Adding Fractions with Unlike Denominators - Worksheet Digital - Free Printable

Let's solve each of these adding unlike fractions problems step by step.

To add fractions with unlike denominators, we follow these steps:

1. Find the least common denominator (LCD) of the two fractions.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add the numerators, keeping the common denominator.
4. Simplify the result if needed.

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Problem 1:

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

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

✔ Answer: $\frac{5}{6}$

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Problem 2:

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

- LCD of 3 and 5 is 15
- Convert:
$$
\frac{1}{3} = \frac{5}{15}, \quad \frac{3}{5} = \frac{9}{15}
$$
- Add:
$$
\frac{5}{15} + \frac{9}{15} = \frac{14}{15}
$$

✔ Answer: $\frac{14}{15}$

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Problem 3:

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

- LCD of 2 and 3 is 6
- Convert:
$$
\frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6}
$$
- Add:
$$
\frac{3}{6} + \frac{4}{6} = \frac{7}{6} = 1\frac{1}{6}
$$

✔ Answer: $1\frac{1}{6}$ or $\frac{7}{6}$

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Problem 4:

$$
\frac{2}{5} + \frac{5}{6}
$$

- LCD of 5 and 6 is 30
- Convert:
$$
\frac{2}{5} = \frac{12}{30}, \quad \frac{5}{6} = \frac{25}{30}
$$
- Add:
$$
\frac{12}{30} + \frac{25}{30} = \frac{37}{30} = 1\frac{7}{30}
$$

✔ Answer: $1\frac{7}{30}$ or $\frac{37}{30}$

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Problem 5:

$$
\frac{5}{6} + \frac{2}{5}
$$

- LCD of 6 and 5 is 30
- Convert:
$$
\frac{5}{6} = \frac{25}{30}, \quad \frac{2}{5} = \frac{12}{30}
$$
- Add:
$$
\frac{25}{30} + \frac{12}{30} = \frac{37}{30} = 1\frac{7}{30}
$$

✔ Answer: $1\frac{7}{30}$ or $\frac{37}{30}$

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Problem 6:

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

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

✔ Answer: $\frac{5}{12}$

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Problem 7:

$$
\frac{3}{7} + \frac{3}{5}
$$

- LCD of 7 and 5 is 35
- Convert:
$$
\frac{3}{7} = \frac{15}{35}, \quad \frac{3}{5} = \frac{21}{35}
$$
- Add:
$$
\frac{15}{35} + \frac{21}{35} = \frac{36}{35} = 1\frac{1}{35}
$$

✔ Answer: $1\frac{1}{35}$ or $\frac{36}{35}$

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Problem 8:

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

- LCD of 5 and 9 is 45
- Convert:
$$
\frac{2}{5} = \frac{18}{45}, \quad \frac{5}{9} = \frac{25}{45}
$$
- Add:
$$
\frac{18}{45} + \frac{25}{45} = \frac{43}{45}
$$

✔ Answer: $\frac{43}{45}$

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Problem 9:

$$
\frac{5}{8} + \frac{1}{2}
$$

- LCD of 8 and 2 is 8
- Convert:
$$
\frac{1}{2} = \frac{4}{8}
$$
- Add:
$$
\frac{5}{8} + \frac{4}{8} = \frac{9}{8} = 1\frac{1}{8}
$$

✔ Answer: $1\frac{1}{8}$ or $\frac{9}{8}$

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Problem 10:

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

- LCD of 6 and 4 is 12
- Convert:
$$
\frac{1}{6} = \frac{2}{12}, \quad \frac{3}{4} = \frac{9}{12}
$$
- Add:
$$
\frac{2}{12} + \frac{9}{12} = \frac{11}{12}
$$

✔ Answer: $\frac{11}{12}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1. $\frac{1}{2} + \frac{1}{3}$ | $\frac{5}{6}$ |
| 2. $\frac{1}{3} + \frac{3}{5}$ | $\frac{14}{15}$ |
| 3. $\frac{1}{2} + \frac{2}{3}$ | $1\frac{1}{6}$ |
| 4. $\frac{2}{5} + \frac{5}{6}$ | $1\frac{7}{30}$ |
| 5. $\frac{5}{6} + \frac{2}{5}$ | $1\frac{7}{30}$ |
| 6. $\frac{1}{4} + \frac{1}{6}$ | $\frac{5}{12}$ |
| 7. $\frac{3}{7} + \frac{3}{5}$ | $1\frac{1}{35}$ |
| 8. $\frac{2}{5} + \frac{5}{9}$ | $\frac{43}{45}$ |
| 9. $\frac{5}{8} + \frac{1}{2}$ | $1\frac{1}{8}$ |
| 10. $\frac{1}{6} + \frac{3}{4}$ | $\frac{11}{12}$ |

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