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Video: Converting Percentages to Fractions

Kathryn Kingham

In order to convert percentages to fractions, we learn that we just need to write the percentage as a numerator in a fraction with a denominator of 100 then simplify that fraction. We run through a series of examples to illustrate the process.

05:18

Video Transcript

Let’s take a quick look on how we convert percents to fractions. Here is an example of that: write fifty percent in fraction form. Percent is written in a format that looks like this, and the word “percent” literally means per hundred.

Let’s start this process by taking the fifty percent and writing it as a fraction with a denominator of one hundred. So we have fifty over one hundred; fifty over one hundred is a fraction form of fifty percent. But when we work with fraction form, we usually want to find the simplest or another way to say it is the reduced fraction form. So let’s try to simplify the fraction fifty over one hundred. We need to think of something that we can divide the numerator and the denominator by. Maybe you recognize almost immediately that both the top and the bottom, the numerator and the denominator, can be divided by fifty. In that case, we end up with the fraction one over two, or one half. Fifty percent in fraction form in simplest terms is one half. But maybe you weren’t sure the best way to simplify fifty over one hundred, and you didn’t immediately think about dividing the numerator and the denominator by fifty. There are a few other ways you could get the same answer. Maybe you noticed that fifty and one hundred are both divisible by ten. This will give you fifty over one hundred equals five tenths, but you’re still not in the simplest form. So you would need to divide again. You’ll then recognise that both five and ten are divisible by five. And again we’ve reduced this fraction fifty over one hundred to one half. We’ve just used two different ways.

Let’s look at another example. Convert two hundred and fifty percent to fraction form. We need to remember here that percent means per one hundred. So we now write two hundred and fifty percent in fraction form out of one hundred, two hundred and fifty as the numerator, one hundred as the denominator. This is one of the fraction forms of two hundred and fifty percent, but we want the simplest fraction form of two hundred and fifty percent, which means we’re going to need to reduce again. Let’s start by dividing the numerator and the denominator by ten. We’re left with twenty-five over ten as another fraction form of two hundred and fifty out of one hundred, but it’s still not the simplest form of this fraction because we recognize that both twenty-five and ten are divisible by five. When we do that we get five halves or five over two as the simplest fraction form. Sometimes thought we don’t just want the simplest fraction form; we might want to write five halves as a mixed number. In that case, I would break up the number into different parts, one part being four over two and another part being one half. The mixed number for five halves is two and one half.

Here’s our last example: find eight percent in simplest fraction form. We start here, just like in all of the other examples. We make eight percent a fraction of eight over one hundred. Now all we need to do here is simplify this fraction to its most reduced form. What is something that both eight and one hundred is divisible by? I’m gonna choose four; we’re gonna divide the numerator and the denominator by four. When you do that you see that eight divided by four is two, one hundred divided by four is twenty-five. Our final answer here being two twenty-fifths. So when you divide the numerator and the denominator by four, you get two twenty-fifths. Two twenty-fifths is eight percent in simplest fraction form. In summary, step one, change the percent to a fraction with a denominator of one hundred. and finally, for step two, simplify this fraction. You might also call this “reduce”. Now you know how to convert percents into fractions.