Percent of a Number

Q: What does 'of' mean in a percent problem?

Multiply. '$30\%$ of $60$' translates word for word into $0.30 \cdot 60$. Any time a percent problem says 'of,' you can replace it with a multiplication sign.

Q: Can a percent of a number be bigger than the number itself?

Yes — whenever the percent is more than $100\%$. Since $125\% = 1.25$, taking $125\%$ of $60$ multiplies it by more than $1$, giving $75$. Under $100\%$ shrinks a number; over $100\%$ grows it.

Percent means 'per hundred.' Saying $40\%$ is just another way of saying $\dfrac{40}{100}$ , or $0.40$ . So finding a percent of a number is really one operation: turn the percent into a decimal, then multiply. $40\%$ of $85$ is $0.40 \cdot 85 = 34$ . That's the whole method.

The reason this skill shows up everywhere — test scores, populations, survey results, nutrition labels — is that percents are how the world reports parts of a whole. Once 'of means multiply' clicks, every one of those problems becomes the same ten seconds of arithmetic.

The two-step method

Step 1: convert the percent to a decimal by moving the decimal point two places left. $40\%$ becomes $0.40$ , $8\%$ becomes $0.08$ , and $125\%$ becomes $1.25$ . The two places come straight from 'per hundred' — you're dividing by $100$ .

Step 2: multiply the decimal by the number. In a percent problem, the word 'of' means multiply. So ' $40\%$ of $85$ ' translates directly to $0.40 \cdot 85$ .

Watch the single-digit percents — they're the classic slip. $8\%$ is $0.08$ , not $0.8$ . If you write $0.8$ , your answer comes out ten times too big.

The 10% mental-math trick

Finding $10\%$ of anything is just moving the decimal point one place left: $10\%$ of $240$ is $24$ . From there you can build lots of percents in your head. Need $5\%$ ? Take half of the $10\%$ . Need $20\%$ ? Double it. Need $15\%$ ? Add the $10\%$ and the $5\%$ together.

This trick is also your error detector. Before multiplying anything, estimate: $40\%$ of $85$ should be a bit less than half of $85$ , so an answer near $34$ makes sense and an answer like $3.4$ or $340$ does not.

Percents over 100

Nothing changes when the percent passes $100$ — the answer just comes out bigger than the original number. $125\%$ of $60$ is $1.25 \cdot 60 = 75$ . This happens constantly with growth: a town at $125\%$ of its old population has more people than before. If your percent is over $100$ and your answer came out smaller than the original, something went wrong.

Worked examples

Example 1: the basic method

Find $30\%$ of $60$ .

Write the percent as a decimal

30\% = 0.30

'Of' means multiply

0.30 \cdot 60

Multiply

0.30 \cdot 60 = 18

Answer: $18$

Example 2: a word problem

A quiz has $80$ questions, and Maya answered $85\%$ of them correctly. How many questions did she get right?

Write the percent as a decimal

85\% = 0.85

Multiply by the total number of questions

0.85 \cdot 80

Multiply

0.85 \cdot 80 = 68

Answer: $68$ questions correct.

Example 3: mental math with the 10% trick

Find $5\%$ of $240$ without a calculator.

Find

10\%

by moving the decimal one place left

10\% \text{ of } 240 = 24

5\%

is half of

10\%

24 \div 2 = 12

Answer: $12$

Example 4: a percent over 100

Find $150\%$ of $42$ .

Write the percent as a decimal

150\% = 1.5

Multiply

1.5 \cdot 42 = 63

Check: more than

100\%

should beat the original

63 > 42

Answer: $63$

Try one yourself

Common questions

How do I turn a percent into a decimal?

Move the decimal point two places to the left, because percent means 'divided by 100.' So $40\%$ becomes $0.40$ , $8\%$ becomes $0.08$ , and $125\%$ becomes $1.25$ .

What does 'of' mean in a percent problem?

Multiply. ' $30\%$ of $60$ ' translates word for word into $0.30 \cdot 60$ . Any time a percent problem says 'of,' you can replace it with a multiplication sign.

Can a percent of a number be bigger than the number itself?

Yes — whenever the percent is more than $100\%$ . Since $125\% = 1.25$ , taking $125\%$ of $60$ multiplies it by more than $1$ , giving $75$ . Under $100\%$ shrinks a number; over $100\%$ grows it.

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Percent of a Number

The two-step method

The 10% mental-math trick

Percents over 100

Worked examples

Example 1: the basic method

Example 2: a word problem

Example 3: mental math with the 10% trick

Example 4: a percent over 100

Try one yourself

Common questions

Keep learning

Percent Change & Discounts

Unit Rate as Slope

Proportional Relationships in Tables & Graphs