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Percent word problem: 100 is what percent of 80?

CCSS.Math: ,

Video transcript

100 is what percent of 80 and these problems tend to kill people because on some level they're kind of simple there's just 180 there and they're asking what percent but then people get confused they say do I divide 100 by the 80 to 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 hundred is some percentage of 80 and that some percentage is what we have to figure out that what percent so if we multiply 80 by this what percent we will get a hundred so let's view it this way we start we have 80 we have 80 if we multiply it by something let's call this something X if we multiply 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 a value for x and what we need to do is then convert it to a percent another way you could view this is you know 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 over 80 you could divide well one they both share a common factor of 20 so 100 divided by 20 is 5 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 over 4 is literally this is literally the same thing as 5/4 so let's figure out what that is let me do it in magenta so 5 divided by 4 5 divided by 4 and we 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 one time 1 times 4 is 4 you subtract you get 5 minus 4 is 1 bring down the next zero and of course the decimal sitting right here so we want to put it right over there so you bring down the next zero you bring down the next zero 4 goes into 10 two times two times four is eight you subtract 10 minus 8 is 2 bring down the next zero bring down the next zero 4 goes into 20 five times 5 times 4 is 20 subtract no remainder so this is exactly this is equal to one point two five five over 4 is the same thing as five divided by four which is equal to one point two five so so far we could say 100 is one point two five times 80 or one point two five of 80 you could even say it but we still haven't expressed it as a percentage this is really just as a as a number as a as a su could call it as a decimal but it's all it's a whole number and a decimal so 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 125 125 percent let me not write it out 125 per cent and that makes complete sense 100 is 125 percent of 80 80 is 100 percent of 80 100 percent is more than 80 it's actually 1 in 1/4 of 80 and you see that right over there so it makes sense it's 125 percent more than a hundred percent but we are done we've solved the problem it is one hundred and twenty five percent of 80