Adding Fractions with Unlike Denominators - Worksheet Digital - Free Printable

You're working on adding unlike fractions — that means the denominators (bottom numbers) are different. To add them, you need to:

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

Let’s solve each problem step-by-step.

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Problem 1:

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

- Simplify $\frac{3}{9} = \frac{1}{3}$
- Now: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

✔ 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: $\frac{10}{18} + \frac{9}{18} = \frac{19}{18}$
- Simplify: $\frac{19}{18} = 1\frac{1}{18}$

✔ Answer: $1\frac{1}{18}$

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Problem 3:

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

- Simplify $\frac{6}{12} = \frac{1}{2}$
- LCD of 6 and 2 is 6
- Convert: $\frac{1}{2} = \frac{3}{6}$
- 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: $\frac{2}{3} = \frac{6}{9}$
- 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: $\frac{2}{3} = \frac{6}{9}$
- 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: $\frac{1}{4} = \frac{2}{8}$
- 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: $\frac{1}{5} = \frac{2}{10}$
- 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: $\frac{2}{3} = \frac{4}{6}$
- 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: Always check if you can simplify fractions *before* adding — it often makes the math easier!

Let me know if you’d like to see visual models or step-by-step work for any specific problem!