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Let’s talk about converting fractions to percents.
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The word “percent” literally can be translated “per hundred” or “per one hundred”.
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We know that fractions represent a part of a whole.
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The first thing that we’ll need to convert a fraction to a percent is a denominator of one hundred.
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Whatever number is in the numerator position, when the denominator is one hundred, is the percent.
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We represent a percent with this symbol.
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So if we had seventeen out of one hundred, we have seventeen percent.
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Here’s an example of something you might see: Convert seventy-seven hundredths to a percent.
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Because we know that a precent is the numerator over one hundred, we can easily recognize that this is seventy-seven percent.
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But sometimes we’ll need to convert something that’s in a slightly different format.
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Here’s an example that says: Convert fourteen-tenths to a percent.
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Remember that our goal is to have a part over the whole with the denominator of one hundred.
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So we need to think of a way to get fourteen-tenths converted into a fraction of something over one hundred.
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When you copy down the problem, you might recognize that it’s very easy to get from ten to one hundred.
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If we multiply the denominator of ten by ten, we come up with one hundred.
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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.
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Here that will mean we’ll multiply fourteen by ten and ten by ten on the denominator.
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Once we’ve converted this into a fraction with a denominator of one hundred, we take the numerator and that’s our percent.
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One hundred and forty percent.
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One hundred and forty percent is the final answer.
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You might also see something that looks like this: thirteen over forty equals some percent.
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Let’s start out by creating a new problem.
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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.
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If we solve this equation for 𝑝, that will be our percent.
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If we multiply both sides by one hundred, we can get our percent 𝑝 by itself.
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I just did a little simplifying here.
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So now we have our percent equals one hundred and thirty over four.
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But this format is not super helpful.
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When we deal with percents, we usually want to have them in a decimal format.
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So I really wanna know what is one hundred and thirty divided by four.
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When you do that division, you get 32.5.
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So our percent equals 32.5.
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And thirty-two and a half percent is our final answer.
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Here’s another example: Four-sevenths equals what percent.
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We set up our problem in the same way four-sevenths equals some number over one hundred.
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Multiply both sides by one hundred, and then we get four hundred sevenths equals 𝑝.
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But 𝑝 equal to four hundred sevenths is not super helpful.
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So we wanna actually do a division here and find out what the decimal representation is.
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When you do that division, you’re going to get an interesting answer.
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What should we do with a number like this?
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We really have two choices here.
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We can round the answer and find an estimated percent, or we can use division and then find the remainder.
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Let’s say you wanted to round, this time, to the nearest tenth.
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You could then just say it’s fifty-seven and one-tenth percent.
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That’s about the percentage.
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But let’s say you really needed a precise answer.
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So we wanna do some division and find the remainder.
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Here’s what I mean by that.
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We’re going to divide four hundred by seven.
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I know that the first number is a five because we do know that it’s going to be fifty-seven and some remainder.
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Okay.
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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.
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So the precise answer is fifty-seven and one-seventh percent.
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One final example: What percent of the pizza did you eat if you ate two slices of this pizza?
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Well, this pizza has eight slices and you ate two of them.
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Two-eighths is the fraction that you ate.
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But another way to write that is one over four.
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So if we look at one-fourth, one-fourth is much easier to convert to a percent.
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In fact, you might even be able to do this one in your head.
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So to get one-fourth into a fraction out of one hundred, we multiply the top and bottom by twenty-five.
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And we know that one-fourth is then twenty-five out of one hundred.
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And the final answer would be twenty-five percent.