Adding unlike fractions worksheet with ten problems for practice.

You're working on Adding Unlike Fractions — which means adding fractions that have different denominators. To do this correctly, you must:

1. Find a common denominator (usually the Least Common Denominator, or LCD).
2. Convert each fraction to an equivalent fraction with that common denominator.
3. Add the numerators, keeping the common denominator.
4. Simplify the result if possible.

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Let’s solve each problem step by step.

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Problem 1:

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

- $\frac{3}{9}$ simplifies to $\frac{1}{3}$ → so this becomes $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

✔ Answer: $\frac{2}{3}$

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Problem 2:

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

- LCD of 9 and 2 is 18
- Convert:
- $\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}$
- $\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}$
- Add: $\frac{10}{18} + \frac{9}{18} = \frac{19}{18} = 1\frac{1}{18}$

✔ Answer: $1\frac{1}{18}$

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Problem 3:

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

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

✔ Answer: $\frac{2}{3}$

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Problem 4:

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

- LCD of 4 and 5 is 20
- Convert:
- $\frac{3}{4} = \frac{15}{20}$
- $\frac{2}{5} = \frac{8}{20}$
- Add: $\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1\frac{3}{20}$

✔ Answer: $1\frac{3}{20}$

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Problem 5:

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

- LCD of 9 and 3 is 9
- Convert:
- $\frac{2}{9} = \frac{2}{9}$
- $\frac{2}{3} = \frac{6}{9}$
- Add: $\frac{2}{9} + \frac{6}{9} = \frac{8}{9}$

✔ Answer: $\frac{8}{9}$

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Problem 6:

$\frac{1}{5} + \frac{1}{6}$

- LCD of 5 and 6 is 30
- Convert:
- $\frac{1}{5} = \frac{6}{30}$
- $\frac{1}{6} = \frac{5}{30}$
- Add: $\frac{6}{30} + \frac{5}{30} = \frac{11}{30}$

✔ Answer: $\frac{11}{30}$

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Problem 7:

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

- LCD of 3 and 9 is 9
- Convert:
- $\frac{2}{3} = \frac{6}{9}$
- $\frac{5}{9} = \frac{5}{9}$
- Add: $\frac{6}{9} + \frac{5}{9} = \frac{11}{9} = 1\frac{2}{9}$

✔ Answer: $1\frac{2}{9}$

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Problem 8:

$\frac{1}{4} + \frac{5}{8}$

- LCD of 4 and 8 is 8
- Convert:
- $\frac{1}{4} = \frac{2}{8}$
- $\frac{5}{8} = \frac{5}{8}$
- Add: $\frac{2}{8} + \frac{5}{8} = \frac{7}{8}$

✔ Answer: $\frac{7}{8}$

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Problem 9:

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

- LCD of 10 and 5 is 10
- Convert:
- $\frac{9}{10} = \frac{9}{10}$
- $\frac{1}{5} = \frac{2}{10}$
- Add: $\frac{9}{10} + \frac{2}{10} = \frac{11}{10} = 1\frac{1}{10}$

✔ Answer: $1\frac{1}{10}$

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Problem 10:

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

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

✔ Answer: $\frac{5}{6}$

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## ✔ Final Answers (in order):

1. $\frac{2}{3}$
2. $1\frac{1}{18}$
3. $\frac{2}{3}$
4. $1\frac{3}{20}$
5. $\frac{8}{9}$
6. $\frac{11}{30}$
7. $1\frac{2}{9}$
8. $\frac{7}{8}$
9. $1\frac{1}{10}$
10. $\frac{5}{6}$

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💡 Tip for Students: Always check if fractions can be simplified *before* finding the LCD — it often makes the math easier! Also, remember to simplify your final answer if possible.

Let me know if you’d like a printable version or more practice problems!