When a quantity grows (gets bigger), then we can compute its PERCENT INCREASE:
[beautiful math coming... please be patient]
$\text{PERCENT INCREASE} =
\frac{\displaystyle{(\text{new amount} - \text{original amount})}}
{\displaystyle\text{original amount}}
$
Some people write this formula with $\,100\%\,$ at the end,
to emphasize that since it is percent increase, it should be reported as a percent.
Recall that $\,100\% = 100\cdot\frac{1}{100} = 1\,$.
So, $\,100\%\,$ is just the number $\,1\,$,
and multiplying by $\,1\,$ doesn't change anything except the name of the number!
So, here's an alternate way to give the formula:
$\text{PERCENT INCREASE} =
\frac{\displaystyle{(\text{new amount} - \text{original amount})}}
{\displaystyle\text{original amount}}\cdot 100\%
$
When a quantity shrinks (gets smaller), then we can compute its PERCENT DECREASE:
[beautiful math coming... please be patient]
$\text{PERCENT DECREASE} =
\frac{\displaystyle{(\text{original amount} - \text{new amount})}}
{\displaystyle\text{original amount}}
$
OR
$\text{PERCENT DECREASE} =
\frac{\displaystyle{(\text{original amount} - \text{new amount})}}
{\displaystyle\text{original amount}}\cdot 100\%
$
Both formulas have the following pattern:
[beautiful math coming... please be patient]
$\text{PERCENT INCREASE/DECREASE} =
\frac{\displaystyle{\text{change in amount}}}
{\displaystyle\text{original amount}}
$
OR
$\text{PERCENT INCREASE/DECREASE} =
\frac{\displaystyle{\text{change in amount}}}
{\displaystyle\text{original amount}}\cdot 100\%
$
Note that when you compute percent increase or decrease,
you always compare how much a quantity has changed to the original amount.
Note also that the numerator in these formulas is always a POSITIVE number
(or zero, if the quantity doesn't change at all).