Printable worksheet for practicing simplifying proper and improper fractions.
A colorful math worksheet titled "Fractions Worksheets: Simplifying proper and improper fractions" with 16 problems for simplifying fractions, featuring a decorative border and two cartoon children in the bottom left corner.
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying proper and improper fraction - Math Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying proper and improper fraction - Math Worksheets ...
Let's solve each of these fractions by simplifying them to their lowest terms. To simplify a fraction, we divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
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- GCD of 7 and 56 is 7
- $\frac{7 \div 7}{56 \div 7} = \frac{1}{8}$
✔ Answer: $\frac{1}{8}$
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- GCD of 200 and 500 is 100
- $\frac{200 \div 100}{500 \div 100} = \frac{2}{5}$
✔ Answer: $\frac{2}{5}$
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- GCD of 15 and 20 is 5
- $\frac{15 \div 5}{20 \div 5} = \frac{3}{4}$
✔ Answer: $\frac{3}{4}$
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- GCD of 56 and 96 is 8
- $\frac{56 \div 8}{96 \div 8} = \frac{7}{12}$
✔ Answer: $\frac{7}{12}$
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- This is an improper fraction (numerator > denominator)
- GCD of 44 and 12 is 4
- $\frac{44 \div 4}{12 \div 4} = \frac{11}{3}$
- Convert to mixed number: $ \frac{11}{3} = 3\frac{2}{3} $
✔ Answer: $3\frac{2}{3}$ or $\frac{11}{3}$
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- GCD of 100 and 32 is 4
- $\frac{100 \div 4}{32 \div 4} = \frac{25}{8}$
- Convert to mixed number: $ \frac{25}{8} = 3\frac{1}{8} $
✔ Answer: $3\frac{1}{8}$ or $\frac{25}{8}$
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- GCD of 152 and 200 is 8
- $\frac{152 \div 8}{200 \div 8} = \frac{19}{25}$
✔ Answer: $\frac{19}{25}$
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- GCD of 342 and 40 is 2
- $\frac{342 \div 2}{40 \div 2} = \frac{171}{20}$
- Convert to mixed number: $ \frac{171}{20} = 8\frac{11}{20} $
✔ Answer: $8\frac{11}{20}$ or $\frac{171}{20}$
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- GCD of 12 and 20 is 4
- $\frac{12 \div 4}{20 \div 4} = \frac{3}{5}$
✔ Answer: $\frac{3}{5}$
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- GCD of 8 and 20 is 4
- $\frac{8 \div 4}{20 \div 4} = \frac{2}{5}$
✔ Answer: $\frac{2}{5}$
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- GCD of 4 and 12 is 4
- $\frac{4 \div 4}{12 \div 4} = \frac{1}{3}$
✔ Answer: $\frac{1}{3}$
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- GCD of 72 and 16 is 8
- $\frac{72 \div 8}{16 \div 8} = \frac{9}{2}$
- Convert to mixed number: $ \frac{9}{2} = 4\frac{1}{2} $
✔ Answer: $4\frac{1}{2}$ or $\frac{9}{2}$
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- GCD of 175 and 250 is 25
- $\frac{175 \div 25}{250 \div 25} = \frac{7}{10}$
✔ Answer: $\frac{7}{10}$
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- GCD of 52 and 100 is 4
- $\frac{52 \div 4}{100 \div 4} = \frac{13}{25}$
✔ Answer: $\frac{13}{25}$
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- GCD of 12 and 32 is 4
- $\frac{12 \div 4}{32 \div 4} = \frac{3}{8}$
✔ Answer: $\frac{3}{8}$
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- GCD of 99 and 108 is 9
- $\frac{99 \div 9}{108 \div 9} = \frac{11}{12}$
✔ Answer: $\frac{11}{12}$
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| Problem | Answer |
|--------|--------|
| 1. $\frac{7}{56}$ | $\frac{1}{8}$ |
| 2. $\frac{200}{500}$ | $\frac{2}{5}$ |
| 3. $\frac{15}{20}$ | $\frac{3}{4}$ |
| 4. $\frac{56}{96}$ | $\frac{7}{12}$ |
| 5. $\frac{44}{12}$ | $3\frac{2}{3}$ or $\frac{11}{3}$ |
| 6. $\frac{100}{32}$ | $3\frac{1}{8}$ or $\frac{25}{8}$ |
| 7. $\frac{152}{200}$ | $\frac{19}{25}$ |
| 8. $\frac{342}{40}$ | $8\frac{11}{20}$ or $\frac{171}{20}$ |
| 9. $\frac{12}{20}$ | $\frac{3}{5}$ |
| 10. $\frac{8}{20}$ | $\frac{2}{5}$ |
| 11. $\frac{4}{12}$ | $\frac{1}{3}$ |
| 12. $\frac{72}{16}$ | $4\frac{1}{2}$ or $\frac{9}{2}$ |
| 13. $\frac{175}{250}$ | $\frac{7}{10}$ |
| 14. $\frac{52}{100}$ | $\frac{13}{25}$ |
| 15. $\frac{12}{32}$ | $\frac{3}{8}$ |
| 16. $\frac{99}{108}$ | $\frac{11}{12}$ |
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1. Find the GCD of numerator and denominator.
2. Divide both by the GCD.
3. If the result is an improper fraction (numerator > denominator), convert it to a mixed number.
4. Always check if the simplified fraction can be reduced further.
Let me know if you'd like a printable version or step-by-step GCD calculations!
