Topic 12 of 12

Percent of an amount

Step 8 · Ratios and negative numbers topics

A percent of an amount is that many hundredths of it, found by multiplying by $\frac{p}{100}$ or by building up from easy percents like 10% and 50%.

What a percent of an amount means

The word percent means "per hundred". So $25\%$ means 25 out of every 100, which is the fraction $\frac{25}{100}$ . That fraction simplifies to $\frac{1}{4}$ . Finding a percent of an amount means taking that fraction of the amount.

For example, $25\%$ of 80 is one quarter of 80. Dividing 80 into 4 equal parts gives 20 in each part, so $25\%$ of 80 is 20. The "of" in a percent problem works like the "of" in "half of 80": it tells you to multiply.

p\% \text{ of } A = \frac{p}{100} \times A

Two ways to work it out

Method 1: build it from easy percents. Because 100 splits nicely, some percents are quick to find. Use these as building blocks.

Percent	Same as	How to find it
50%	one half	divide by 2
25%	one quarter	divide by 4
10%	one tenth	divide by 10
1%	one hundredth	divide by 100
5%	half of 10%	find 10%, then halve it

Example: Building up from 10%

Find $35\%$ of 80.

Find $10\%$ : $80 \div 10 = 8$ .
Find $30\%$ , which is three tens: $3 \times 8 = 24$ .
Find $5\%$ , which is half of $10\%$ : $8 \div 2 = 4$ .
Add: $30\% + 5\% = 35\%$ , so $24 + 4 = 28$ .

Answer28

Method 2: use the fraction directly. Multiply the amount by $\frac{p}{100}$ . Check the answer above: $\frac{35}{100} \times 80 = \frac{2800}{100} = 28$ . Both methods agree. Building up is good for mental maths, and the fraction method always works.

Using percents in real problems

Percents often appear in shops. A discount is a percent of the original price. You find the discount first, then subtract it to get the new price.

Example: A sale price

A jacket costs $48. It is on sale for $25\%$ off. What is the sale price?

Find the discount: $25\%$ of 48 is $48 \div 4 = 12$ .
Subtract it from the original price: $48 - 12 = 36$ .

Answer$36

A percent can also be more than 100. Since $100\%$ is the whole amount, $150\%$ is the whole plus another half. So $150\%$ of 40 is $40 + 20 = 60$ .

A quick check: if the percent is less than $100\%$ , your answer must be smaller than the amount. If it is more than $100\%$ , the answer must be bigger. You can use this to catch slips. To review turning percents into decimals, look back at the lesson on decimals and percents.

Try it yourself

Work each one on paper first, then open the answer to check.

Find 20% of 90.
Show answer
18
Find 75% of 48.
Show answer
36
Find 35% of 200.
Show answer
70
A shirt costs $70 and is 30% off. What is the sale price?
Show answer
$49
Find 150% of 24.
Show answer
36
Find 12% of 50.
Show answer
6