Reciprocals worksheet for practicing finding reciprocals of mixed fractions.

Let's solve the problem step by step.

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Understanding the Task

The worksheet asks you to write the reciprocals of mixed fractions.

A reciprocal of a number is 1 divided by that number. For a fraction, you flip the numerator and denominator.

But here, we're dealing with mixed numbers, so first we need to:
1. Convert the mixed number to an improper fraction.
2. Then take the reciprocal (flip the numerator and denominator).

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Example Given in the Worksheet

> $ 2 \frac{5}{12} \longrightarrow \frac{29}{12} \longrightarrow \frac{12}{29} $

Let’s verify this:
- $ 2 \frac{5}{12} = \frac{(2 \times 12) + 5}{12} = \frac{24 + 5}{12} = \frac{29}{12} $
- Reciprocal: $ \frac{12}{29} $

✔ Correct.

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Now let’s solve each problem.

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Solutions

#### 1) $ 3 \frac{2}{5} $
- Convert: $ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $
- Reciprocal: $ \frac{5}{17} $

✔ Answer: $ \frac{5}{17} $

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#### 2) $ 1 \frac{4}{9} $
- Convert: $ \frac{(1 \times 9) + 4}{9} = \frac{13}{9} $
- Reciprocal: $ \frac{9}{13} $

✔ Answer: $ \frac{9}{13} $

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#### 3) $ 5 \frac{3}{7} $
- Convert: $ \frac{(5 \times 7) + 3}{7} = \frac{35 + 3}{7} = \frac{38}{7} $
- Reciprocal: $ \frac{7}{38} $

✔ Answer: $ \frac{7}{38} $

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#### 4) $ 3 \frac{2}{7} $
- Convert: $ \frac{(3 \times 7) + 2}{7} = \frac{21 + 2}{7} = \frac{23}{7} $
- Reciprocal: $ \frac{7}{23} $

✔ Answer: $ \frac{7}{23} $

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#### 5) $ 2 \frac{8}{15} $
- Convert: $ \frac{(2 \times 15) + 8}{15} = \frac{30 + 8}{15} = \frac{38}{15} $
- Reciprocal: $ \frac{15}{38} $

✔ Answer: $ \frac{15}{38} $

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#### 6) $ 4 \frac{9}{17} $
- Convert: $ \frac{(4 \times 17) + 9}{17} = \frac{68 + 9}{17} = \frac{77}{17} $
- Reciprocal: $ \frac{17}{77} $

✔ Answer: $ \frac{17}{77} $

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#### 7) $ 1 \frac{3}{5} $
- Convert: $ \frac{(1 \times 5) + 3}{5} = \frac{8}{5} $
- Reciprocal: $ \frac{5}{8} $

✔ Answer: $ \frac{5}{8} $

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#### 8) $ 3 \frac{4}{9} $
- Convert: $ \frac{(3 \times 9) + 4}{9} = \frac{27 + 4}{9} = \frac{31}{9} $
- Reciprocal: $ \frac{9}{31} $

✔ Answer: $ \frac{9}{31} $

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#### 9) $ 5 \frac{1}{2} $
- Convert: $ \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} $
- Reciprocal: $ \frac{2}{11} $

✔ Answer: $ \frac{2}{11} $

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#### 10) $ 2 \frac{7}{12} $
- Convert: $ \frac{(2 \times 12) + 7}{12} = \frac{24 + 7}{12} = \frac{31}{12} $
- Reciprocal: $ \frac{12}{31} $

✔ Answer: $ \frac{12}{31} $

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#### 11) $ 3 \frac{2}{15} $
- Convert: $ \frac{(3 \times 15) + 2}{15} = \frac{45 + 2}{15} = \frac{47}{15} $
- Reciprocal: $ \frac{15}{47} $

✔ Answer: $ \frac{15}{47} $

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#### 12) $ 1 \frac{11}{15} $
- Convert: $ \frac{(1 \times 15) + 11}{15} = \frac{26}{15} $
- Reciprocal: $ \frac{15}{26} $

✔ Answer: $ \frac{15}{26} $

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#### 13) $ 4 \frac{3}{7} $
- Convert: $ \frac{(4 \times 7) + 3}{7} = \frac{28 + 3}{7} = \frac{31}{7} $
- Reciprocal: $ \frac{7}{31} $

✔ Answer: $ \frac{7}{31} $

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#### 14) $ 2 \frac{4}{9} $
- Convert: $ \frac{(2 \times 9) + 4}{9} = \frac{18 + 4}{9} = \frac{22}{9} $
- Reciprocal: $ \frac{9}{22} $

✔ Answer: $ \frac{9}{22} $

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#### 15) $ 1 \frac{8}{17} $
- Convert: $ \frac{(1 \times 17) + 8}{17} = \frac{25}{17} $
- Reciprocal: $ \frac{17}{25} $

✔ Answer: $ \frac{17}{25} $

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#### 16) $ 2 \frac{4}{11} $
- Convert: $ \frac{(2 \times 11) + 4}{11} = \frac{22 + 4}{11} = \frac{26}{11} $
- Reciprocal: $ \frac{11}{26} $

✔ Answer: $ \frac{11}{26} $

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✔ Final Answers:

| Problem | Answer |
|--------|----------------|
| 1) | $ \frac{5}{17} $ |
| 2) | $ \frac{9}{13} $ |
| 3) | $ \frac{7}{38} $ |
| 4) | $ \frac{7}{23} $ |
| 5) | $ \frac{15}{38} $ |
| 6) | $ \frac{17}{77} $ |
| 7) | $ \frac{5}{8} $ |
| 8) | $ \frac{9}{31} $ |
| 9) | $ \frac{2}{11} $ |
| 10) | $ \frac{12}{31} $ |
| 11) | $ \frac{15}{47} $ |
| 12) | $ \frac{15}{26} $ |
| 13) | $ \frac{7}{31} $ |
| 14) | $ \frac{9}{22} $ |
| 15) | $ \frac{17}{25} $ |
| 16) | $ \frac{11}{26} $ |

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🔍 Summary of Steps:

1. Convert mixed number → improper fraction: Multiply whole number by denominator, add numerator, keep denominator.
2. Take reciprocal: Flip numerator and denominator.

This method works for all mixed numbers.

Let me know if you'd like this as a printable answer key!