Grade 5 worksheet for adding unlike fractions, featuring 14 practice problems with varying denominators.

Let's solve each problem on the "Adding Unlike Fractions" worksheet step by step. The goal is to add fractions with different denominators by finding a common denominator, converting the fractions, and then adding.

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Problem 1:

$$
\frac{1}{4} + \frac{2}{9}
$$

- Find the least common denominator (LCD) of 4 and 9 → LCM(4, 9) = 36
- Convert:
$$
\frac{1}{4} = \frac{9}{36}, \quad \frac{2}{9} = \frac{8}{36}
$$
- Add:
$$
\frac{9}{36} + \frac{8}{36} = \frac{17}{36}
$$

✔ Answer: $\boxed{\frac{17}{36}}$

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Problem 2:

$$
\frac{8}{12} + \frac{8}{11}
$$

- LCD of 12 and 11 → 132
- Convert:
$$
\frac{8}{12} = \frac{88}{132}, \quad \frac{8}{11} = \frac{96}{132}
$$
- Add:
$$
\frac{88}{132} + \frac{96}{132} = \frac{184}{132}
$$
- Simplify:
$$
\frac{184}{132} = \frac{46}{33} = 1\frac{13}{33}
$$

✔ Answer: $\boxed{1\frac{13}{33}}$

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Problem 3:

$$
\frac{2}{7} + \frac{8}{10}
$$

- Simplify $\frac{8}{10} = \frac{4}{5}$
- LCD of 7 and 5 → 35
- Convert:
$$
\frac{2}{7} = \frac{10}{35}, \quad \frac{4}{5} = \frac{28}{35}
$$
- Add:
$$
\frac{10}{35} + \frac{28}{35} = \frac{38}{35} = 1\frac{3}{35}
$$

✔ Answer: $\boxed{1\frac{3}{35}}$

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Problem 4:

$$
\frac{1}{6} + \frac{6}{11}
$$

- LCD of 6 and 11 → 66
- Convert:
$$
\frac{1}{6} = \frac{11}{66}, \quad \frac{6}{11} = \frac{36}{66}
$$
- Add:
$$
\frac{11}{66} + \frac{36}{66} = \frac{47}{66}
$$

✔ Answer: $\boxed{\frac{47}{66}}$

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Problem 5:

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

- LCD of 9 and 3 → 9
- Convert:
$$
\frac{1}{3} = \frac{3}{9}
$$
- Add:
$$
\frac{5}{9} + \frac{3}{9} = \frac{8}{9}
$$

✔ Answer: $\boxed{\frac{8}{9}}$

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Problem 6:

$$
\frac{9}{12} + \frac{2}{12}
$$

- Same denominator → just add numerators:
$$
\frac{9+2}{12} = \frac{11}{12}
$$

✔ Answer: $\boxed{\frac{11}{12}}$

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Problem 7:

$$
\frac{7}{7} + \frac{1}{4}
$$

- $\frac{7}{7} = 1$
- So: $1 + \frac{1}{4} = 1\frac{1}{4}$

✔ Answer: $\boxed{1\frac{1}{4}}$

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Problem 8:

$$
\frac{1}{4} + \frac{6}{9}
$$

- Simplify $\frac{6}{9} = \frac{2}{3}$
- LCD of 4 and 3 → 12
- Convert:
$$
\frac{1}{4} = \frac{3}{12}, \quad \frac{2}{3} = \frac{8}{12}
$$
- Add:
$$
\frac{3}{12} + \frac{8}{12} = \frac{11}{12}
$$

✔ Answer: $\boxed{\frac{11}{12}}$

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Problem 9:

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

- Simplify $\frac{4}{10} = \frac{2}{5}$
- Now: $\frac{2}{5} + \frac{4}{5} = \frac{6}{5} = 1\frac{1}{5}$

✔ Answer: $\boxed{1\frac{1}{5}}$

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Problem 10:

$$
\frac{1}{2} + \frac{8}{11}
$$

- LCD of 2 and 11 → 22
- Convert:
$$
\frac{1}{2} = \frac{11}{22}, \quad \frac{8}{11} = \frac{16}{22}
$$
- Add:
$$
\frac{11}{22} + \frac{16}{22} = \frac{27}{22} = 1\frac{5}{22}
$$

✔ Answer: $\boxed{1\frac{5}{22}}$

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Problem 11:

$$
\frac{1}{11} + \frac{2}{12}
$$

- Simplify $\frac{2}{12} = \frac{1}{6}$
- LCD of 11 and 6 → 66
- Convert:
$$
\frac{1}{11} = \frac{6}{66}, \quad \frac{1}{6} = \frac{11}{66}
$$
- Add:
$$
\frac{6}{66} + \frac{11}{66} = \frac{17}{66}
$$

✔ Answer: $\boxed{\frac{17}{66}}$

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Problem 12:

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

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

✔ Answer: $\boxed{\frac{2}{3}}$

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Problem 13:

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

- LCD of 5 and 8 → 40
- Convert:
$$
\frac{3}{5} = \frac{24}{40}, \quad \frac{3}{8} = \frac{15}{40}
$$
- Add:
$$
\frac{24}{40} + \frac{15}{40} = \frac{39}{40}
$$

✔ Answer: $\boxed{\frac{39}{40}}$

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Problem 14:

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

- Simplify $\frac{6}{9} = \frac{2}{3}$
- LCD of 3 and 2 → 6
- Convert:
$$
\frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}
$$
- Add:
$$
\frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1\frac{1}{6}
$$

✔ Answer: $\boxed{1\frac{1}{6}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{17}{36}$ |
| 2 | $1\frac{13}{33}$ |
| 3 | $1\frac{3}{35}$ |
| 4 | $\frac{47}{66}$ |
| 5 | $\frac{8}{9}$ |
| 6 | $\frac{11}{12}$ |
| 7 | $1\frac{1}{4}$ |
| 8 | $\frac{11}{12}$ |
| 9 | $1\frac{1}{5}$ |
| 10 | $1\frac{5}{22}$ |
| 11 | $\frac{17}{66}$ |
| 12 | $\frac{2}{3}$ |
| 13 | $\frac{39}{40}$ |
| 14 | $1\frac{1}{6}$ |

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