Conversion of mixed numbers to improper fractions worksheets ... - Free Printable

Let's go through the Fractions Worksheet and verify each conversion from a mixed number to an improper fraction. The general formula for converting a mixed number $ a \frac{b}{c} $ into an improper fraction is:

$$
\text{Improper Fraction} = \frac{(a \times c) + b}{c}
$$

We’ll check each one step by step.

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1. $ 4 \frac{6}{8} = \frac{19}{4} $

- First, simplify $ \frac{6}{8} = \frac{3}{4} $
- So, $ 4 \frac{3}{4} $
- $ (4 \times 4) + 3 = 16 + 3 = 19 $
- Improper fraction: $ \frac{19}{4} $ ✔

✔ Correct

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2. $ 16 \frac{1}{2} = \frac{33}{2} $

- $ (16 \times 2) + 1 = 32 + 1 = 33 $
- $ \frac{33}{2} $ ✔

✔ Correct

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3. $ 5 \frac{5}{20} = \frac{21}{4} $

- Simplify $ \frac{5}{20} = \frac{1}{4} $
- So, $ 5 \frac{1}{4} $
- $ (5 \times 4) + 1 = 20 + 1 = 21 $
- $ \frac{21}{4} $ ✔

✔ Correct

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4. $ 20 \frac{1}{12} = \frac{241}{12} $

- $ (20 \times 12) + 1 = 240 + 1 = 241 $
- $ \frac{241}{12} $ ✔

✔ Correct

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5. $ 3 \frac{47}{50} = \frac{197}{50} $

- $ (3 \times 50) + 47 = 150 + 47 = 197 $
- $ \frac{197}{50} $ ✔

✔ Correct

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6. $ 10 \frac{1}{3} = \frac{31}{3} $

- $ (10 \times 3) + 1 = 30 + 1 = 31 $
- $ \frac{31}{3} $ ✔

✔ Correct

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7. $ 1 \frac{1}{10} = \frac{11}{10} $

- $ (1 \times 10) + 1 = 10 + 1 = 11 $
- $ \frac{11}{10} $ ✔

✔ Correct

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8. $ 18 \frac{2}{25} = \frac{452}{25} $

- $ (18 \times 25) + 2 = 450 + 2 = 452 $
- $ \frac{452}{25} $ ✔

✔ Correct

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9. $ 19 \frac{13}{15} = \frac{298}{15} $

- $ (19 \times 15) + 13 = 285 + 13 = 298 $
- $ \frac{298}{15} $ ✔

✔ Correct

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10. $ 19 \frac{1}{4} = \frac{77}{4} $

- $ (19 \times 4) + 1 = 76 + 1 = 77 $
- $ \frac{77}{4} $ ✔

✔ Correct

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11. $ 8 \frac{1}{5} = \frac{41}{5} $

- $ (8 \times 5) + 1 = 40 + 1 = 41 $
- $ \frac{41}{5} $ ✔

✔ Correct

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12. $ 13 \frac{3}{16} = \frac{211}{16} $

- $ (13 \times 16) + 3 = 208 + 3 = 211 $
- $ \frac{211}{16} $ ✔

✔ Correct

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13. $ 6 \frac{1}{12} = \frac{73}{12} $

- $ (6 \times 12) + 1 = 72 + 1 = 73 $
- $ \frac{73}{12} $ ✔

✔ Correct

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14. $ 8 \frac{20}{100} = \frac{41}{5} $

- Simplify $ \frac{20}{100} = \frac{1}{5} $
- So, $ 8 \frac{1}{5} $
- $ (8 \times 5) + 1 = 40 + 1 = 41 $
- $ \frac{41}{5} $ ✔

✔ Correct

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15. $ 20 \frac{14}{18} = \frac{187}{9} $

- Simplify $ \frac{14}{18} = \frac{7}{9} $
- So, $ 20 \frac{7}{9} $
- $ (20 \times 9) + 7 = 180 + 7 = 187 $
- $ \frac{187}{9} $ ✔

✔ Correct

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16. $ 16 \frac{24}{50} = \frac{412}{25} $

- Simplify $ \frac{24}{50} = \frac{12}{25} $
- So, $ 16 \frac{12}{25} $
- $ (16 \times 25) + 12 = 400 + 12 = 412 $
- $ \frac{412}{25} $ ✔

✔ Correct

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17. $ 13 \frac{4}{5} = \frac{69}{5} $

- $ (13 \times 5) + 4 = 65 + 4 = 69 $
- $ \frac{69}{5} $ ✔

✔ Correct

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18. $ 5 \frac{2}{8} = \frac{21}{4} $

- Simplify $ \frac{2}{8} = \frac{1}{4} $
- So, $ 5 \frac{1}{4} $
- $ (5 \times 4) + 1 = 20 + 1 = 21 $
- $ \frac{21}{4} $ ✔

✔ Correct

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19. $ 1 \frac{3}{4} = \frac{7}{4} $

- $ (1 \times 4) + 3 = 4 + 3 = 7 $
- $ \frac{7}{4} $ ✔

✔ Correct

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20. $ 1 \frac{1}{3} = \frac{4}{3} $

- $ (1 \times 3) + 1 = 3 + 1 = 4 $
- $ \frac{4}{3} $ ✔

✔ Correct

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21. $ 2 \frac{3}{18} = \frac{13}{6} $

- Simplify $ \frac{3}{18} = \frac{1}{6} $
- So, $ 2 \frac{1}{6} $
- $ (2 \times 6) + 1 = 12 + 1 = 13 $
- $ \frac{13}{6} $ ✔

✔ Correct

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✔ Final Answer: All answers are correct!

All 21 conversions from mixed numbers to improper fractions have been correctly solved.

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🔍 Summary of Key Steps:

To convert a mixed number $ a \frac{b}{c} $ to an improper fraction:
1. Multiply the whole number $ a $ by the denominator $ c $
2. Add the numerator $ b $
3. Place the result over the original denominator $ c $

Example:
$ 5 \frac{2}{8} = \frac{(5 \times 8) + 2}{8} = \frac{40 + 2}{8} = \frac{42}{8} = \frac{21}{4} $ after simplifying.

> Note: In this worksheet, simplification was done before or after conversion — always aim to reduce fractions when possible.

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✔ All answers on the worksheet are correct. Great job!