Converting a Percent to a Fraction
This is much easier than you may think: just put the number over 100 and simplify. For example, 5% = 5/100 = 1/25, and 150% = 150/100 = 1 ½.
Why does this work? If you think about it, the definition of a percent is really just “out of a hundred.” If you have 50% of something, what you’re really saying is that you have fifty out of a hundred, or 50/100.
Converting a Fraction to a Percent – Method 1
Converting a fraction to a percent is more difficult, and there are two methods you can use to do it. In the first method, you would change the fraction so that it has 100 in its denominator. This method only works easily if the denominator is a factor of 100.
For example, let’s say that you were trying to convert 21/25 to a percent. You know that 25 X 4 = 100. In order to multiply the denominator by 4, you also have to multiply the numerator by 4. So 21/25 X 4/4 = 84/100. Because the definition of percent is “out of a hundred,” 84/100 is the same thing as 84%. So 21/25 = 84%.
You can do this with less complex fractions as well. For example, let’s say you wanted to convert 2/5 to a percent. You know that 5 X 20 = 100, so you can multiply the numerator and denominator by 20, which gives you 2/5 X 20/20 = 40/100 = 40%.
Converting a Fraction to a Percent – Method 2
The first method seems simple enough, but remember that it only works if the denominator is a factor of a hundred. What do you do if the denominator is not a factor of 100? You use this second, two-step method:
Convert the fraction to a decimal.
Convert the decimal to a percent.
For example, to convert the fraction ¼ to a decimal, you would first convert it to a fraction (1 / 4 = .25). Then you would convert the decimal to a percent (.25 = 25%).
With these methods under your belt, you’ll be acing your math tests in no time!
This post is part of the series: Fraction, Decimal, and Percent Conversions
- Converting Decimals to Percents and Percents to Decimals
- Converting Fractions to Decimals and Decimals to Fractions
- Converting Percents to Fractions and Fractions to Percents