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Percents

lesson · about 3 minutes

Convert fractions to percents and take common percents of amounts.

Best in your head · no pen, no calculator why?

Opens at level 8. You're level 1. You can read and practice here now.

the idea

Percent means per hundred. 25% is 25 out of 100, which is the fraction 1/4 and the decimal 0.25: three ways to write one amount.

To change a percent to a decimal, divide by 100, which moves the point two places left. To go the other way, multiply by 100. A few pairs are worth knowing by heart: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, and 1/10 = 10%.

To find a percent of an amount, build it from pieces you can work out in your head.

techniques

Move the point two places

Changing a percent to a decimal, or a decimal to a percent.

Percent to decimal: divide by 100. The point moves two places left, so 60% is 0.6.
Decimal to percent: multiply by 100. The point moves two places right, so 0.375 is 37.5%.
Add zeros if you run out of digits: 5% is 0.05.

worked example

Example: Write 12.5% as a decimal.

Divide by 100: move the point two places left.
12.5 becomes 0.125.

Answer: 0.125

Start from one part

Changing a fraction with 2, 4, 5, 8 or 10 on the bottom into a percent.

Find one part as a percent: 100 ÷ 8 = 12.5, so 1/8 = 12.5%.
Multiply by the top number.
Learn the halves, quarters, fifths and tenths by heart. Eighths are half of quarters.

worked example

Example: Write 3/5 as a percent.

1/5 = 20%.
3/5 = 3 × 20% = 60%.

Answer: 60%

more: Know the equivalents

Build from 10%, 5% and 1%

Finding a percent of an amount.

10% is the amount ÷ 10, and 1% is the amount ÷ 100.
5% is half of 10%. 20% is double 10%, and 30% is three times it.
15% = 10% + 5%, and 35% = 25% + 10%.
25% is a quarter, 12.5% is an eighth, and 75% is the whole minus a quarter.

worked example

Example: What is 35% of 60?

25% is a quarter: 60 ÷ 4 = 15.
10% is 60 ÷ 10 = 6.
15 + 6 = 21.

Answer: 21

more: Build from 10%, 5% and 1%

watch out for

Moving the point only one place. 60% is 0.6, not 6, because percent means per hundred.
Keeping the decimal and adding a percent sign. 0.375 is 37.5%, not 0.375%.
Treating 5% as a fifth. A fifth is 20%; 5% is half of 10%.
Stopping at 10% when the question asks for 15%. Add the 5% as well.

practice

Percent to decimal

worked example

Write 5% as a decimal.

Answer: 0.05

Percent means per hundred: 5 ÷ 100 = 0.05.

Fraction to percent

worked example

Write 0.9 as a percent.

Answer: 90%

Multiply by 100: 0.9 × 100 = 90, so 0.9 = 90%.

1%, 5%, 10%

worked example

What is 10% of 1,500?

Answer: 150

10% is one tenth: 1,500 ÷ 10 = 150.

Build a percent

worked example

What is 75% of 164?

Answer: 123

75% is the whole minus one quarter: 164 − 41 = 123.