Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets - Free Printable

Sure! Let’s solve each of these adding mixed numbers problems step by step. The general method is:

1. Add the whole numbers together.
2. Add the fractions together — if they have different denominators, find a common denominator first.
3. Simplify the fraction part (if needed) and convert any improper fraction to a mixed number.
4. Combine with the whole number sum.

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

- Whole numbers: \( 2 + 3 = 5 \)
- Fractions: \( \frac{1}{4} + \frac{1}{3} \) → LCD = 12
- \( \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12} \)
- Sum: \( \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \)
- Final answer: \( \boxed{5\frac{7}{12}} \)

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

- Whole numbers: \( 5 + 1 = 6 \)
- Fractions: \( \frac{1}{3} + \frac{2}{5} \) → LCD = 15
- \( \frac{1}{3} = \frac{5}{15}, \quad \frac{2}{5} = \frac{6}{15} \)
- Sum: \( \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \)
- Final answer: \( \boxed{6\frac{11}{15}} \)

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

- Whole numbers: \( 4 + 2 = 6 \)
- Fractions: \( \frac{1}{2} + \frac{1}{5} \) → LCD = 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: \( \boxed{6\frac{7}{10}} \)

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4. \( 6\frac{1}{3} + 3\frac{1}{6} \)

- Whole numbers: \( 6 + 3 = 9 \)
- Fractions: \( \frac{1}{3} + \frac{1}{6} \) → LCD = 6
- \( \frac{1}{3} = \frac{2}{6}, \quad \frac{1}{6} = \frac{1}{6} \)
- Sum: \( \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \)
- Final answer: \( \boxed{9\frac{1}{2}} \)

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5. \( 2\frac{1}{7} + 2\frac{3}{4} \)

- Whole numbers: \( 2 + 2 = 4 \)
- Fractions: \( \frac{1}{7} + \frac{3}{4} \) → LCD = 28
- \( \frac{1}{7} = \frac{4}{28}, \quad \frac{3}{4} = \frac{21}{28} \)
- Sum: \( \frac{4}{28} + \frac{21}{28} = \frac{25}{28} \)
- Final answer: \( \boxed{4\frac{25}{28}} \)

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6. \( 7\frac{1}{7} + 4\frac{1}{4} \)

- Whole numbers: \( 7 + 4 = 11 \)
- Fractions: \( \frac{1}{7} + \frac{1}{4} \) → LCD = 28
- \( \frac{1}{7} = \frac{4}{28}, \quad \frac{1}{4} = \frac{7}{28} \)
- Sum: \( \frac{4}{28} + \frac{7}{28} = \frac{11}{28} \)
- Final answer: \( \boxed{11\frac{11}{28}} \)

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7. \( 3\frac{4}{5} + 6\frac{1}{2} \)

- Whole numbers: \( 3 + 6 = 9 \)
- Fractions: \( \frac{4}{5} + \frac{1}{2} \) → LCD = 10
- \( \frac{4}{5} = \frac{8}{10}, \quad \frac{1}{2} = \frac{5}{10} \)
- Sum: \( \frac{8}{10} + \frac{5}{10} = \frac{13}{10} = 1\frac{3}{10} \)
- Add the whole number: \( 9 + 1 = 10 \), so total = \( 10\frac{3}{10} \)
- Final answer: \( \boxed{10\frac{3}{10}} \)

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8. \( 2\frac{3}{8} + 8\frac{2}{6} \)

First, simplify \( \frac{2}{6} = \frac{1}{3} \)

- Whole numbers: \( 2 + 8 = 10 \)
- Fractions: \( \frac{3}{8} + \frac{1}{3} \) → LCD = 24
- \( \frac{3}{8} = \frac{9}{24}, \quad \frac{1}{3} = \frac{8}{24} \)
- Sum: \( \frac{9}{24} + \frac{8}{24} = \frac{17}{24} \)
- Final answer: \( \boxed{10\frac{17}{24}} \)

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9. \( 6\frac{1}{8} + 5\frac{1}{3} \)

- Whole numbers: \( 6 + 5 = 11 \)
- Fractions: \( \frac{1}{8} + \frac{1}{3} \) → LCD = 24
- \( \frac{1}{8} = \frac{3}{24}, \quad \frac{1}{3} = \frac{8}{24} \)
- Sum: \( \frac{3}{24} + \frac{8}{24} = \frac{11}{24} \)
- Final answer: \( \boxed{11\frac{11}{24}} \)

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10. \( 3\frac{2}{5} + 4\frac{1}{9} \)

- Whole numbers: \( 3 + 4 = 7 \)
- Fractions: \( \frac{2}{5} + \frac{1}{9} \) → LCD = 45
- \( \frac{2}{5} = \frac{18}{45}, \quad \frac{1}{9} = \frac{5}{45} \)
- Sum: \( \frac{18}{45} + \frac{5}{45} = \frac{23}{45} \)
- Final answer: \( \boxed{7\frac{23}{45}} \)

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## ✔ Final Answers Summary:

1. \( \boxed{5\frac{7}{12}} \)
2. \( \boxed{6\frac{11}{15}} \)
3. \( \boxed{6\frac{7}{10}} \)
4. \( \boxed{9\frac{1}{2}} \)
5. \( \boxed{4\frac{25}{28}} \)
6. \( \boxed{11\frac{11}{28}} \)
7. \( \boxed{10\frac{3}{10}} \)
8. \( \boxed{10\frac{17}{24}} \)
9. \( \boxed{11\frac{11}{24}} \)
10. \( \boxed{7\frac{23}{45}} \)

Let me know if you’d like to see visual diagrams or step-by-step fraction addition visuals for any problem!