What Are Percentages?
To help students understand calculating math percentages, it can be helpful to first help them understand the meaning of the word percent. Here’s a possible approach for doing so.
The word percent means ‘per 100’ or ‘out of 100’ or ‘for every 100.’ Whichever explanation most helps your students to understand the concept of percentages can be used. Example statements along with the meanings above can help to make the meaning clear. For example: The statement, ‘30% of the houses in this town are white,’ can be interpreted to mean any of the following:
- 30 houses per 100 in this town are white
- 30 houses our of every 100 in this town are white
- 30 houses for every 100 in this town are white
Calculating a Percentage of a Number
One type of percentage calculation is calculating a specified percentage of a number. For example: What is 30% of 20? One way of
explaining this process is to remind students that in mathematics ‘of’ means ‘times.’ Also, as discussed above 30% means 30 per 100 or 30/100. This leads to the set of calculations shown in the box at the right. A step by step procedure for calculating 30% of 20 is:
- Replace 30% with 30/100
- Replace ‘of’ with ‘times’
- Carry out the multiplication of (30/100) times 20 to get the answer: 6
Calculating Percentages
Another type of percentage calculation is one like: ‘18 is what percentage of 60?‘ This calculation is accomplished by dividing the first number by the second, moving the decimal point two places to the right, and placing a % sign at the end. For the example given above:
- Divide the first number by the second: 18/60 = 0.30
- Move the decimal point two places to the right, giving 30
- Place a % sign after the number to give the answer: 30%
How to Calculate Percentages from Fractions
To convert a fraction to percentage, the steps are essentially the same as those in the last section. That is, divide the numerator of the fraction by its denominator, move the decimal point two places to the right, and place a % sign at the end. For example, convert 5/6 to its equivalent percent:
- Divide the numerator of the fraction by the denominator: 5/6 = 0.8333333
- Move the decimal point two places to the right, giving 83.333
- Round off to the desired precision (use 2 decimal points here), to give 83.33
- Place a % sign after the number to give the answer: 83.33%
Note that step three (rounding off to the desired precision) is needed only when the division doesn’t come out exactly.
How to Convert a Percentage to a Fraction
Converting a percentage to a fraction is essentially the reverse of the procedure in the last section. That is, remove the % sign, write a fraction with 100 as the denominator and the percent as the numerator, and reduce the fraction to its simplest form if necessary. For example, convert 22% to a fraction:
- Remove the % sign: 22% → 22
- Write a fraction with 100 as the denominator and the percent as the numerator: 22/100
- Reduce the fraction to its simplest form (in this case divide numerator and denominator by 2) to give the answer: 11/50
How to Calculate Percentages from Decimals and Vice Versa
As you can see below, these two types of percentage calculation are the easiest.
To calculate percentages from decimals, move the decimal point two places to the right (or multiply by 100) and add a % sign after the number. For example, convert 0.56 to a percentage:
- Move the decimal point two places to the right: 0.56 → 56
- Add a percent sign at the end: 56 → 56%
To convert a percentage to a decimal (this one may be the easiest of all!), remove the % sign and move the decimal point two places to the left (equivalent to dividing by 100). For example, convert 38.5% to a decimal:
- Remove the % sign: 38.5% → 38.5
- Move the decimal point two places to the left to get the answer: 38.5 → 0.385