Formula

One quantity as a percentage of another

Arithmetic • Percentage

Formula

\frac{a}{b} \times 100%

For

b \neq = 0

, the quantity

a

expressed as a percentage of

b

\frac{a}{b} \times 100%

. The base

b

is whatever the word 'of' attaches to, and choosing it is the whole of the work.

How to use it

1Name the base before dividing: 'what percent of $b$ is $a$ ' puts $b$ underneath, never $a$ .
2To compare shares across groups of different sizes, each share must be taken on its own group's base.
3To test a share against $50%$ without dividing, compare $2 a$ with $b$ ; against $25%$ , compare $4 a$ with $b$ .

In a batch of

240

bulbs,

18

are defective. What percentage of the batch is defective?

Step-by-step

1
$\frac{18}{240}$
Why: The base is the batch size $240$ , because the question asks for a percentage of the batch.
2
$\frac{18}{240} \times 100% = \frac{1800}{240} % = 7.5%$

Answer

7.5%

Watch out

Percentages on different bases cannot be added or averaged:

20%

of one group and

30%

of another do not make

25%

of the two together unless the groups are the same size. Reversing the base replaces

\frac{a}{b}

\frac{b}{a}

, a different number entirely.

Builds on

x %

Also known as

what percent of b is a, percentage share, express as a percentage, a as a percentage of b, reverse percentage, percentage of another quantity