Addition of Fractions worksheet with ten problems involving fractions with like denominators.

You're working on a worksheet titled “Addition of Fractions”. All the problems involve adding fractions with the same denominator, which is the easiest type of fraction addition.

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📌 Key Rule for Adding Fractions with Like Denominators:

> Keep the denominator the same, and add the numerators.

Then, if possible, simplify the result (reduce to lowest terms).

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Let’s solve each problem step by step:

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🔹 Row 1

1.
\[
\frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \frac{2}{3}
\]

✔ Already simplified.

2.
\[
\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7} = \frac{5}{7}
\]

✔ Already simplified.

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🔹 Row 2

3.
\[
\frac{1}{5} + \frac{3}{5} = \frac{1+3}{5} = \frac{4}{5}
\]

✔ Already simplified.

4.
\[
\frac{1}{9} + \frac{7}{9} = \frac{1+7}{9} = \frac{8}{9}
\]

✔ Already simplified.

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🔹 Row 3

5.
\[
\frac{1}{5} + \frac{2}{5} + \frac{1}{5} = \frac{1+2+1}{5} = \frac{4}{5}
\]

✔ Already simplified.

6.
\[
\frac{1}{4} + \frac{3}{4} + \frac{3}{4} = \frac{1+3+3}{4} = \frac{7}{4}
\]

➡️ This is an improper fraction. You can leave it as \(\frac{7}{4}\), or convert to a mixed number:
\[
\frac{7}{4} = 1 \frac{3}{4}
\]

✔ Either is acceptable unless specified otherwise.

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🔹 Row 4

7.
\[
\frac{7}{8} + \frac{1}{8} + \frac{3}{8} = \frac{7+1+3}{8} = \frac{11}{8}
\]

➡️ Improper fraction → Convert to mixed number:
\[
\frac{11}{8} = 1 \frac{3}{8}
\]

✔ Answer: \(1 \frac{3}{8}\) or \(\frac{11}{8}\)

8.
\[
\frac{2}{3} + \frac{1}{3} + \frac{2}{3} = \frac{2+1+2}{3} = \frac{5}{3}
\]

➡️ Improper fraction → Mixed number:
\[
\frac{5}{3} = 1 \frac{2}{3}
\]

✔ Answer: \(1 \frac{2}{3}\) or \(\frac{5}{3}\)

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🔹 Row 5

9.
\[
\frac{3}{5} + \frac{4}{5} + \frac{2}{5} = \frac{3+4+2}{5} = \frac{9}{5}
\]

➡️ Improper → Mixed number:
\[
\frac{9}{5} = 1 \frac{4}{5}
\]

✔ Answer: \(1 \frac{4}{5}\) or \(\frac{9}{5}\)

10.
\[
\frac{1}{4} + \frac{3}{4} + \frac{1}{4} = \frac{1+3+1}{4} = \frac{5}{4}
\]

➡️ Improper → Mixed number:
\[
\frac{5}{4} = 1 \frac{1}{4}
\]

✔ Answer: \(1 \frac{1}{4}\) or \(\frac{5}{4}\)

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## ✔ Final Answers (in simplest form):

| Problem | Answer |
|---------|---------------|
| 1 | \(\frac{2}{3}\) |
| 2 | \(\frac{5}{7}\) |
| 3 | \(\frac{4}{5}\) |
| 4 | \(\frac{8}{9}\) |
| 5 | \(\frac{4}{5}\) |
| 6 | \(\frac{7}{4}\) or \(1\frac{3}{4}\) |
| 7 | \(\frac{11}{8}\) or \(1\frac{3}{8}\) |
| 8 | \(\frac{5}{3}\) or \(1\frac{2}{3}\) |
| 9 | \(\frac{9}{5}\) or \(1\frac{4}{5}\) |
| 10 | \(\frac{5}{4}\) or \(1\frac{1}{4}\) |

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## 💡 Tip for Students:
When adding fractions with the same denominator, just focus on adding the top numbers (numerators). The bottom number (denominator) stays the same. Always check if your answer can be simplified or turned into a mixed number!

Let me know if you want to practice subtracting fractions next! 😊