Decimals and Percentages · Grade 6

How do you work out a price after a discount or a price rise?

Work out the discount and subtract it, or multiply directly by what is left: a thirty per cent discount means paying seventy per cent. A price rise works the same way with a hundred and ten per cent. A rise and a fall of the same percentage do not cancel out, because each is calculated from a different whole.

Learning objectives

Two ways, one of them short

The long way: work out how much the discount is in money and subtract it from the price. It is always correct and easy to explain, and it is the way to start.

The short way: a twenty per cent discount means there is eighty per cent left to pay, so multiply directly by 0.8. One step instead of two, and less room for error.

A price rise is the same idea. An increase of fifteen per cent means paying a hundred and fifteen per cent, which is multiplying by 1.15.

Why they do not cancel

A price of a hundred that rises by ten per cent becomes a hundred and ten. Now a ten per cent discount is calculated from a hundred and ten, not from a hundred, so it is eleven rather than ten.

The result is ninety-nine, not a hundred. The percentage is the same but the whole it was taken from is different, and that is exactly the principle this whole topic rests on: a percentage always asks, of what.

Comparing two offers

Two shops with different deals cannot be compared by the size of the percentage alone, because the original prices differ. Work out the final price in each and compare that.

Two successive discounts in the same shop do not add up either. Twenty per cent and then another ten per cent is not thirty per cent, because the second is taken from the already reduced price.

Worked examples

  1. A coat costs 250 with a 20 per cent discount. What is the final price?

    1. A 20 per cent discount means paying 80 per cent
    2. Convert: 80 per cent is 0.8
    3. Multiply: 250 times 0.8

    Answer: 200

  2. An item costing 80 rises by 15 per cent. What does it cost now?

    1. A 15 per cent rise means 115 per cent of the price
    2. Convert: 1.15
    3. Multiply: 80 times 1.15

    Answer: 92

  3. A price of 100 rises by 10 per cent and then falls by 10 per cent. What is it now?

    1. After the rise: 100 times 1.1 is 110
    2. The discount is taken from 110, not from 100
    3. 10 per cent of 110 is 11
    4. Subtract: 110 minus 11

    Answer: 99 — not 100

Common mistakes

Adding two successive discounts
The second discount is taken from the already reduced price. Twenty and then ten is twenty-eight per cent, not thirty, so work them out one after the other.
Multiplying by the discount rather than by what is left
Multiplying by 0.2 gives the discount itself, not the price to pay. For the final price in one step, multiply by 0.8.
Comparing offers by the size of the percentage
A large percentage off a high price can cost more than a small one off a low price. The only comparison that means anything is between the two final prices.

What to remember

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