Adding fractions worksheet for practicing fraction addition problems.

Let's solve the Adding Fractions worksheet step by step. The goal is to add fractions with unlike denominators, and we're told to rewrite them as mixed numbers if needed.

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🔷 Step 1: Understand the Rule

To add fractions:
- Find a common denominator (LCM of the denominators).
- Convert each fraction to an equivalent fraction with that common denominator.
- Add the numerators.
- Simplify the result and convert to a mixed number if necessary.

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We’ll go through each problem one by one.

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✔ Problem 1:

$ \frac{1}{4} + \frac{3}{8} $

- LCM of 4 and 8 is 8.
- Convert $ \frac{1}{4} = \frac{2}{8} $
- Now: $ \frac{2}{8} + \frac{3}{8} = \frac{5}{8} $
- Answer: $ \frac{5}{8} $ → already proper, no need for mixed number.

✔ Final answer: $ \frac{5}{8} $

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✔ Problem 2:

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

- LCM of 4 and 6 is 12.
- $ \frac{3}{4} = \frac{9}{12} $, $ \frac{1}{6} = \frac{2}{12} $
- $ \frac{9}{12} + \frac{2}{12} = \frac{11}{12} $

✔ Final answer: $ \frac{11}{12} $

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✔ Problem 3:

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

- LCM of 2 and 3 is 6.
- $ \frac{1}{2} = \frac{3}{6} $, $ \frac{2}{3} = \frac{4}{6} $
- $ \frac{3}{6} + \frac{4}{6} = \frac{7}{6} $
- $ \frac{7}{6} = 1\frac{1}{6} $ (since 7 ÷ 6 = 1 remainder 1)

✔ Final answer: $ 1\frac{1}{6} $

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✔ Problem 4:

$ \frac{2}{3} + \frac{1}{4} $

- LCM of 3 and 4 is 12.
- $ \frac{2}{3} = \frac{8}{12} $, $ \frac{1}{4} = \frac{3}{12} $
- $ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} $

✔ Final answer: $ \frac{11}{12} $

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✔ Problem 5:

$ \frac{3}{4} + \frac{1}{2} $

- LCM of 4 and 2 is 4.
- $ \frac{1}{2} = \frac{2}{4} $
- $ \frac{3}{4} + \frac{2}{4} = \frac{5}{4} $
- $ \frac{5}{4} = 1\frac{1}{4} $

✔ Final answer: $ 1\frac{1}{4} $

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✔ Problem 6:

$ \frac{2}{5} + \frac{1}{3} $

- LCM of 5 and 3 is 15.
- $ \frac{2}{5} = \frac{6}{15} $, $ \frac{1}{3} = \frac{5}{15} $
- $ \frac{6}{15} + \frac{5}{15} = \frac{11}{15} $

✔ Final answer: $ \frac{11}{15} $

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✔ Problem 7:

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

- LCM of 2 and 3 is 6.
- $ \frac{1}{2} = \frac{3}{6} $, $ \frac{1}{3} = \frac{2}{6} $
- $ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} $

✔ Final answer: $ \frac{5}{6} $

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✔ Problem 8:

$ \frac{3}{8} + \frac{1}{4} $

- LCM of 8 and 4 is 8.
- $ \frac{1}{4} = \frac{2}{8} $
- $ \frac{3}{8} + \frac{2}{8} = \frac{5}{8} $

✔ Final answer: $ \frac{5}{8} $

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✔ Problem 9:

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

- LCM of 3 and 6 is 6.
- $ \frac{2}{3} = \frac{4}{6} $
- $ \frac{4}{6} + \frac{1}{6} = \frac{5}{6} $

✔ Final answer: $ \frac{5}{6} $

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✔ Problem 10:

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

- LCM of 3 and 4 is 12.
- $ \frac{1}{3} = \frac{4}{12} $, $ \frac{1}{4} = \frac{3}{12} $
- $ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} $

✔ Final answer: $ \frac{7}{12} $

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✔ Problem 11:

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

- LCM of 4 and 5 is 20.
- $ \frac{3}{4} = \frac{15}{20} $, $ \frac{2}{5} = \frac{8}{20} $
- $ \frac{15}{20} + \frac{8}{20} = \frac{23}{20} $
- $ \frac{23}{20} = 1\frac{3}{20} $

✔ Final answer: $ 1\frac{3}{20} $

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✔ Problem 12:

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

- LCM of 2 and 5 is 10.
- $ \frac{1}{2} = \frac{5}{10} $, $ \frac{1}{5} = \frac{2}{10} $
- $ \frac{5}{10} + \frac{2}{10} = \frac{7}{10} $

✔ Final answer: $ \frac{7}{10} $

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## ✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{5}{8} $ |
| 2 | $ \frac{11}{12} $ |
| 3 | $ 1\frac{1}{6} $ |
| 4 | $ \frac{11}{12} $ |
| 5 | $ 1\frac{1}{4} $ |
| 6 | $ \frac{11}{15} $ |
| 7 | $ \frac{5}{6} $ |
| 8 | $ \frac{5}{8} $ |
| 9 | $ \frac{5}{6} $ |
| 10 | $ \frac{7}{12} $ |
| 11 | $ 1\frac{3}{20} $ |
| 12 | $ \frac{7}{10} $ |

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📝 Summary Tips:

- Always find the least common denominator (LCD).
- Convert both fractions to have the same denominator.
- Add the numerators.
- Simplify and write as a mixed number if the result is improper (numerator > denominator).

Let me know if you'd like this in printable format or want help visualizing any steps!