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100 is what percent of 80?

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These problems tend to kill people because on some level

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they're kind of simple, they're just 100 and an 80

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there, and they're asking what percent.

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But then people get confused.

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They say, do I divide the 100 by the 80?

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The 80 by 100?

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Or is it something else going on?

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And you really just have to think through what the

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language is saying.

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They're saying that this value right here, this 100, is some

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percentage of 80, and that some percentage is what we

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have to figure out.

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What percent?

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So if we multiply 80 by this what percent, we will get 100.

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So let's view it this way.

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We have 80.

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If we multiply it by something, let's call this

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something x.

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Let me do that in a different color.

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If we multiply 80 by something, we are

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going to get 100.

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And we need to figure out what we need to multiply

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80 by to get 100.

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And if we just solve this equation as it is, we're going

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to get a value for x.

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And what we need to do is then convert it to a percent.

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Another way you could have viewed this is 100 is what you

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get when you multiply what by 80?

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And then you would have gotten this number, and then you

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could convert it to a percent.

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So this is essentially the equation and now

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we can solve it.

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If we divide both sides of this equation by 80, so you

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divide the left-hand side by 80, the right-hand side

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by 80, you get x.

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x is equal to 100/80.

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They both share a common factor of 20, so 100 divided

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by 20 is 5, and 80 divided by 20 is 4.

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So in simplest form, x is equal to 5/4, but I've only

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expressed it as a fraction.

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But they want to know what percent of 80.

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If they just said 100 is what fraction of

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80, we would be done.

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We could say 100 is 5/4 of 80, and we would

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be absolutely correct.

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But they want to say what percent?

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So we have to convert this to a percent, and the easiest

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thing to do is to first convert it into a decimal, so

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let's do that.

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5/4 is literally the same thing as 5 divided by 4, so

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let's figure out what that is.

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Let me do it in magenta.

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So 5 divided by 4.

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You want to have all the decimals there, so let's put

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some zeroes out here.

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4 goes into 5 one time.

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Let me switch up the colors.

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1 times 4 is 4.

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You subtract.

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You get 5 minus 4 is 1.

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Bring down the next zero.

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And of course, the decimal is sitting right here, so we want

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to put it right over there.

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So you bring down the next zero.

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4 goes into 10 two times.

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2 times 4 is 8.

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You subtract.

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10 minus 8 is 2.

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Bring down the next zero.

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4 goes into 20 five times.

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5 times 4 is 20.

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Subtract.

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No remainder.

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So this is equal to 1.25.

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5/4 is the same thing as 5 divided by 4,

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which is equal to 1.25.

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So far, we could say, 100 is 1.25 times 80, or 1.25 of 80,

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you could even say, But we still haven't expressed it as

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a percentage.

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This is really just as a number.

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I guess you could call it a decimal, but it's a whole

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number and a decimal.

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It would be a mixed number if we didn't do it as a decimal.

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It's 1 and 1/4, or 1 and 25 hundredths, however you want

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to read it.

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So to write it as a percent, you literally just have to

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multiply this times 100, or shift the decimal over twice.

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So this is going to be equal to, as a percent, if you just

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shift the decimal over twice, this is equal to 125%.

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And that makes complete sense.

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100 is 125% of 80.

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80 is 100% of 80.

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100% percent is more than 80.

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It's actually 1 and 1/4 of 80, and you see that right over

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there, so it makes sense.

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It's 125%.

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It's more than 100%.

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But we are done.

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We've solved the problem.

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It is a 125% of 80.

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