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Finding the whole from a percent

Find the original amount when you know a part and its percentage.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Hidden whole

Choose the whole-number answers to generate. The given part can be a decimal.

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mathsprig-1
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1329bb55
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Finding the whole from a percentFinding the whole from a percent. Practice. 12.5 is 50% of what number? 10 is 50% of what number? 16 is 25% of what number? 19.5 is 25% of what number? 20 is 25% of what number? 15.4 is 20% of what number? 48.5 is 50% of what number? 21.75 is 75% of what number? 48.5 is 50% of what number? 4.6 is 10% of what number? 18.2 is 20% of what number? 28.5 is 50% of what number?Name __________________________Date _______________Finding the whole from a percentFind the whole quantity. All answers are whole numbers.Worked example20 is 25% of what number? → 8025% = 1/4.1.12.5 is 50% of what number?2.10 is 50% of what number?3.16 is 25% of what number?4.19.5 is 25% of what number?5.20 is 25% of what number?6.15.4 is 20% of what number?7.48.5 is 50% of what number?8.21.75 is 75% of what number?9.48.5 is 50% of what number?10.4.6 is 10% of what number?11.18.2 is 20% of what number?12.28.5 is 50% of what number?MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 1329bb55
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Practice + answer key · 2 pages

Ratios & percentages

What you’ll practice

Use a known part and percent to recover the whole.

If 20 is one quarter of the whole, the whole must be four times as large. Use the given percentage to work backward from the part to the original amount.

How this skill works

If part = whole × p/100, then whole = part × 100/p.

A part representing less than 100% should give a larger whole. Substituting the whole into the original percentage checks the result.

Worked example

20 is 25% of what number?
  1. 25% = 1/4.
  2. 20 ÷ 1/4 = 20 × 4 = 80.
  3. Check: 25% of 80 is 20.

Answer: 80

Teaching notes

  • Do not calculate 25% of the part; that moves in the wrong direction.
Practice questions
  1. 12.5 is 50% of what number?
  2. 10 is 50% of what number?
  3. 16 is 25% of what number?
  4. 19.5 is 25% of what number?
  5. 20 is 25% of what number?
  6. 15.4 is 20% of what number?
  7. 48.5 is 50% of what number?
  8. 21.75 is 75% of what number?
  9. 48.5 is 50% of what number?
  10. 4.6 is 10% of what number?
  11. 18.2 is 20% of what number?
  12. 28.5 is 50% of what number?
Answers and steps
  1. 25
    1. 12.5 × 100 ÷ 50 = 25.
    2. Check: 50% of 25 is 12.5.
  2. 20
    1. 10 × 100 ÷ 50 = 20.
    2. Check: 50% of 20 is 10.
  3. 64
    1. 16 × 100 ÷ 25 = 64.
    2. Check: 25% of 64 is 16.
  4. 78
    1. 19.5 × 100 ÷ 25 = 78.
    2. Check: 25% of 78 is 19.5.
  5. 80
    1. 20 × 100 ÷ 25 = 80.
    2. Check: 25% of 80 is 20.
  6. 77
    1. 15.4 × 100 ÷ 20 = 77.
    2. Check: 20% of 77 is 15.4.
  7. 97
    1. 48.5 × 100 ÷ 50 = 97.
    2. Check: 50% of 97 is 48.5.
  8. 29
    1. 21.75 × 100 ÷ 75 = 29.
    2. Check: 75% of 29 is 21.75.
  9. 97
    1. 48.5 × 100 ÷ 50 = 97.
    2. Check: 50% of 97 is 48.5.
  10. 46
    1. 4.6 × 100 ÷ 10 = 46.
    2. Check: 10% of 46 is 4.6.
  11. 91
    1. 18.2 × 100 ÷ 20 = 91.
    2. Check: 20% of 91 is 18.2.
  12. 57
    1. 28.5 × 100 ÷ 50 = 57.
    2. Check: 50% of 57 is 28.5.