Fractions Worksheets | Printable Fractions Worksheets for Teachers - Free Printable

Sure! Let’s solve each of these Adding Mixed Numbers problems step by step.

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🔢 General Strategy:

To add mixed numbers:
1. Add the whole numbers together.
2. Add the fractions — if they have different denominators, find a common denominator first.
3. If the sum of the fractions is an improper fraction, convert it to a mixed number and add the whole part to your previous whole number sum.
4. Simplify the final answer if needed.

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Let’s solve each one:

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1) \( 4\frac{1}{2} + 6\frac{1}{5} \)

- Whole numbers: \( 4 + 6 = 10 \)
- Fractions: \( \frac{1}{2} + \frac{1}{5} \)
- Common denominator = 10
- \( \frac{1}{2} = \frac{5}{10}, \quad \frac{1}{5} = \frac{2}{10} \)
- Sum: \( \frac{5}{10} + \frac{2}{10} = \frac{7}{10} \)
- Final answer: \( \boxed{10\frac{7}{10}} \)

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2) \( 2\frac{5}{10} + 5\frac{3}{5} \)

- First, simplify \( \frac{5}{10} = \frac{1}{2} \), so we have \( 2\frac{1}{2} + 5\frac{3}{5} \)
- Whole numbers: \( 2 + 5 = 7 \)
- Fractions: \( \frac{1}{2} + \frac{3}{5} \)
- Common denominator = 10
- \( \frac{1}{2} = \frac{5}{10}, \quad \frac{3}{5} = \frac{6}{10} \)
- Sum: \( \frac{5}{10} + \frac{6}{10} = \frac{11}{10} = 1\frac{1}{10} \)
- Add to whole number: \( 7 + 1 = 8 \), plus \( \frac{1}{10} \)
- Final answer: \( \boxed{8\frac{1}{10}} \)

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3) \( 3\frac{4}{5} + 8\frac{1}{3} \)

- Whole numbers: \( 3 + 8 = 11 \)
- Fractions: \( \frac{4}{5} + \frac{1}{3} \)
- Common denominator = 15
- \( \frac{4}{5} = \frac{12}{15}, \quad \frac{1}{3} = \frac{5}{15} \)
- Sum: \( \frac{12}{15} + \frac{5}{15} = \frac{17}{15} = 1\frac{2}{15} \)
- Add to whole number: \( 11 + 1 = 12 \), plus \( \frac{2}{15} \)
- Final answer: \( \boxed{12\frac{2}{15}} \)

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4) \( 2\frac{4}{5} + 8\frac{3}{4} \)

- Whole numbers: \( 2 + 8 = 10 \)
- Fractions: \( \frac{4}{5} + \frac{3}{4} \)
- Common denominator = 20
- \( \frac{4}{5} = \frac{16}{20}, \quad \frac{3}{4} = \frac{15}{20} \)
- Sum: \( \frac{16}{20} + \frac{15}{20} = \frac{31}{20} = 1\frac{11}{20} \)
- Add to whole number: \( 10 + 1 = 11 \), plus \( \frac{11}{20} \)
- Final answer: \( \boxed{11\frac{11}{20}} \)

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5) \( 3\frac{2}{3} + 5\frac{1}{4} \)

- Whole numbers: \( 3 + 5 = 8 \)
- Fractions: \( \frac{2}{3} + \frac{1}{4} \)
- Common denominator = 12
- \( \frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12} \)
- Sum: \( \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \)
- Final answer: \( \boxed{8\frac{11}{12}} \)

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6) \( 6\frac{4}{10} + 5\frac{3}{4} \)

- Simplify \( \frac{4}{10} = \frac{2}{5} \), so \( 6\frac{2}{5} + 5\frac{3}{4} \)
- Whole numbers: \( 6 + 5 = 11 \)
- Fractions: \( \frac{2}{5} + \frac{3}{4} \)
- Common denominator = 20
- \( \frac{2}{5} = \frac{8}{20}, \quad \frac{3}{4} = \frac{15}{20} \)
- Sum: \( \frac{8}{20} + \frac{15}{20} = \frac{23}{20} = 1\frac{3}{20} \)
- Add to whole number: \( 11 + 1 = 12 \), plus \( \frac{3}{20} \)
- Final answer: \( \boxed{12\frac{3}{20}} \)

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7) \( 2\frac{1}{4} + 7\frac{2}{10} \)

- Simplify \( \frac{2}{10} = \frac{1}{5} \), so \( 2\frac{1}{4} + 7\frac{1}{5} \)
- Whole numbers: \( 2 + 7 = 9 \)
- Fractions: \( \frac{1}{4} + \frac{1}{5} \)
- Common denominator = 20
- \( \frac{1}{4} = \frac{5}{20}, \quad \frac{1}{5} = \frac{4}{20} \)
- Sum: \( \frac{5}{20} + \frac{4}{20} = \frac{9}{20} \)
- Final answer: \( \boxed{9\frac{9}{20}} \)

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8) \( 6\frac{1}{2} + 4\frac{4}{5} \)

- Whole numbers: \( 6 + 4 = 10 \)
- Fractions: \( \frac{1}{2} + \frac{4}{5} \)
- Common denominator = 10
- \( \frac{1}{2} = \frac{5}{10}, \quad \frac{4}{5} = \frac{8}{10} \)
- Sum: \( \frac{5}{10} + \frac{8}{10} = \frac{13}{10} = 1\frac{3}{10} \)
- Add to whole number: \( 10 + 1 = 11 \), plus \( \frac{3}{10} \)
- Final answer: \( \boxed{11\frac{3}{10}} \)

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9) \( 2\frac{1}{2} + 9\frac{6}{10} \)

- Simplify \( \frac{6}{10} = \frac{3}{5} \), so \( 2\frac{1}{2} + 9\frac{3}{5} \)
- Whole numbers: \( 2 + 9 = 11 \)
- Fractions: \( \frac{1}{2} + \frac{3}{5} \)
- Common denominator = 10
- \( \frac{1}{2} = \frac{5}{10}, \quad \frac{3}{5} = \frac{6}{10} \)
- Sum: \( \frac{5}{10} + \frac{6}{10} = \frac{11}{10} = 1\frac{1}{10} \)
- Add to whole number: \( 11 + 1 = 12 \), plus \( \frac{1}{10} \)
- Final answer: \( \boxed{12\frac{1}{10}} \)

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10) \( 5\frac{5}{10} + 8\frac{1}{2} \)

- Simplify \( \frac{5}{10} = \frac{1}{2} \), so \( 5\frac{1}{2} + 8\frac{1}{2} \)
- Whole numbers: \( 5 + 8 = 13 \)
- Fractions: \( \frac{1}{2} + \frac{1}{2} = 1 \)
- Total: \( 13 + 1 = 14 \)
- Final answer: \( \boxed{14} \)

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## ✔ Final Answers Summary:

1) \( \boxed{10\frac{7}{10}} \)
2) \( \boxed{8\frac{1}{10}} \)
3) \( \boxed{12\frac{2}{15}} \)
4) \( \boxed{11\frac{11}{20}} \)
5) \( \boxed{8\frac{11}{12}} \)
6) \( \boxed{12\frac{3}{20}} \)
7) \( \boxed{9\frac{9}{20}} \)
8) \( \boxed{11\frac{3}{10}} \)
9) \( \boxed{12\frac{1}{10}} \)
10) \( \boxed{14} \)

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Let me know if you’d like to see any step explained in more detail! 😊