Adding Fractions with Unlike Denominators - Worksheet Digital - Free Printable

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

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

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

✔ 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 or after adding — it makes calculations easier!

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