Video: Converting Percentages to Fractions

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.

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Video Transcript

Let’s take a quick look on how we convert percents to fractions. Here is an example of that.

Write 50 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 50 percent and writing it as a fraction with the denominator of 100. So, we have 50 over 100. 50 over 100 is a fraction form of 50 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 50 over 100. 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 50. In that case, we end up with the fraction one over two, or one-half. 50 percent in fraction form in simplest terms is one-half.

But maybe you weren’t sure the best way to simplify 50 over 100, and you didn’t immediately think about dividing the numerator and the denominator by 50. There are a few other ways you could get the same answer. Maybe you noticed that 50 and 100 are both divisible by 10. This will give you 50 over 100 equals five-tenths, but you’re still not in the simplest form. So, you would need to divide again. You’ll then recognize that both five and 10 are divisible by five. And again, we’ve reduced this fraction 50 over 100 to one-half. We’ve just used two different ways. Let’s look at another example.

Convert 250 percent to fraction form.

We need to remember here that percent means per 100. So, we now write 250 percent in fraction form out of 100, 250 as the numerator, 100 as the denominator. This is one of the fraction forms of 250 percent, but we want the simplest fraction form of 250 percent, which means we’re going to need to reduce again. Let’s start by dividing the numerator and the denominator by 10. We’re left with 25 over 10 as another fraction form of 250 out of 100, but it’s still not the simplest form of this fraction because we recognize that both 25 and 10 are divisible by five. When we do that we get five-halves, or five over two as the simplest fraction form.

Sometimes though, 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 100. Now, all we need to do here is simplify this fraction to its most reduced form. What is something that both eight and 100 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, 100 divided by four is 25, 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 the denominator of 100. And finally, for step two, simplify this fraction. You might also call this reduce. Now, you know how to convert percents into fractions.

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