Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

Let's solve each of these division of mixed numbers problems step by step.

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🔧 Step-by-step Process:

To divide mixed numbers:
1. Convert mixed numbers to improper fractions.
2. Change the division into multiplication by flipping the second fraction (reciprocal).
3. Multiply the fractions.
4. Simplify and convert back to a mixed number if needed.

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✔ Problem 1:

$ 1\frac{4}{6} \div 7\frac{1}{2} $

- Convert to improper fractions:
- $ 1\frac{4}{6} = \frac{6}{6} + \frac{4}{6} = \frac{10}{6} = \frac{5}{3} $ (simplified)
- $ 7\frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} $

- Now divide:
$$
\frac{5}{3} \div \frac{15}{2} = \frac{5}{3} \times \frac{2}{15} = \frac{10}{45} = \frac{2}{9}
$$

✔ Answer: $ \frac{2}{9} $

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✔ Problem 2:

$ 3\frac{4}{5} \div 5\frac{3}{5} $

- Convert:
- $ 3\frac{4}{5} = \frac{19}{5} $
- $ 5\frac{3}{5} = \frac{28}{5} $

- Divide:
$$
\frac{19}{5} \div \frac{28}{5} = \frac{19}{5} \times \frac{5}{28} = \frac{19}{28}
$$

✔ Answer: $ \frac{19}{28} $

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✔ Problem 3:

$ 3\frac{1}{3} \div 9\frac{2}{3} $

- Convert:
- $ 3\frac{1}{3} = \frac{10}{3} $
- $ 9\frac{2}{3} = \frac{29}{3} $

- Divide:
$$
\frac{10}{3} \div \frac{29}{3} = \frac{10}{3} \times \frac{3}{29} = \frac{10}{29}
$$

✔ Answer: $ \frac{10}{29} $

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✔ Problem 4:

$ 8\frac{1}{4} \div 5\frac{2}{4} $

- Simplify $ 5\frac{2}{4} = 5\frac{1}{2} $, but keep as is for now.
- Convert:
- $ 8\frac{1}{4} = \frac{33}{4} $
- $ 5\frac{2}{4} = \frac{22}{4} = \frac{11}{2} $

- Divide:
$$
\frac{33}{4} \div \frac{11}{2} = \frac{33}{4} \times \frac{2}{11} = \frac{66}{44} = \frac{3}{2} = 1\frac{1}{2}
$$

✔ Answer: $ 1\frac{1}{2} $

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✔ Problem 5:

$ 4\frac{1}{8} \div 2\frac{1}{2} $

- Convert:
- $ 4\frac{1}{8} = \frac{33}{8} $
- $ 2\frac{1}{2} = \frac{5}{2} $

- Divide:
$$
\frac{33}{8} \div \frac{5}{2} = \frac{33}{8} \times \frac{2}{5} = \frac{66}{40} = \frac{33}{20} = 1\frac{13}{20}
$$

✔ Answer: $ 1\frac{13}{20} $

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✔ Problem 6:

$ 7\frac{1}{2} \div 6\frac{1}{2} $

- Convert:
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ 6\frac{1}{2} = \frac{13}{2} $

- Divide:
$$
\frac{15}{2} \div \frac{13}{2} = \frac{15}{2} \times \frac{2}{13} = \frac{30}{26} = \frac{15}{13} = 1\frac{2}{13}
$$

✔ Answer: $ 1\frac{2}{13} $

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✔ Problem 7:

$ 4\frac{1}{3} \div 2\frac{1}{7} $

- Convert:
- $ 4\frac{1}{3} = \frac{13}{3} $
- $ 2\frac{1}{7} = \frac{15}{7} $

- Divide:
$$
\frac{13}{3} \div \frac{15}{7} = \frac{13}{3} \times \frac{7}{15} = \frac{91}{45} = 2\frac{1}{45}
$$

✔ Answer: $ 2\frac{1}{45} $

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✔ Problem 8:

$ 1\frac{1}{6} \div 1\frac{8}{9} $

- Convert:
- $ 1\frac{1}{6} = \frac{7}{6} $
- $ 1\frac{8}{9} = \frac{17}{9} $

- Divide:
$$
\frac{7}{6} \div \frac{17}{9} = \frac{7}{6} \times \frac{9}{17} = \frac{63}{102} = \frac{21}{34}
$$

✔ Answer: $ \frac{21}{34} $

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✔ Problem 9:

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

- Convert:
- $ 5\frac{1}{2} = \frac{11}{2} $
- $ 1\frac{1}{3} = \frac{4}{3} $

- Divide:
$$
\frac{11}{2} \div \frac{4}{3} = \frac{11}{2} \times \frac{3}{4} = \frac{33}{8} = 4\frac{1}{8}
$$

✔ Answer: $ 4\frac{1}{8} $

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✔ Problem 10:

$ 9\frac{4}{5} \div 5\frac{2}{5} $

- Convert:
- $ 9\frac{4}{5} = \frac{49}{5} $
- $ 5\frac{2}{5} = \frac{27}{5} $

- Divide:
$$
\frac{49}{5} \div \frac{27}{5} = \frac{49}{5} \times \frac{5}{27} = \frac{49}{27} = 1\frac{22}{27}
$$

✔ Answer: $ 1\frac{22}{27} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{2}{9} $ |
| 2 | $ \frac{19}{28} $ |
| 3 | $ \frac{10}{29} $ |
| 4 | $ 1\frac{1}{2} $ |
| 5 | $ 1\frac{13}{20} $ |
| 6 | $ 1\frac{2}{13} $ |
| 7 | $ 2\frac{1}{45} $ |
| 8 | $ \frac{21}{34} $ |
| 9 | $ 4\frac{1}{8} $ |
| 10 | $ 1\frac{22}{27} $ |

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Let me know if you'd like this in a printable format or with explanations for each! 😊