Finding the Percent of Change Between Numbers

There are two methods that will yield the same results

100% on blackboard
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There are two methods of finding the percent of change between two numbers. The first is to find the ratio of the amount of change to the original amount. If the new number is greater than the old number, then that ratio is the percent of increase, which will be a positive. If the new number is less than the old number, then that ratio is the percent of decrease, which will be a negative. So, the first thing to determine when finding the percent of change is whether you're looking at an increase or a decrease.

Method 1: A Problem With an Increase

Say one person had $200 in a savings account last month and now has $225. That's an increase. The problem is to find the percent of increase in money.

First, subtract to find the amount of change:

225 - 25 = 200. The increase is 25.

Next, divide the amount of change by the original amount:

25 ÷ 200 = 0.125

Now, to change the decimal to a percent, multiply the number by 100:

0.125 X 100 = 12.5

The answer is 12.5%. So that's the percent of change, an increase of 12.5% in the savings account.

Method 1: A Problem With a Decrease

Say one person weighed 150 pounds last year and now weighs 125 pounds. That's a decrease. The problem is to find the percent of decrease in weight (the weight loss). 

First, subtract to find the amount of change:

150 - 125 = 25. The decrease is 25.

Next, divide the amount of change by the original amount:

25 ÷ 150 = 0.167

Now, to change the decimal to a percent, multiply the number by 100:

0.167 x 100 = 16.7

The answer is 16.7%. So that's the percent of change, a decrease of 16.7% in body weight.

Method 2: A Problem With an Increase

The second method of finding the percent of change between two numbers involves finding the ratio between the new number and the original number.

Use the same example for this method of finding the percent of increase: One person had $200 in a savings account last month and now has $225. The problem is to find the percent of increase in money.

First, divide the new amount by the original amount:

225 / 200 = 1.125

Next, to change the decimal to a percent, multiply the result by 100:

1.125 X 100 = 112.5%

Now, subtract 100 percent from the result:

112.5% - 100% = 12.5%

That's the same result as in Method 1: an increase of 12.5% in the savings account.

Method 2: A Problem With a Decrease

Use the same example for the second method of finding the percent of decrease: One person weighed 150 pounds last year and now weighs 125 pounds. The problem is to find the percent of decrease in weight.

First, divide the new amount by the original amount:

125 / 150 = 0.833

Next, to change the decimal to a percent, multiply the result by 100:

0.833 X 100 = 83.3%

Now, subtract 100% from the result:

83.3% - 100% = -16.7%

That's the same result as in Method 1: a decrease of 16.7% in body weight.