Study notes

Percentage

Expressing a part as a percentage, finding a percentage of a quantity, and everyday money percentages.

Learn it step by step

Percentage means out of 100

$38% = \frac{38}{100}$ . A percentage always compares a part to a whole of 100 equal parts.

38%

is 38 shaded squares out of 100.

Expressing a part of a whole as a percentage

Write the part as a fraction of the whole, then multiply by 100%: 15 out of 20 pupils is $\frac{15}{20} \times 100% = 75%$ .

Finding a percentage of a quantity

Change the percent to a fraction (or decimal) and multiply: $20%$ of $$50$ is $\frac{20}{100} \times 50 = $10$ .

The shaded part is

20%

of the whole

$50

Discount, GST, and interest are all percentage-of-a-quantity problems

A discount takes a percentage OFF the price; GST and interest ADD a percentage ON. A 15% discount on $$40$ takes off $$6$ , giving a new price of $$34$ .

Worked examples

Express 18 out of 25 as a percentage.

Write as a fraction: $\frac{18}{25}$ .
Multiply by 100%: $\frac{18}{25} \times 100% = 72%$ .

Find 35% of \$60.

Change 35% to a fraction: $\frac{35}{100}$ .
Multiply: $\frac{35}{100} \times 60 = 21$ .
35% of \$60 is \$21.

A bag costs \$50. It is on sale with a 12% discount. Find the sale price.

Find the discount: $12% of 50 = 6$ .
Subtract from the original price: $50 - 6 = 44$ .
The sale price is \$44.

A savings account pays 4% annual interest. Find the interest earned on \$300 in one year.

Find 4% of \$300.
$\frac{4}{100} \times 300 = 12$ .
The interest earned is \$12.

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