Finding the Percent of Change Between Numbers

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 youre 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. Thats 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 à · 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 thats 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. Thats 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 à · 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 thats 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% Thats 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% Thats the same result as in Method 1: a  decrease of 16.7% in body weight.