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Video: Converting Fractions to Percentages

Kathryn Kingham

We learn how to create and solve simple equations in order to convert fractions to percentages. For instance, to convert 4/7 to a percentage, solve 4/7 = 𝑝/100, or to convert 13/40 to a percentage, solve 13/40 = 𝑝/100.

07:16

Video Transcript

Let’s talk about converting fractions to percents. The word “percent” literally can be translated “per hundred” or “per one hundred”.

We know that fractions represent a part of a whole. The first thing that we’ll need to convert a fraction to a percent is a denominator of one hundred. Whatever number is in the numerator position, when the denominator is one hundred, is the percent. We represent a percent with this symbol. So if we had seventeen out of one hundred, we have seventeen percent.

Here’s an example of something you might see: Convert seventy-seven hundredths to a percent. Because we know that a present is the numerator over one hundred, we can easily recognize that this is seventy-seven percent.

But sometimes we’ll need to convert something that’s in a slightly different format. Here’s an example that says: Convert fourteen-tenths to a percent. Remember that our goal is to have a part over the whole with the denominator of one hundred. So we need to think of a way to get fourteen-tenths converted into a fraction of something over one hundred. When you copy down the problem, you might recognize that it’s very easy to get from ten to one hundred. If we multiply the denominator of ten by ten, we come up with one hundred. But if we’re going to work with fractions, we always have to keep them equivalent by multiplying the numerator and the denominator by the same thing. Here that will mean we’ll multiply fourteen by ten and ten by ten on the denominator. Once we’ve converted this into a fraction with a denominator of one hundred, we take the numerator and that’s our percent. One hundred and forty percent. One hundred and forty percent is the final answer.

You might also see something that looks like this: thirteen over forty equals some percent. Let’s start out by creating a new problem. Now that we’ve set up the problem, we know that we’re going to be looking for some numerator over one hundred and I’m gonna call that 𝑝. If we solve this equation for 𝑝, that will be our percent. If we multiply both sides by one hundred, we can get our percent 𝑝 by itself. I just did a little simplifying here. So now we have our percent equals one hundred and thirty over four. But this format is not super helpful. When we deal with percents, we usually want to have them in a decimal format. So I really wanna know what is one hundred and thirty divided by four. When you do that division, you get thirty-two and a half. So our percent equals thirty-two and a half. And thirty-two and a half percent is our final answer.

Here’s another example: Four-sevenths equals what percent. We set up our problem in the same way four-sevenths equals some number over one hundred. Multiply both sides by one hundred, and then we get four hundred sevenths equals 𝑝. But 𝑝 equal to four hundred sevenths is not super helpful. So we wanna actually do a division here and find out what the decimal representation is. When you do that division, you’re going to get an interesting answer. What should we do with a number like this? We really have two choices here. We can round the answer and find an estimated percent, or we can use division and then find the remainder. Let’s say you wanted to round, this time, to the nearest tenth. You could then just say it’s fifty-seven and one-tenth percent. That’s about the percentage. But let’s say you really needed a precise answer. So we wanna do some division and find the remainder. Here’s what I mean by that. We’re going to divide four hundred by seven. I know that the first number is a five because we do know that it’s going to be fifty-seven and some remainder. Okay. Since I know that it’s fifty-seven with some reminder, I can look closely at the division problem and see that the remainder is one. So the precise answer is fifty-seven and one-seventh percent.

One final example: What percent of the pizza did you eat if you ate two slices of this pizza? Well, this pizza has eight slices and you ate two of them. Two-eighths is the fraction that you ate. But another way to write that is one over four. So if we look at one-fourth, one-fourth is much easier to convert to a percent. In fact, you might even be able to do this one in your head. So to get one-fourth into a fraction out of one hundred, we multiply the top and bottom by twenty-five. And we know that one-fourth is then twenty-five out of one hundred. And the final answer would be twenty-five percent.