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We need to divide 0.25 into 1.03075.

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Now the first thing you want to do when your divisor, the

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number that you're dividing into the other number, is a

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decimal, is to multiply it by 10 enough times so that it

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becomes a whole number so you can shift the

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decimal to the right.

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So every time you multiply something by 10, you're

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shifting the decimal over to the right once.

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So in this case, we want to switch it over the

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right once and twice.

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So 0.25 times 10 twice is the same thing as 0.25 times 100,

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and we'll turn the 0.25 into 25.

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Now if you do that with the divisor, you also have to do

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that with the dividend, the number that

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you're dividing into.

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So we also have to multiply this by 10 twice, or another

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way of doing it is shift the decimal over

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to the right twice.

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So we shift it over once, twice.

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It will sit right over here.

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And to see why that makes sense, you just have to

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realize that this expression right here, this division

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problem, is the exact same thing as having 1.03075

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divided by 0.25.

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And so we're multiplying the 0.25 by 10 twice.

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We're essentially multiplying it by 100.

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Let me do that in a different color.

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We're multiplying it by 100 in the denominator.

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This is the divisor.

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We're multiplying it by 100, so we also have to do the same

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thing to the numerator, if we don't want to change this

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expression, if we don't want to change the number.

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So we also have to multiply that by 100.

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And when you do that, this becomes 25, and

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this becomes 103.075.

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Now let me just rewrite this.

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Sometimes if you're doing this in a workbook or something,

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you don't have to rewrite it as long as you remember where

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the decimal is.

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But I'm going to rewrite it, just so it's

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a little bit neater.

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So we multiplied both the divisor and

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the dividend by 100.

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This problem becomes 25 divided into 103.075.

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These are going to result in the exact same quotient.

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They're the exact same fraction, if you want to view

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it that way.

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We've just multiplied both the numerator and the denominator

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by 100 to shift the decimal over to the right twice.

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Now that we've done that, we're ready to divide.

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So the first thing, we have 25 here, and there's always a

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little bit of an art to dividing something by a

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multiple-digit number, so we'll see how well we can do.

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So 25 does not go into 1.

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25 does not go into 10.

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25 does go into 103.

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We know that 4 times 25 is 100, so 25 goes

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into 100 four times.

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4 times 5 is 20.

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4 times 2 is 8, plus 2 is 100.

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We knew that.

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Four quarters is $1.00.

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It's 100 cents.

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And now we subtract.

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103 minus 100 is going to be 3, and now we can

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bring down this 0.

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So we bring down that 0 there.

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25 goes into 30 one time.

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And if we want, we could immediately put

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this decimal here.

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We don't have to wait until the end of the problem.

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This decimal sits right in that place, so we could always

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have that decimal sitting right there in our quotient or

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in our answer.

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So we were at 25 goes into 30 one time.

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1 times 25 is 25, and then we can subtract.

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30 minus 25, well, that's just 5.

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I mean, we can do all this borrowing business, or

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regrouping.

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This can become a 10.

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This becomes a 2.

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10 minus 5 is 5.

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2 minus 2 is nothing.

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But anyway, 30 minus 25 is 5.

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Now we can bring down this 7.

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25 goes into 57 two times, right?

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25 times 2 is 50.

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25 goes into 57 two times.

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2 times 25 is 50.

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And now we subtract again.

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57 minus 50 is 7.

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And now we're almost done.

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We bring down that 5 right over there.

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25 goes into 75 three times.

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3 times 25 is 75.

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3 times 5 is 15.

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Regroup the 1.

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We can ignore that.

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That was from before.

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3 times 2 is 6, plus 1 is 7.

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So you can see that.

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And then we subtract, and then we have no remainder.

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So 25 goes into 103.075 exactly 4.123 times, which

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makes sense, because 25 goes into 100 about four times.

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This is a little bit larger than 100, so it's going to be

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a little bit more than four times.

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And that's going to be the exact same answer as the

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number of times that 0.25 goes into 1.03075.

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This will also be 4.123.

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So this fraction, or this expression, is the exact same

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thing as 4.123.

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And we're done!

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