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# Percent word problem: 100 is what percent of 80?

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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.