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we're asked to identify the percent amount and base in this problem and they asked us 150 is 25% of what number they don't ask us to solve it but it's too tempting so what I want to do is first answer this question that they're not even asking us to solve but first I want to answer this question and then we can think about what the percent the amount and the base is because those are just just words those are just definitions the important thing is to be able to solve a problem like this so they're saying 150 they're saying 150 is 25% of what number or another way to view this 150 is 25% of some number so let's if we say that X so let's let X X is equal to the number the number that 150 is 25% of right that's what we need to figure out 150 is 25% of what number that number right here we're seeing is X so that tells us that if we start with X and if we were to take 25% of X if we were to take 25% of X so 25% of X you could imagine this same thing as multiplying it by 25% which is the same thing as multiplying it if you view it as a decimal times 0.25 times X these two statements are identical so if you start with that number you take 25% of it or you multiply it by 0.25 that is going to be equal to 150 that is going to be equal to 150 150 is 25% of this number and then you can solve for X so let's just start with this one over here so if we just have if let me just write it separately so you understand what I'm doing 0.25 times some number is equal to 150 now there's two ways we can do this we can divide both sides of this equation by 0.25 or if you recognize that well you know four quarters make a dollar you could say let's multiply both sides of this equation by or you could do either one I'll do the first because that's how we normally do algebra problems like this but so let's just multiply both by 0.25 multiply this times or multiply it by 0.25 that will just be an X and then the right-hand side will be 150 divided by 0.25 and the reason why I want to do this it really is this good practice dividing by a decimal so let's do that so we want to figure out what a hundred fifty divided by 0.25 is and we've done this before when you divide by a decimal what you can do is you can make the number that you're dividing into the nut other number you can turn this into a whole number by essentially shifting the decimal two to the right but if you do that for the number in the denominator you also do it to the numerator so right now this is you could view this as one hundred fifty point zero zero two five times 100 you're shifting the decimal two to the right then you'd also have to do that with 150 so then it becomes 15 thousand shifted two to the right so our decimal place becomes like this so 150 divided by 0.25 is the same thing as fifteen thousand divided by 25 and let's just work it out really fast so 25 goes into doesn't go into fit doesn't go into one doesn't go into 15 it goes into 150 what is that six times right it goes into 100 four times so it goes in 150 six times six times six times 0.25 is or actually this is now 25 we've shifted the decimal the decimal sitting right over there so six times 25 is 150 you subtract you get no remainder bring down this 0 right here 25 goes into 0 zero times zero times 25 is zero subtract no remainder bring down this last zero 25 goes into 0 zero times zero times 25 is zero subtract no remainder so 150 divided by 0.25 is equal to 600 and you might have been able to do that in your head because when we were at this point in our equation 0.25 X is equal to 150 you could have just multiplied both sides of this equation times 4 4 times 0.25 five is the same thing as 4 times 1/4 which is a whole and 4 times 150 is 600 so you would have gotten it either way and this makes total sense because 100 150 is 25% of some number that means 150 should be 1/4 of that number it should be a lot smaller than the number and it is 150 is 1/4 of 600 now let's answer their actual question identify the percent identify the percent well it looks like 25% that's the percent is 25% the amount and the base in this problem and based on how they're wording it I assume amount means when you take the 25% of the base so they're saying that the amount is my best sense of it is that the amount is equal to the percent is equal to the percent times the base times the base let me do the basin of green so the base is the number you're taking the percent of the amount is the the the quantity that that percentage represents so here we already saw the percent the percent is 25% that's the percent the number that we're taking 25% of or the base is the base is X you know this right here what number X these are that is the base the value of it is 600 we figured it out and the amount is 150 this right here is the amount the amount is 150 150 is 25% of the base of 600 the important thing is how do you solve this problem you know the words themselves you know that those are all really just definitions