How to Convert Fraction to Percent Part 1

In the previous post, we have learned how to convert percent to fraction. In these series of posts, we learn the opposite: how to convert fraction to percent. I am going to teach you three methods, the last one would be used if you forgot the other two methods, or if the first two methods would not work. Please be reminded though to understand the concept (please do not just memorize).

The first method can be used for fractions whose denominators can be easily related to 100 by multiplication or division. Recall that from Converting Percent to Fraction, I have mentioned that when we say percent it means “per hundred.” In effect, n% can be represented by n/100. Therefore, if you have a fraction and you can turn it into n/100 (by multiplication/division), then you have turned it into percent.

Example 1: What is the equivalent of 1/5 in percent?

How do we relate the denominator 5 to 100? By multiplying it by 20. Therefore, we also multiply its numerator by 20:

\displaystyle \frac{1 \times 20}{5 \times 20} = \frac{20}{100}

Now, since we have 100 as denominator, the answer in percent is therefore the numerator. Therefore, the equivalent of 1/5 in percent is 20%.

Example 2: What is 3/25 in percent?

Again, how do you related 25 to 100? By multiplying it by 4. Therefore,

\displaystyle \frac{3 \times 4}{25 \times 4} = \frac{12}{100}

Therefore, the equivalent of 3/25 in percent is 12%.

Example 3: What is 23/200 in percent?

In this example, we can relate 200 to 100 by dividing it by 2. So, we also divide the numerator by 2. That is

\displaystyle \frac{23 \div 2}{200 \div 2} = \frac{11.5}{100}

Therefore, the answer is 11.5%

There are two important things to remember in using the method above.

(1) in changing the form the fractions to n/100, the only operations that you can use are multiplication and division and

(2) whatever you do to the numerator, you also do to the denominator.

Note that multiplying the denominator (or dividing it) by the same number does not change its value, it only change its representation (fraction, percent or decimal).

Why It Works

When  you are relating a fraction a/b to n/100, you are actually using ratio and proprotion. For example, in the first example, you are actually solving the equation

\displaystyle \frac{1}{5} = \frac{n}{100}.

The equation will result to n = \frac{100}{5} which is equal to 20. Now, this is just the same as multiplying both the numerator and the denominator by 20.

Note that the method of “relating to 100 by multiplication or division” can only work easily for denominators that divides 100 or can be divided by 100. Other fractions (try 1/7), you have to use ratio and proportion and manual division.

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