Percent of increase

Just like the name suggests, the percent of increase is the amount of increase out of one hundred.

The amount of increase is the final amount minus the original amount. For example, if you are looking for the percent of increase from 4 to 6, the original amount is 4 and the final amount is 6.

Then, as you can see in the formula below, you need to do the followings:

• 1. Divide the amount of increase by the original amount.

• 2. Multiply the answer you found in step 1 by 100.

• 3. Put the percent sign (%) next to the answer you found in step 2.

A few more examples showing how to find the percent of increase

Example #1:

Find the percent of increase from 4 to 6.

Amount of increase is 6 − 4 = 2

Original amount is 4

2 / 4 = 0.50

multiply 0.50 by one hundred to get the answer as a percent.

0.50 × 100 = 50, so the answer is 50%.

To check the answer, do the following:

4 × 50% = (4 × 50)/100 = 200/100 = 2 and 4 + 2 = 6

Notice that to convert 2 / 4 as a percent, we can multiply 4 by 25 and multiply 2 by 25

(2 × 25)/(4 × 25) = 50/100 or 50 per hundred or 50%

When the denominator can divide 100, it may be easier to do it like that.

Example #2:

Find the percent of increase from 5 to 10.

Amount of increase is 10 − 5 = 5

Original amount is 5

5 / 5 = 1

multiply 1 by one hundred to get the answer as a percent

1 × 100 = 100, so the answer is 100%.

To check the answer, do the following:

5 × 100% = (5 × 100)/100 = 500/100 = 5 and 5 + 5 = 10

Once again, we can convert 5 / 5 into percent by multiplying the numerator and the denominator by 25

(5 × 25)/(5 × 25) = 100/100 or 100 per hundred or 100%

A tricky example?

Find the percent of increase from -4 to 8.

Amount of increase is 8 − -4 = 12

Original amount is -4

12 / -4 = -3

multiply -3 by one hundred to get the answer as a percent

-3 × 100 = -300, so the answer is -300%.

The reason I called this example tricky is because many people feel like the negative sign next to 300 does not really reflect an increase from -4 to 8

However, let's check the answer like we did for the two problems above!

-4 × -300% = (-4 × -300)/100 = 1200/100 = 12 and -4 + 12 = 8

If you don't include the negative sign, you will get -1200/100 = -12 and -4 + -12 = -16 instead of 8