Rukasha Maths

GCSE maths Beta

Percentages and changing amounts · Revision guide

Foundation · Ratio · 1 page in the PDF

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Learning objectives

  • Use multipliers for percentage increases and decreases.
  • Reverse a change and calculate repeated percentage changes.

Key ideas

A percentage means a fraction out of one hundred.

p%=p100p\%=\frac p{100}

Multiply by the appropriate change multiplier.

increase: 1+p100,decrease: 1−p100\text{increase: }1+\frac p{100},\qquad\text{decrease: }1-\frac p{100}

For a non-zero multiplier, divide the changed amount to recover the original.

original=changed amountmultiplier\text{original}=\frac{\text{changed amount}}{\text{multiplier}}

Repeated changes apply to the current amount; multiply by every multiplier in sequence.

A full percentage decrease leaves zero; its original amount cannot be recovered from that zero alone.

Worked examples

Example 1

A coat costs fifty-four pounds after a quarter-price discount. Find its original price.

discount=25%,multiplier=1−0.25=0.75\text{discount}=25\%,\qquad\text{multiplier}=1-0.25=0.75
original price=£540.75=£72\text{original price}=\frac{\text{£54}}{0.75}=\text{£72}

Check by applying the discount.

£72×0.75=£54\text{£72}\times0.75=\text{£54}
£72\text{£72}

Example 2

Find the amount after two years of annual compound interest.

£200 at 5%:£200×1.052=£220.50\text{£200 at }5\%:\qquad\text{£200}\times1.05^2=\text{£220.50}
£220.50\text{£220.50}

Watch out

A reverse percentage is not undone by adding the same percentage. Divide by the original multiplier.