3} + \frac{2}{9} $

LCM of 3 and 9 is 9.

$$
\frac{1}{3} = \frac{3}{9}
\Rightarrow \frac{3}{9} + \frac{2}{9} = \frac{5}{9}
$$

✔ Answer: $ \frac{5}{9} $

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12. $ \frac{1}{5} + \frac{1}{10} $

LCM of 5 and 10 is 10.

$$
\frac{1}{5} = \frac{2}{10}
\Rightarrow \frac{2}{10} + \frac{1}{10} = \frac{3}{10}
$$

✔ Answer: $ \frac{3}{10} $

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

LCM of 3 and 6 is 6.

$$
\frac{2}{3} = \frac{4}{6}
\Rightarrow \frac{4}{6} + \frac{1}{6} = \frac{5}{6}
$$

✔ Answer: $ \frac{5}{6} $

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14. $ \frac{1}{4} + \frac{1}{8} $

Same as #10 → $ \frac{3}{8} $

✔ Answer: $ \frac{3}{8} $

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

LCM of 2 and 6 is 6.

$$
\frac{1}{2} = \frac{3}{6}
\Rightarrow \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}
$$

✔ Answer: $ \frac{2}{3} $

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

LCM of 4 and 8 is 8.

$$
\frac{3}{4} = \frac{6}{8}
\Rightarrow \frac{6}{8} + \frac{1}{8} = \frac{7}{8}
$$

✔ Answer: $ \frac{7}{8} $

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17. $ \frac{1}{2} + \frac{1}{10} $

LCM of 2 and 10 is 10.

$$
\frac{1}{2} = \frac{5}{10}
\Rightarrow \frac{5}{10} + \frac{1}{10} = \frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $

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18. $ \frac{1}{3} + \frac{1}{12} $

LCM of 3 and 12 is 12.

$$
\frac{1}{3} = \frac{4}{12}
\Rightarrow \frac{4}{12} + \frac{1}{12} = \frac{5}{12}
$$

✔ Answer: $ \frac{5}{12} $

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

LCM of 5 and 10 is 10.

$$
\frac{2}{5} = \frac{4}{10}
\Rightarrow \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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

Again, same as #2 and #9 → $ \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{13}{20} $ |
| 2 | $ \frac{1}{2} $ |
| 3 | $ \frac{13}{14} $ |
| 4 | $ \frac{13}{15} $ |
| 5 | $ \frac{5}{9} $ |
| 6 | $ \frac{3}{8} $ |
| 7 | $ \frac{5}{8} $ |
| 8 | $ \frac{1}{4} $ |
| 9 | $ \frac{1}{2} $ |
| 10 | $ \frac{3}{8} $ |
| 11 | $ \frac{5}{9} $ |
| 12 | $ \frac{3}{10} $ |
| 13 | $ \frac{5}{6} $ |
| 14 | $ \frac{3}{8} $ |
| 15 | $ \frac{2}{3} $ |
| 16 | $ \frac{7}{8} $ |
| 17 | $ \frac{3}{5} $ |
| 18 | $ \frac{5}{12} $ |
| 19 | $ \frac{1}{2} $ |
| 20 | $ \frac{1}{2} $ |

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🔍 Key Tips:

- Always find the least common denominator (LCD).
- Convert both fractions to have that denominator.
- Add the numerators and keep the denominator.
- Simplify the result if possible.

Let me know if you'd like this as a printable PDF or with step-by-step visuals!