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Proportional Reasoning-1

Two ratios that are equal

Two cement mixes are labelled 3 : 4 and 9 : 12. Do they match?

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Two ratios: 3 : 4 and 9 : 12.
Step 1 of 3
  1. Two ratios: 3 : 4 and 9 : 12.
  2. Outer numbers: 3 × 12 = 36.
  3. Inner numbers: 4 × 9 = 36 — a match.

The rule

Yes, they match: multiplying across gives 36 both times.

Two equal ratios are in proportion. Write them as a : b :: c : d. Read it as a is to b as c is to d. Multiply across: a × d and b × c. Here a and d are the outer numbers. The inner numbers are b and c. Equal products mean a match.

  • 3 : 4 and 8 : 10: 3 × 10 = 30 and 4 × 8 = 32. These differ, so no match.
  • To find ? in 3 : 4 = 15 : ?, multiply across. 3 × ? = 4 × 15 = 60, so ? = 60 ÷ 3 = 20.

Jump to lesson

This track

  1. 0 Start here
  2. 1 How much more, and how many times
  3. 2 What 3 : 2 says, and what it does not
  4. 3 The same comparison in bigger numbers
  5. 4 Match the units, then cut it down
  6. 5 Sharing an amount in a ratio
  7. 6 Checkpoint: comparing, writing and sharing
  8. 7 Two ratios that are equal
  9. 8 Find the value of one
  10. 9 When two amounts grow together
  11. 10 A rate is a ratio with units on it
  12. 11 A scale is a ratio you can walk
  13. 12 Checkpoint: proportion, rates and scales
  14. 13 The big picture
  15. 14 Track quiz

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