# Percent of increase

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

Once we know what the increase is, just divide the increase by the original amount and express the answer as a percent.

Thus, the formula to use is : Amount of increase / Original amount

I will illustrate what I just said with examples.

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

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