Every time you see percents pop up, they have a secret: They're actually fractions and decimals in disguise, and the process of converting a percent into a fraction or decimal is the same. The only difference is where you stop in the calculation process, and how you choose to write out the result.
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To convert a percent to a fraction, write the percent over 100, and then reduce the resulting fraction to its lowest terms if necessary.
Defining Percents as a Fraction
Before you start converting percents into fractions, take a moment to review what a percent actually is. Percent means "per 100" or "out of 100," so the fraction is already implied: Whatever percent you're calculating tells you how many parts out of 100 you're dealing with. So if you're calculating 30 percent off a sale price, you're removing 30 out of 100 parts of that price. If you're trying to improve your test grade by 20 percent, you're working to add 20 out of 100 parts of your current grade. Once you understand this, converting a percent into a fraction is as simple as writing out that implied fraction.
Writing the Percent as a Fraction
Write out the "per 100" or "out of 100" that's implied by the term percent. For example, if you're dealing with 30 percent, you'd have:
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And if you're asked to write 20 percent as a fraction, you'd have:
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Instead of writing 30/100 or 20/100 as fractions, you could also say you're dividing the percent by 100. That's the same process you'd use to convert a percentage to a decimal; for example, 30 percent ÷ 100 = 0.3 is how you'd write 30 percent as a decimal, and 20 percent ÷ 100 = 0.2 is how you'd write 20 percent as a decimal. 20/100 and 20 ÷ 100 mean exactly the same thing; the only difference is in how you write them, and whether you carry the calculation all the way to its end or let it stand as a fraction.
Writing the Fraction in its Simplest Form
If you're writing percents as fractions for a math class, your teacher might ask you to reduce the fraction to lowest terms, or to write it in its simplest form. Before you start this, take a moment to remember that you can do just about anything to the numerator (top number) of a fraction as long as you perform the exact same operation on the denominator (bottom number) of the fraction. So if you wanted to multiply the top number in the fraction 30/100, which represents 30 percent, by 2, you could do it – as long as you also multiply the bottom number by 2. But that makes the fraction larger and more complicated, so instead of multiplying, you can to find some common factors in the numerator and denominator and divide instead.
Finding the Greatest Common Factor
Examine both the numerator and the denominator of your fraction. Do they share any common factors? If yes, identify the greatest factor and factor it out of both the numerator and denominator. Often, identifying the factors is a matter of brute force. For example, consider 30 percent, which in the previous example became the fraction 30/100.
The numerator, 30, has the following factors:
1, 2, 3, 5, 6, 10, 15, 30
The denominator, 100, has the following factors:
1, 2, 4, 5, 10, 20, 25, 50, 100
When you examine both lists, you'll see that the greatest common factor – that is, the greatest factor both numbers share – is 10. Once you factor 10 out of both numbers, you'll be left with the fraction 3/10. The numbers 3 and 10 share no common factors aside from 1, so the fraction is now written in lowest terms or, if you prefer, its simplest form.