Percentages: Converting Fractions, Decimals and Percents

Q: What is the quickest way to find a percentage of a number in my head?

Start from 10\% (divide by 10) and 1\% (divide by 100), then combine them. For 15\%, add 10\% and half of it.

What a percentage really is, how to move between fractions, decimals and percentages, how to find a percentage of an amount, and how to work backwards to the original.

3 min read Supports 3 lessons

Percent comes from the Latin per centum, "for each hundred". A percentage is simply a fraction with denominator $100$ , written with a $\%$ sign instead.

$35\% = \tfrac{35}{100}$

35 out of 100 squares: $35\% = \frac{35}{100} = 0.35 = \frac{7}{20}$ .

Because everything is out of a hundred, percentages make comparisons easy. Is $\frac{17}{20}$ better than $\frac{41}{50}$ ? As percentages, $85\%$ beats $82\%$ at a glance.

Three ways to write a number

Conversions

\frac{a}{b} \xrightarrow{\;a \div b\;} \text{decimal} \xrightarrow{\;\times 100\;} \text{percent}

Going backwards: divide by $100$ to get a decimal, then write it as a fraction and simplify.

$\frac{3}{8}$
Fraction to percentage.

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Tip

Learn the classics by heart: $\frac12 = 50\%$ , $\frac14 = 25\%$ , $\frac34 = 75\%$ , $\frac15 = 20\%$ , $\frac{1}{10} = 10\%$ , $\frac13 \approx 33.3\%$ .

A percentage of an amount

"Of" means multiply. To find $p\%$ of $x$ , convert $p\%$ to a decimal and multiply.

Percentage of a quantity

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

15% = 12

85% = 68

total = 80 (100 parts)

$15\%$ of $80$ is $0.15 \times 80 = 12$ .

For mental arithmetic, build from easy pieces. $10\%$ is a tenth, so $10\%$ of $80$ is $8$ . Half of that, $5\%$ , is $4$ . Together, $15\%$ is $12$ .

Working backwards

If you know a percentage of a number but not the number itself, write an equation and divide.

Worked example

$30\%$ of a number is $24$ . What is the number?

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Write it as an equation.
$0.3 \times x = 24$

Check: $30\%$ of $80$ is $24$ . ✓

Percentages over 100

Nothing stops a percentage going above $100$ . $150\%$ of $40$ is $1.5 \times 40 = 60$ : the whole amount plus half again. This idea is the key to percentage increases.

Watch out

Percentages need a reference amount. "Prices rose $10\%$ " means $10\%$ of the old price. Be clear what the $100\%$ is.

Common questions

How do I turn a fraction into a percentage?: Divide the numerator by the denominator to get a decimal, then multiply by $100$ . For example $\frac{3}{8} = 0.375 = 37.5\%$ .
What is the quickest way to find a percentage of a number in my head?: Start from $10\%$ (divide by $10$ ) and $1\%$ (divide by $100$ ), then combine them. For $15\%$ , add $10\%$ and half of it.

Practise percentages

The Fractions, Decimals & Percents lesson has worked examples and unlimited practice that adapts to you.

Open the lesson

Common questions

How do I turn a fraction into a percentage?

Divide the numerator by the denominator to get a decimal, then multiply by $100$ . For example $\frac{3}{8} = 0.375 = 37.5\%$ .

What is the quickest way to find a percentage of a number in my head?

Start from $10\%$ (divide by $10$ ) and $1\%$ (divide by $100$ ), then combine them. For $15\%$ , add $10\%$ and half of it.