Formula

$x %$ of a quantity

Arithmetic • Percentage

Formula

x % of N = \frac{x N}{100}

For any quantity

N

x %

N

means

\frac{x}{100} \times N

, so a score of

x %

out of a maximum

M

\frac{x M}{100}

marks.

How to use it

1Use it to turn a percentage statement about an unknown total into an algebraic expression in that total.
2Two percentages of the same total differ by $\frac{( y - x ) N}{100}$ , which is how an unknown total is recovered from a known gap.
3Keep $x$ as the number of percent, not as a decimal, so the $100$ stays visible and the units stay honest.

A candidate scoring

35%

of the maximum marks gets

210

marks. What is the maximum?

Step-by-step

1
$\frac{35 M}{100} = 210$
Why: Write the percentage of the unknown maximum as a product.
2
$M = \frac{210 \times 100}{35} = 600$

Answer

600

Watch out

Distinct from a percentage change:

x %

N

is a share of

N

, whereas an increase of

x %

multiplies

N

1 + \frac{x}{100}

. Confusing the two is the usual source of an answer that is off by exactly

N

Also known as

percentage of a number, x percent of N, take a percentage of a total