Question

What is the percent change of 1 to 12?

Answer 1

(a) 12 is `1200%` of 1.
(b) The increase from 1 to 12 is `1100%`.
(That is, 12 is 1100% more than 1.)

Explanation:

(a) On a scale where the number `1` is marked as `100%`, we would like to know the percent value that `12` is matched with.

In math words:

"1 is to 100% as 12 is to what?"

`1/(100%) = 12/(square)`

Solving for the box, we get

`square = (12 xx 100%) / 1" " = 1200%`

(b) If we are interested in the increase (or the change from 1 to 12, we do the same thing, but we compare "1 is 100%" to the difference between 12 and 1.

`1/(100%) = (12-1)/(square)`

Solving for the box:

`square = (11 xx 100%)/1 " "=1100%`

This may seem rather large, but we remember that 12 itself is already 12 times larger than 1, and 1 is like our whole (our 100%). So it makes sense that a number that's 12 times larger than what we're calling 100% would itself be considered 1200%.