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Fractions in Disguise

Comparing two groups of different sizes

In section A, 27 of 40 seeds sprouted (began to grow). In section B, 18 of 25. Which did better?

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Section A: 27 of 40.
Step 1 of 3
  1. Section A: 27 of 40.
  2. Section B: 18 of 25.
  3. Put both on one shared 0-to-100 scale.

The rule

Section B did better. A larger share of its seeds sprouted: 72%, against 67.5%.

Compare shares, not counts. A share is a count divided by its own total. Write each share as a percentage.

  • Section A: 27 ÷ 40 = 0.675. Then 0.675 × 100 = 67.5, so 67.5%.
  • Section B: 18 ÷ 25 = 0.72. Then 0.72 × 100 = 72, so 72%.
  • Section B has the smaller count and the bigger share.

Two tests can have different totals too. 33 ÷ 40 = 0.825, so 33 out of 40 is 82.5%. 45 ÷ 60 = 0.75, so 45 out of 60 is 75%. The first test has the larger share.

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This track

  1. 0 Start here
  2. 1 A comparison with a hundred underneath
  3. 2 Three names for one amount
  4. 3 Taking a percentage of an amount
  5. 4 One amount said as a percentage of another
  6. 5 Measured against what you started with
  7. 6 An equal rise and fall do not cancel
  8. 7 Comparing two groups of different sizes
  9. 8 Where percentages are used
  10. 9 The big picture
  11. 10 Track quiz

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