The idea

Percentage change and multipliers

Why every percentage increase or decrease is a single multiplication, how to build the multiplier, and why "percentage change" is always measured against the original amount.

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Ratio, proportion & rates of change · Percentages & growth

Percentage change and multipliers

Why every percentage increase or decrease is a single multiplication, how to build the multiplier, and why "percentage change" is always measured against the original amount.

Why it works

Per hundred

"Per cent" means per hundred — a percentage is just a fraction with 100 on the bottom.

37\%

\frac{37}{100} = 0.37

. That single fact is the whole topic: once a percentage is a decimal, everything is ordinary multiplication.

One multiplication, not two steps

Suppose a £

80

coat goes up by

15\%

. The slow way is "find

15\%

, then add it on":

0.15 \times 80 = 12

, then

80 + 12 = 92

. But look at what that actually does — you keep the original (

100\%

of it) and add

15\%

more, so you end up with

115\%

of the start:

\times\,1.15 \ \text{(up 15\%)} \qquad \times\,0.85 \ \text{(down 15\%)}

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