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Unit 7: Numeracy skillscrumpled paper

Ratio

Ratio is crudely explained as the proportion in which something or some things are shared. In other words, an expression of how the shares of the total compare with each other.

Example 1

Ann, Betty and Chris win a total of £1200 in a lottery. The money is shared according to how much each staked in the lottery. Ann is to receive 2 times as much as Chris. Betty is to receive 3 times as much as Chris. How much should each receive?

You need to begin by establishing the total number of shares.

  • Begin by allocating 1 share to Chris
  • Ann will then have 2 shares (2 times Chris’s share)
  • Betty will receive 3 shares (3 times Chris’s share)
  • Thus the total prize is to be shared 6 ways (1+2+3)
  • So one share will be £1200 divided by 6, so £200
  • Chris will receive £200, Ann £400 (2 times Chris’s share), and Betty £600 (3 times Chris’s share)
  • Check that the shares (£200 +£400 + £600) total £1200
  • Different phraseology of this question could be.....
    £1200 is to be shared out between Chris, Ann and Betty, in the RATIO of 1:2:3 respectively.
    How much will each receive?

Example 2

A school collected money for a new laboratory, using three methods, raffle, sponsored walk and fete. The total collected was £5200 in the ratio of 5:2:3 for each method in the order - raffle, walk, fete. How much did each method raise?

  • 5:2:3 expresses the proportions (‘shares’)
  • The total number of shares is 5+2+3, a total of 10
  • The total collected was £5200
  • Each share was £5200 / 10 giving. £520
  • The raffle raised 5 ‘shares’ of £520 = £2600
    The walk raised 2 ‘shares’ of £520 = £1040
    The fete raised 3 ‘shares’ of £520 = £1560
  • CHECK the total by addition = £5200

Try these questions:

  • i. 5 brothers inherit a total of £70000 in the proportions 1:1:2:3:3 How much did each receive?
  • ii. In a darts game Ben scored twice as many points as Alan. Chris scored three times as many as Ben. Doug scored half as many as Chris. The total number of points of the 4 players added together was 480. How many points did each player score?

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Creative Commons License
SMILE - Numeracy skills by Tom Frank, Eric Williams and Clare Wright, University of Birmingham Careers Centre adapted by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution 3.0 Unported License.