percentages.co.uk

Fractions, Decimals and Percentages Worksheet

KS3-GCSE | Years 6-11Mixed30 questions

Free to print and use in your classroom. No sign-up required.

Common Equivalents

FractionDecimalPercentage
1/20.550%
1/40.2525%
3/40.7575%
1/100.110%
1/50.220%
2/50.440%
3/50.660%
4/50.880%
1/30.333...33.3%
2/30.667...66.7%
1/80.12512.5%
3/80.37537.5%
5/80.62562.5%
7/80.87587.5%

Convert between fractions, decimals and percentages. Show your working where required. Give answers to 1 decimal place unless told otherwise.

Section A: Fraction to Percentage

  1. 1. Convert 1/2 to a percentage.

  2. 2. Convert 3/4 to a percentage.

  3. 3. Convert 1/5 to a percentage.

  4. 4. Convert 7/10 to a percentage.

  5. 5. Convert 3/8 to a percentage.

  6. 6. Convert 5/8 to a percentage.

  7. 7. Convert 2/3 to a percentage. Give your answer to 1 decimal place.

  8. 8. Convert 7/20 to a percentage.

  9. 9. Convert 9/25 to a percentage.

  10. 10. Convert 5/6 to a percentage. Give your answer to 1 decimal place.

Section B: Percentage to Fraction

Give all fractions in their simplest form.

  1. 11. Convert 40% to a fraction in its simplest form.

  2. 12. Convert 65% to a fraction in its simplest form.

  3. 13. Convert 12.5% to a fraction in its simplest form.

  4. 14. Convert 37.5% to a fraction in its simplest form.

  5. 15. Convert 80% to a fraction in its simplest form.

  6. 16. Convert 35% to a fraction in its simplest form.

  7. 17. Convert 62.5% to a fraction in its simplest form.

  8. 18. Convert 22% to a fraction in its simplest form.

  9. 19. Convert 45% to a fraction in its simplest form.

  10. 20. Convert 66.7% (recurring) to a fraction in its simplest form.

Section C: Decimals and Mixed Conversions

  1. 21. Convert 0.35 to a percentage.

  2. 22. Convert 0.625 to a percentage.

  3. 23. Convert 0.08 to a percentage.

  4. 24. Convert 72% to a decimal.

  5. 25. Convert 4.5% to a decimal.

  6. 26. Convert 0.005 to a percentage.

  7. 27. Arrange in order from smallest to largest: 0.4,  45%,  3/8,  0.42. Show your working.

  8. 28. Which is greater: 5/8 or 62%? Show your working.

  9. 29. Convert 1.25 to a percentage.

  10. 30. A student says 0.125 = 12.5% = 1/8. Are they correct? Explain your answer.

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Worked Answers

Section A: Fraction to Percentage

  1. 1. 1/2 = 1 ÷ 2 = 0.5 = 50%
  2. 2. 3/4 = 3 ÷ 4 = 0.75 = 75%
  3. 3. 1/5 = 1 ÷ 5 = 0.2 = 20%
  4. 4. 7/10 = 7 ÷ 10 = 0.7 = 70%
  5. 5. 3/8 = 3 ÷ 8 = 0.375 = 37.5%
  6. 6. 5/8 = 5 ÷ 8 = 0.625 = 62.5%
  7. 7. 2/3 = 2 ÷ 3 = 0.6666... = 66.7% (to 1 d.p.)
  8. 8. 7/20: multiply numerator and denominator by 5 to get 35/100 = 35%
  9. 9. 9/25: multiply by 4/4 to get 36/100 = 36%
  10. 10. 5/6 = 5 ÷ 6 = 0.8333... = 83.3% (to 1 d.p.)

Section B: Percentage to Fraction

  1. 11. 40% = 40/100 = 2/5 (divide by 20)
  2. 12. 65% = 65/100 = 13/20 (divide by 5)
  3. 13. 12.5% = 12.5/100 = 125/1000 = 1/8 (divide by 125)
  4. 14. 37.5% = 37.5/100 = 375/1000 = 3/8 (divide by 125)
  5. 15. 80% = 80/100 = 4/5 (divide by 20)
  6. 16. 35% = 35/100 = 7/20 (divide by 5)
  7. 17. 62.5% = 62.5/100 = 625/1000 = 5/8 (divide by 125)
  8. 18. 22% = 22/100 = 11/50 (divide by 2)
  9. 19. 45% = 45/100 = 9/20 (divide by 5)
  10. 20. 66.7% recurring = 2/3. Because 1/3 = 33.3...%, so 2/3 = 66.6...% ≈ 66.7%.

Section C: Decimals and Mixed Conversions

  1. 21. 0.35 × 100 = 35%
  2. 22. 0.625 × 100 = 62.5%
  3. 23. 0.08 × 100 = 8%
  4. 24. 72% ÷ 100 = 0.72
  5. 25. 4.5% ÷ 100 = 0.045
  6. 26. 0.005 × 100 = 0.5%
  7. 27. Convert all to percentages: 0.4 = 40%; 45% = 45%; 3/8 = 37.5%; 0.42 = 42%. Order: 3/8 (37.5%) < 0.4 (40%) < 0.42 (42%) < 45%
  8. 28. 5/8 = 62.5%. Since 62.5% > 62%, 5/8 is greater.
  9. 29. 1.25 × 100 = 125%
  10. 30. Yes, the student is correct. 0.125 × 100 = 12.5%, and 12.5/100 = 125/1000 = 1/8. All three values are equivalent.

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