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Year 9 Maths | Understand, justify, check

Apply each percentage to the current amount

Two percentage changes act in sequence, so the second usually applies to a different base. Keeping track of that changing amount is essential when comparing sale offers or interpreting a price that falls and then rises.

What to notice

A 20% discount leaves 80% of the price. The multiplier 0.8 expresses the amount retained. A later 10% discount then acts on that reduced amount, not the starting price.

What to do

Write one multiplier for each change and apply them in order. Keep intermediate calculations exact, then interpret the final amount and compare it with the original base.

Why it works

Multipliers expose which amount a percentage acts on. Adding the advertised percentages ignores the changing base and can overstate a combined discount.

Work through an example

A $100 item is discounted by 20%, then by a further 10%. Find the final price.

0Start100First80Final72
Price in dollars: Start 100, after first discount 80, after second discount 72. All bars start at zero.
  1. After the first discount, $100 × 0.8 = $80.
  2. The second discount leaves $80 × 0.9 = $72.
  3. The overall saving is $28, so the combined discount is 28%, not 30%.

A common mistake

An equal percentage decrease and increase do not cancel. The increase is calculated from the lower amount, so it does not restore the original price.

A strategy to try

Use an easy starting value, such as $100, to test a claim about percentage changes. Then express the pattern as a product of multipliers.

Try it now

Try three questions

No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.

1. A $200 item has a 10% discount, then a further 20% discount. What is the final price?
Help: a starting point

Find the amount remaining after the first 10% discount.

Help: the next step

Apply the further 20% discount to that new price.

2. A price is reduced by 20%, then by a further 25%. What percentage of the original price is saved overall?
Help: a starting point

Multiply the two retained-price fractions rather than adding the discounts.

Help: the next step

Subtract the retained fraction from one whole, then express it as a percentage.

3. A $100 price falls by 20%, then rises by 20%. What is the final price?
Help: a starting point

Calculate the reduced price first.

Help: the next step

For the increase, multiply that reduced price by 1.2.

For parents and carers

Ask which price forms the base at each step. The questions include a final price, a combined saving and a decrease followed by an increase. This is arithmetic practice, not advice about purchasing or financial products.

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