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We're asked to identify the percent, amount, and base in

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this problem.

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And they ask us, 150 is 25% of what number?

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They don't ask us to solve it, but it's too tempting.

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So what I want to do is first answer this question that

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they're not even asking us to solve.

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But first, I want to answer this question.

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And then we can think about what the percent, the amount,

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and the base is, because those are just words.

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Those are just definitions.

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The important thing is to be able to solve a

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problem like this.

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So they're saying 150 is 25% of what number?

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Or another way to view this, 150 is 25% of some number.

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So let's let x, x is equal to the number that

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150 is 25% of, right?

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That's what we need to figure out.

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150 is 25% of what number?

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That number right here we're seeing is x.

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So that tells us that if we start with x, and if we were

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to take 25% of x, you could imagine, that's the same thing

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as multiplying it by 25%, which is the same thing as

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multiplying it, if you view it as a decimal,

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times 0.25 times x.

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These two statements are identical.

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So if you start with that number, you take 25% of it, or

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you multiply it by 0.25, that is going to be equal to 150.

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150 is 25% of this number.

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And then you can solve for x.

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So let's just start with this one over here.

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Let me just write it separately, so you understand

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what I'm doing.

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0.25 times some number is equal to 150.

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Now there's two ways we can do this.

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We can divide both sides of this equation by 0.25, or if

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you recognize that four quarters make a dollar, you

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could say, let's multiply both sides of this equation by 4.

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You could do either one.

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I'll do the first, because that's how we normally do

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algebra problems like this.

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So let's just multiply both by 0.25.

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That will just be an x.

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And then the right-hand side will be 150 divided by 0.25.

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And the reason why I wanted to is really it's just good

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practice dividing by a decimal.

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So let's do that.

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So we want to figure out what 150 divided by 0.25 is.

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And we've done this before.

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When you divide by a decimal, what you can do is you can

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make the number that you're dividing into the other

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number, you can turn this into a whole number by essentially

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shifting the decimal two to the right.

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But if you do that for the number in the denominator, you

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also have to do that to the numerator.

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So right now you can view this as 150.00.

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If you multiply 0.25 times 100, you're shifting the

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decimal two to the right.

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Then you'd also have to do that with 150, so then it

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becomes 15,000.

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Shift it two to the right.

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So our decimal place becomes like this.

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So 150 divided by 0.25 is the same thing as

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15,000 divided by 25.

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And let's just work it out really fast.

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So 25 doesn't go into 1, doesn't go into 15, it goes

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into 150, what is that?

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Six times, right?

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If it goes into 100 four times, then it goes

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into 150 six times.

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6 times 0.25 is-- or actually, this is now a 25.

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We've shifted the decimal.

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This decimal is sitting right over there.

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So 6 times 25 is 150.

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You subtract.

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You get no remainder.

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Bring down this 0 right here.

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25 goes into 0 zero times.

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0 times 25 is 0.

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Subtract.

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No remainder.

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Bring down this last 0.

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25 goes into 0 zero times.

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0 times 25 is 0.

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Subtract.

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No remainder.

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So 150 divided by 0.25 is equal to 600.

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And you might have been able to do that in your head,

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because when we were at this point in our equation, 0.25x

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is equal to 150, you could have just multiplied both

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sides of this equation times 4.

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4 times 0.25 is the same thing as 4 times

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1/4, which is a whole.

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And 4 times 150 is 600.

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So you would have gotten it either way.

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And this makes total sense.

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If 150 is 25% of some number, that means 150 should be 1/4

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of that number.

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It should be a lot smaller than that number, and it is.

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150 is 1/4 of 600.

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Now let's answer their actual question.

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Identify the percent.

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Well, that looks like 25%, that's the percent.

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The amount and the base in this problem.

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And based on how they're wording it, I assume amount

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means when you take the 25% of the base, so they're saying

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that the amount-- as my best sense of it-- is that the

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amount is equal to the percent times the base.

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Let me do the base in green.

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So the base is the number you're taking the percent of.

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The amount is the quantity that that percentage

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represents.

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So here we already saw the percent is 25%.

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That's the percent.

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The number that we're taking 25% of, or the base, is x.

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The value of it is 600.

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We figured it out.

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And the amount is 150.

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This right here is the amount.

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The amount is 150.

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150 is 25% of the base, of 600.

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The important thing is how you solve this problem.

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The words themselves, you know, those are all really

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just definitions.

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