# Calculating Percent Increase and Decrease

Want more practice with percents and related concepts?

- Changing Decimals to Percents
- Changing Percents to Decimals
- Writing Expressions Involving Percent Increase and Decrease
- Problems Involving Percent Increase and Decrease
- More Problems Involving Percent Increase and Decrease

When a quantity grows (gets bigger), then we can compute its percent increase.

When a quantity shrinks (gets smaller), then we can compute its percent decrease.

These concepts are thoroughly explored on this page.

## Percent Increase

When a quantity grows (gets bigger),
then we can compute its *percent increase*:

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*.

So, here's an alternative way to give the formula:

Recall that $\,100\% = 100\cdot\frac{1}{100} = 1\,.$
So, $\,100\%\,$ is just the number
$\,1\,.$
Multiplying by $\,1\,$ doesn't change anything
except the *name* of the number!
(See examples below.)

By the way, there's a very optimistic percent T-shirt here. Wear it and watch people smile!

## Visualizing Percent Increase

Percent to increase by:

Type a nonnegative number in the box above, and then:

If $\,\text{percent increase} = 75\%\,,$

then the formula

## Percent Decrease

When a quantity shrinks (gets smaller),
then we can compute its *percent decrease*:

or

Both formulas have the following pattern:

or

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).

## Visualizing Percent Decrease

Percent to decrease by:

Type a number between $\,0\,$ and $\,100\,$ in the box above,
and then:

If $\,\text{percent decrease} = 25\%\,,$

then the formula

## Examples

*original*price?

Answer: $\,\$5\,$

This will be the denominator.

or

Notes:

No matter which version of the formula
you choose to use,
be sure to give your answer as a *percent*.

The units have been suppressed
(left out) in the calculations above.
This is common practice when it is
*known* that units will cancel,
since it makes things look simpler.

Here is the same result, with the units in place:

In a correct use of the formulas for percent increase and decrease, the units of the numerator and denominator will always be the same, so the units will always cancel.

*original*quantity?

Answer: $\,90\,$

This will be the denominator.

Note: In the exercises below, if an answer does not come out exact, then it is rounded to two decimal places.

*original*price?

Answer: $\,\$16\,$

This will be the denominator.