How to Convert Percent to Fraction

In Civil Service Examinations, as well as other examinations in basic mathematics, knowing how to convert  percent, fractions, and decimals to each other is very advantageous especially if you can do it mentally. Let us try with the following example.

A P640 shirt is marked 25% discount. How much will you have to pay for it?

It seems that you need a pencil for this problem, but you can actually do it in your head. Read it to believe it.

The equivalent of 25% in fraction is 1/4, therefore, you have to take away the fourth of the price. Now, 1/4 of 640 seems difficult but what if we try to split it to 600 + 40? Now, 1/4 of 600 is 150, which means that from the 600, you have 450 left. Now, 1/4 of 40 is 10, which means that you have 30 left. So, 450 + 30 is 480 and that is the discounted price of the t-shirt.

Now, with a little bit of practice, you would be able to do this on your own and you won’t have to use a pen to perform calculations for problems such as this.

How to Convert Percent to Fraction

There is one important concept to remember when converting percent to fraction. That is, when you say percent, it means per hundred. The word cent comes from the Latin word centum which means “hundred”. In effect, when you say, 60%, it means 60 per hundred, 0.4% means 0.4 per hundred, 125% means 125 per hundred. When you say x per hundred, you can also represent it by the fraction x/100. This means that the percentages above can be represented as

\displaystyle \frac{60}{100}, \frac{0.4}{100}, \frac{125}{100}

respectively. Now, all we have left to do is to convert these fractions to lowest terms.

Example 1: \frac{60}{100}

Recall that to convert a fraction to lowest terms, we find the greatest common factor (GCF) of its numerator and denominator and then divide them both by the GCF.  The GCF of 60 and 100 is 20, so

\displaystyle \frac{60 \div 20}{100 \div 20} = \frac{3}{5}

Therefore, the equivalent of 60% in fraction is \frac{3}{5}.

Example 2: \frac{0.4}{100}

In this example, we have a decimal point at the numerator and a whole number at the denominator. We have to “get rid” of the decimal point. To do this, we can multiply both the numerator and the denominator by 10 (since 0.4 x 10 = 4). Therefore, we have

\displaystyle \frac{0.4 \times 10}{100 \times 10} = \frac{4}{1000}.

Now, the greatest common factor of 4 and 1000 is 4, so we divide both the numerator and the denominator by 4. The final result is \frac{1}{250}.

Therefore, the equivalent fraction of 0.4% is \frac{1}{250}.

Example 3: \frac{125}{100}

The greatest common factor of 125 and 100 is 25, so we divide both the numerator and the denominator by 25. In doing this, we get \frac{5}{4}.

Therefore, the equivalent fraction of 125% is \frac{5}{4}

Summary

There are three steps to remember in converting percent to fractions.

  1. Make a fraction from the given percent with the given as numerator and 100 as denominator.
  2. Eliminate the decimal points (if there are any) by multiplying the numerator and denominator by the same number which is a power of 10 (10, 100, 1000 and so on).
  3. Reduce the resulting fraction to lowest terms.

That’s it. You can now convert any given percent to fraction.

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2 Responses

  1. April 2, 2015

    […] How to Convert Percent to Fraction […]

  2. April 7, 2015

    […] have already learned how to convert percent to fraction. This post allows you to practice what you have already […]

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