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1. $\frac{7}{56}$
- GCD of 7 and 56 is 7
- $\frac{7 \div 7}{56 \div 7} = \frac{1}{8}$
✔ Answer: $\frac{1}{8}$
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2. $\frac{200}{500}$
- GCD of 200 and 500 is 100
- $\frac{200 \div 100}{500 \div 100} = \frac{2}{5}$
✔ Answer: $\frac{2}{5}$
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3. $\frac{15}{20}$
- GCD of 15 and 20 is 5
- $\frac{15 \div 5}{20 \div 5} = \frac{3}{4}$
✔ Answer: $\frac{3}{4}$
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4. $\frac{56}{96}$
- GCD of 56 and 96 is 8
- $\frac{56 \div 8}{96 \div 8} = \frac{7}{12}$
✔ Answer: $\frac{7}{12}$
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5. $\frac{44}{12}$
- This is an improper fraction (numerator > denominator)
- GCD of 44 and 12 is 4
- $\frac{44 \div 4}{12 \div 4} = \frac{11}{3}$
- Convert to mixed number: $ \frac{11}{3} = 3\frac{2}{3} $
✔ Answer: $3\frac{2}{3}$ or $\frac{11}{3}$
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6. $\frac{100}{32}$
- GCD of 100 and 32 is 4
- $\frac{100 \div 4}{32 \div 4} = \frac{25}{8}$
- Convert to mixed number: $ \frac{25}{8} = 3\frac{1}{8} $
✔ Answer: $3\frac{1}{8}$ or $\frac{25}{8}$
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7. $\frac{152}{200}$
- GCD of 152 and 200 is 8
- $\frac{152 \div 8}{200 \div 8} = \frac{19}{25}$
✔ Answer: $\frac{19}{25}$
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8. $\frac{342}{40}$
- GCD of 342 and 40 is 2
- $\frac{342 \div 2}{40 \div 2} = \frac{171}{20}$
- Convert to mixed number: $ \frac{171}{20} = 8\frac{11}{20} $
✔ Answer: $8\frac{11}{20}$ or $\frac{171}{20}$
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9. $\frac{12}{20}$
- GCD of 12 and 20 is 4
- $\frac{12 \div 4}{20 \div 4} = \frac{3}{5}$
✔ Answer: $\frac{3}{5}$
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10. $\frac{8}{20}$
- GCD of 8 and 20 is 4
- $\frac{8 \div 4}{20 \div 4} = \frac{2}{5}$
✔ Answer: $\frac{2}{5}$
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11. $\frac{4}{12}$
- GCD of 4 and 12 is 4
- $\frac{4 \div 4}{12 \div 4} = \frac{1}{3}$
✔ Answer: $\frac{1}{3}$
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12. $\frac{72}{16}$
- GCD of 72 and 16 is 8
- $\frac{72 \div 8}{16 \div 8} = \frac{9}{2}$
- Convert to mixed number: $ \frac{9}{2} = 4\frac{1}{2} $
✔ Answer: $4\frac{1}{2}$ or $\frac{9}{2}$
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13. $\frac{175}{250}$
- GCD of 175 and 250 is 25
- $\frac{175 \div 25}{250 \div 25} = \frac{7}{10}$
✔ Answer: $\frac{7}{10}$
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14. $\frac{52}{100}$
- GCD of 52 and 100 is 4
- $\frac{52 \div 4}{100 \div 4} = \frac{13}{25}$
✔ Answer: $\frac{13}{25}$
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15. $\frac{12}{32}$
- GCD of 12 and 32 is 4
- $\frac{12 \div 4}{32 \div 4} = \frac{3}{8}$
✔ Answer: $\frac{3}{8}$
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16. $\frac{99}{108}$
- GCD of 99 and 108 is 9
- $\frac{99 \div 9}{108 \div 9} = \frac{11}{12}$
✔ Answer: $\frac{11}{12}$
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1. $\frac{7}{56}$ | $\frac{1}{8}$ |
| 2. $\frac{200}{500}$ | $\frac{2}{5}$ |
| 3. $\frac{15}{20}$ | $\frac{3}{4}$ |
| 4. $\frac{56}{96}$ | $\frac{7}{12}$ |
| 5. $\frac{44}{12}$ | $3\frac{2}{3}$ or $\frac{11}{3}$ |
| 6. $\frac{100}{32}$ | $3\frac{1}{8}$ or $\frac{25}{8}$ |
| 7. $\frac{152}{200}$ | $\frac{19}{25}$ |
| 8. $\frac{342}{40}$ | $8\frac{11}{20}$ or $\frac{171}{20}$ |
| 9. $\frac{12}{20}$ | $\frac{3}{5}$ |
| 10. $\frac{8}{20}$ | $\frac{2}{5}$ |
| 11. $\frac{4}{12}$ | $\frac{1}{3}$ |
| 12. $\frac{72}{16}$ | $4\frac{1}{2}$ or $\frac{9}{2}$ |
| 13. $\frac{175}{250}$ | $\frac{7}{10}$ |
| 14. $\frac{52}{100}$ | $\frac{13}{25}$ |
| 15. $\frac{12}{32}$ | $\frac{3}{8}$ |
| 16. $\frac{99}{108}$ | $\frac{11}{12}$ |
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🔍 Tips for Simplifying Fractions:
1. Find the GCD of numerator and denominator.
2. Divide both by the GCD.
3. If the result is an improper fraction (numerator > denominator), convert it to a mixed number.
4. Always check if the simplified fraction can be reduced further.
Let me know if you'd like a printable version or step-by-step GCD calculations!
Parent Tip: Review the logic above to help your child master the concept of proper fractions worksheet.
