Study notes

Percentage

Percentages of a quantity, percentage increase and decrease, and everyday money percentages like discount and GST.

Learn it step by step

Percentage means out of 100

$45% = \frac{45}{100}$ . To find a percentage of a quantity, change the percent to a fraction (or decimal) and multiply: $20%$ of $$50$ is $\frac{20}{100} \times 50 = $10$ .

45%

is 45 shaded squares out of 100.

Percentage increase or decrease compares to the original

Percentage change is always worked out compared to the ORIGINAL amount, not the new amount: $percentage change = \frac{change}{original} \times 100%$ .

A rise from 40 to 50 is a 25% increase (10 out of the original 40).

Discount means a percentage taken off the price

A 20% discount on a $$60$ item takes off $20%$ of $$60 = $12$ , so the new price is $$60 - $12 = $48$ .

GST adds a percentage on top of the price

GST works the opposite way from discount: it is added on. A price of $$100$ with 9% GST becomes $$100 + 9% of $100 = $109$ .

Reverse percentage: find the whole from a part

If you know a percentage of a number, work backwards to find the whole: if $40%$ of a number is $24$ , then $1%$ is $24 \div 40 = 0.6$ , so $100%$ (the whole number) is $0.6 \times 100 = 60$ .

Worked examples

Find 15% of \$80.

Change 15% to a fraction: $\frac{15}{100}$ .
Multiply: $\frac{15}{100} \times 80 = 12$ .
15% of \$80 is \$12.

A shirt costs \$45. After a discount it costs \$36. What is the percentage discount?

Discount amount: $45 - 36 = 9$ .
Percentage: $\frac{9}{45} \times 100% = 20%$ .

A meal costs \$60 before 9% GST. Find the total bill.

GST amount: $9% of 60 = 5.40$ .
Total: $60 + 5.40 = $65.40$ .

35% of the pupils in a class are boys. If there are 14 boys, how many pupils are in the class?

35% of the class is 14 pupils.
1% is $14 \div 35 = 0.4$ pupils.
100% (the whole class) is $0.4 \times 100 = 40$ pupils.

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