Convert mixed numbers to improper fractions with this educational math worksheet.

Let's solve the problem of converting mixed numbers to improper fractions step by step.

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🔷 How to Convert a Mixed Number to an Improper Fraction:

A mixed number has the form:
$$
a \frac{b}{c}
$$
where:
- $ a $ is the whole number,
- $ b $ is the numerator,
- $ c $ is the denominator.

To convert it to an improper fraction, follow these steps:

1. Multiply the whole number ($ a $) by the denominator ($ c $).
2. Add the numerator ($ b $) to that product.
3. Place the result over the original denominator ($ c $).

So:
$$
a \frac{b}{c} = \frac{a \times c + b}{c}
$$

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Now, let's apply this to each problem:

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✔ Solutions:

1. $ 9\frac{1}{9} = \frac{9 \times 9 + 1}{9} = \frac{81 + 1}{9} = \frac{82}{9} $

2. $ 3\frac{8}{9} = \frac{3 \times 9 + 8}{9} = \frac{27 + 8}{9} = \frac{35}{9} $

3. $ 8\frac{7}{12} = \frac{8 \times 12 + 7}{12} = \frac{96 + 7}{12} = \frac{103}{12} $

4. $ 7\frac{7}{9} = \frac{7 \times 9 + 7}{9} = \frac{63 + 7}{9} = \frac{70}{9} $

5. $ 3\frac{11}{15} = \frac{3 \times 15 + 11}{15} = \frac{45 + 11}{15} = \frac{56}{15} $

6. $ 3\frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $

7. $ 4\frac{2}{7} = \frac{4 \times 7 + 2}{7} = \frac{28 + 2}{7} = \frac{30}{7} $

8. $ 7\frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3} $

9. $ 5\frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} $

10. $ 2\frac{7}{10} = \frac{2 \times 10 + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10} $

11. $ 3\frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} $

12. $ 4\frac{5}{7} = \frac{4 \times 7 + 5}{7} = \frac{28 + 5}{7} = \frac{33}{7} $

13. $ 3\frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8} $

14. $ 6\frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8} $

15. $ 5\frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{30 + 5}{6} = \frac{35}{6} $

16. $ 7\frac{4}{15} = \frac{7 \times 15 + 4}{15} = \frac{105 + 4}{15} = \frac{109}{15} $

17. $ 4\frac{2}{9} = \frac{4 \times 9 + 2}{9} = \frac{36 + 2}{9} = \frac{38}{9} $

18. $ 9\frac{1}{6} = \frac{9 \times 6 + 1}{6} = \frac{54 + 1}{6} = \frac{55}{6} $

19. $ 7\frac{5}{8} = \frac{7 \times 8 + 5}{8} = \frac{56 + 5}{8} = \frac{61}{8} $

20. $ 1\frac{5}{9} = \frac{1 \times 9 + 5}{9} = \frac{9 + 5}{9} = \frac{14}{9} $

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✔ Final Answers (Listed):

| Mixed Number | Improper Fraction |
|--------------|-------------------|
| $ 9\frac{1}{9} $ | $ \frac{82}{9} $ |
| $ 3\frac{8}{9} $ | $ \frac{35}{9} $ |
| $ 8\frac{7}{12} $ | $ \frac{103}{12} $ |
| $ 7\frac{7}{9} $ | $ \frac{70}{9} $ |
| $ 3\frac{11}{15} $ | $ \frac{56}{15} $ |
| $ 3\frac{2}{5} $ | $ \frac{17}{5} $ |
| $ 4\frac{2}{7} $ | $ \frac{30}{7} $ |
| $ 7\frac{1}{3} $ | $ \frac{22}{3} $ |
| $ 5\frac{1}{7} $ | $ \frac{36}{7} $ |
| $ 2\frac{7}{10} $ | $ \frac{27}{10} $ |
| $ 3\frac{4}{5} $ | $ \frac{19}{5} $ |
| $ 4\frac{5}{7} $ | $ \frac{33}{7} $ |
| $ 3\frac{3}{8} $ | $ \frac{27}{8} $ |
| $ 6\frac{1}{8} $ | $ \frac{49}{8} $ |
| $ 5\frac{5}{6} $ | $ \frac{35}{6} $ |
| $ 7\frac{4}{15} $ | $ \frac{109}{15} $ |
| $ 4\frac{2}{9} $ | $ \frac{38}{9} $ |
| $ 9\frac{1}{6} $ | $ \frac{55}{6} $ |
| $ 7\frac{5}{8} $ | $ \frac{61}{8} $ |
| $ 1\frac{5}{9} $ | $ \frac{14}{9} $ |

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✔ All conversions are now complete!
Let me know if you'd like a printable version or help with reducing any fractions (though they're already in simplest form unless specified).