Percent word problem: 100 is what percent of 80?

CCSS Math: 6.RP.A.3, 6.RP.A.3c

Video transcript

100 is what percent of 80? These problems tend to kill people because on some level they're kind of simple, they're just 100 and an 80 there, and they're asking what percent. But then people get confused. They say, do I divide the 100 by the 80? The 80 by 100? Or is it something else going on? And you really just have to think through what the language is saying. They're saying that this value right here, this 100, is some percentage of 80, and that some percentage is what we have to figure out. What percent? So if we multiply 80 by this what percent, we will get 100. So let's view it this way. We have 80. If we multiply it by something, let's call this something x. Let me do that in a different color. If we multiply 80 by something, we are going to get 100. And we need to figure out what we need to multiply 80 by to get 100. And if we just solve this equation as it is, we're going to get a value for x. And what we need to do is then convert it to a percent. Another way you could have viewed this is 100 is what you get when you multiply what by 80? And then you would have gotten this number, and then you could convert it to a percent. So this is essentially the equation and now we can solve it. If we divide both sides of this equation by 80, so you divide the left-hand side by 80, the right-hand side by 80, you get x. x is equal to 100/80. They both share a common factor of 20, so 100 divided by 20 is 5, and 80 divided by 20 is 4. So in simplest form, x is equal to 5/4, but I've only expressed it as a fraction. But they want to know what percent of 80. If they just said 100 is what fraction of 80, we would be done. We could say 100 is 5/4 of 80, and we would be absolutely correct. But they want to say what percent? So we have to convert this to a percent, and the easiest thing to do is to first convert it into a decimal, so let's do that. 5/4 is literally the same thing as 5 divided by 4, so let's figure out what that is. Let me do it in magenta. So 5 divided by 4. You want to have all the decimals there, so let's put some zeroes out here. 4 goes into 5 one time. Let me switch up the colors. 1 times 4 is 4. You subtract. You get 5 minus 4 is 1. Bring down the next zero. And of course, the decimal is sitting right here, so we want to put it right over there. So you bring down the next zero. 4 goes into 10 two times. 2 times 4 is 8. You subtract. 10 minus 8 is 2. Bring down the next zero. 4 goes into 20 five times. 5 times 4 is 20. Subtract. No remainder. So this is equal to 1.25. 5/4 is the same thing as 5 divided by 4, which is equal to 1.25. So far, we could say, 100 is 1.25 times 80, or 1.25 of 80, you could even say, But we still haven't expressed it as a percentage. This is really just as a number. I guess you could call it a decimal, but it's a whole number and a decimal. It would be a mixed number if we didn't do it as a decimal. It's 1 and 1/4, or 1 and 25 hundredths, however you want to read it. So to write it as a percent, you literally just have to multiply this times 100, or shift the decimal over twice. So this is going to be equal to, as a percent, if you just shift the decimal over twice, this is equal to 125%. And that makes complete sense. 100 is 125% of 80. 80 is 100% of 80. 100% percent is more than 80. It's actually 1 and 1/4 of 80, and you see that right over there, so it makes sense. It's 125%. It's more than 100%. But we are done. We've solved the problem. It is a 125% of 80.