Fractions, decimals, and percentages are different ways to express a proportion. None is automatically more accurate than another. A percentage means a fraction out of 100. For example, if five cookies are eaten from a package of ten, the fraction eaten is 5/10 = 1/2, which is 0.5 or 50%. The remaining five cookies also represent 50% of the original package. When you combine percentages from different groups, their sizes matter; averaging the percentages can give the wrong answer.
Finding Percentages
Just like most things in math, finding a percentage takes a little work. When solving percentage word problems, it’s best to convert the statement into numbers. For example, the problem may ask to find sixteen percent of 1,400.
First, convert 16% to a decimal by dividing by 100: 16/100 = 0.16. Then multiply by the original quantity: 0.16 x 1,400 = 224. Thus, sixteen percent of 1,400 is 224. To convert a decimal back to a percentage, multiply it by 100.
Increase or Decrease Percentage
At some point, it may be necessary to find the difference between two numbers and identify the increase or decrease percentage. Just like identifying percentages, this is a simple process. If one week a business has 100 candy bars on hand and next week they have 25, the store owner might want to know what percentage of their stock was sold.
First, the two numbers will need to be compared. The two numbers will have a difference that needs to be found. 100 minus 25 leaves a difference of 75. The difference will then need to be divided by the original number, 75 / 100 = .75. Then the answer is multiplied by one hundred for an answer of %75. This means %75 of the store’s candy bar stock was sold.
Percentage by Ratio
There are times when someone will be given a ratio, such as 14 out of 50 and asked to find the percentage. This is done by dividing the numerator by the denominator, or 14 / 50. The answer of .28 can then be converted by multiplying by 100. So, with the ratio of 14 out of 50, 14 would be %28.
Simple Percentages
There are some percentages that are incredibly simple to find. A little logic goes a long way in math. For example, finding ten percent of something is done by dividing the number by ten. Finding five percent means dividing the original number by twenty, or halving its ten-percent value. Twenty-five percent is one-quarter, so dividing a number by four gives the answer.