Percent changes are used a lot in real-life. They can help you determine the rate that something is increasing or decreasing. It also gives you a way to compare your results with other data. A few things that you will need to know before doing these problems is that if the original number increases then it is also a percent increase and if the number gets smaller, then it is a percent decrease or a negative percent change.

You many want to use your handy percent proportion to help you figure these problems out.

\(\frac{{IS}}{{OF}} = \frac{\% }{{100}}\)

Example 1:

What is the percent change from 36 to 99?

First, you need to subtract to figure out how much exactly this value has changed.

99 – 36 = 63

Now, we need to determine what percent 63 is of the original number 36. We are looking for the percent, so that is our x. Our “IS” will be 63 and our “OF” is 36.

\(\frac{{IS}}{{OF}} = \frac{\% }{{100}}\)

\(\frac{{63}}{{36}} = \frac{x}{{100}}\)          Now, cross multiply.

\(63 \bullet 100 = x \bullet 36\)
\(6300 = 36x\)
\(175 = x\)

It is a 175% increase.

Example 2:

If you don’t like using this proportion, there is another way of solving these.

What is the percent change from 42 to 91?

We still need to subtract to figure out the change in the value.

91 – 42 = 49

change in value \( \bullet {\rm{1}}00{\rm{ }} = {\rm{ }}\% \)

original value

\(\frac{{49}}{{42}} \bullet 100 = 116.7\% \)

It is a 116.7% increase.

Example 3:

What is the percent change from 76 to 57?

This time the value is decreasing so it will be a negative percent change.

57 – 76 = -19

change in value \( \bullet {\rm{1}}00{\rm{ }} = {\rm{ }}\% \)

original value

\(\frac{{ - 19}}{{76}} \bullet 100 =  - 25\% \)

You can state your answer in two ways.

It is a 25% decrease.

It has a percent change of -25%.