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We need to divide 0.25[br]into 1.03075.

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

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

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

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becomes a whole number[br]so you can shift the

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decimal to the right.

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So every time you multiply[br]something by 10, you're

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shifting the decimal over[br]to the right once.

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So in this case, we want[br]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[br]same thing as 0.25 times 100,

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and we'll turn the[br]0.25 into 25.

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

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that with the dividend,[br]the number that

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you're dividing into.

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

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way of doing it is shift[br]the decimal over

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to the right twice.

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So we shift it over[br]once, twice.

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It will sit right over here.

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And to see why that makes[br]sense, you just have to

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realize that this expression[br]right here, this division

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problem, is the exact same[br]thing as having 1.03075

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divided by 0.25.

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

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We're essentially multiplying[br]it by 100.

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Let me do that in a[br]different color.

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We're multiplying it by 100[br]in the denominator.

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This is the divisor.

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

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

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

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So we also have to multiply[br]that by 100.

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And when you do that,[br]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[br]in a workbook or something,

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

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the decimal is.

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

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a little bit neater.

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So we multiplied both[br]the divisor and

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the dividend by 100.

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This problem becomes 25[br]divided into 103.075.

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These are going to result in[br]the exact same quotient.

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

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it that way.

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We've just multiplied both the[br]numerator and the denominator

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by 100 to shift the decimal[br]over to the right twice.

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

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

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little bit of an art to dividing[br]something by a

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multiple-digit number, so we'll[br]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[br]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[br]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[br]immediately put

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this decimal here.

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

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

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have that decimal sitting right[br]there in our quotient or

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in our answer.

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So we were at 25 goes[br]into 30 one time.

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1 times 25 is 25, and then[br]we can subtract.

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30 minus 25, well,[br]that's just 5.

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I mean, we can do all this[br]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[br]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[br]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[br]we have no remainder.

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So 25 goes into 103.075 exactly[br]4.123 times, which

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

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

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a little bit more[br]than four times.

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

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number of times that 0.25[br]goes into 1.03075.

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This will also be 4.123.

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So this fraction, or this[br]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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