Video transcript
We need to divide 0.25into 1.03075. Now the first thing you want todo when your divisor, the number that you're dividing intothe other number, is a decimal, is to multiply it by10 enough times so that it becomes a whole numberso you can shift the decimal to the right. So every time you multiplysomething by 10, you're shifting the decimal overto the right once. So in this case, we wantto switch it over the right once and twice. So 0.25 times 10 twice is thesame thing as 0.25 times 100, and we'll turn the0.25 into 25. Now if you do that with thedivisor, you also have to do that with the dividend,the number that you're dividing into. So we also have to multiply thisby 10 twice, or another way of doing it is shiftthe decimal over to the right twice. So we shift it overonce, twice. It will sit right over here. And to see why that makessense, you just have to realize that this expressionright here, this division problem, is the exact samething as having 1.03075 divided by 0.25. And so we're multiplyingthe 0.25 by 10 twice. We're essentially multiplyingit by 100. Let me do that in adifferent color. We're multiplying it by 100in the denominator. This is the divisor. We're multiplying it by 100, sowe also have to do the same thing to the numerator, if wedon't want to change this expression, if we don't wantto change the number. So we also have to multiplythat by 100. And when you do that,this becomes 25, and this becomes 103.075. Now let me just rewrite this. Sometimes if you're doing thisin a workbook or something, you don't have to rewrite it aslong as you remember where the decimal is. But I'm going to rewriteit, just so it's a little bit neater. So we multiplied boththe divisor and the dividend by 100. This problem becomes 25divided into 103.075. These are going to result inthe exact same quotient. They're the exact same fraction,if you want to view it that way. We've just multiplied both thenumerator and the denominator by 100 to shift the decimalover to the right twice. Now that we've done that,we're ready to divide. So the first thing, we have 25here, and there's always a little bit of an art to dividingsomething by a multiple-digit number, so we'llsee how well we can do. So 25 does not go into 1. 25 does not go into 10. 25 does go into 103. We know that 4 times 25is 100, so 25 goes into 100 four times. 4 times 5 is 20. 4 times 2 is 8, plus 2 is 100. We knew that. Four quarters is $1.00. It's 100 cents. And now we subtract. 103 minus 100 is going tobe 3, and now we can bring down this 0. So we bring down that 0 there. 25 goes into 30 one time. And if we want, we couldimmediately put this decimal here. We don't have to wait untilthe end of the problem. This decimal sits right in thatplace, so we could always have that decimal sitting rightthere in our quotient or in our answer. So we were at 25 goesinto 30 one time. 1 times 25 is 25, and thenwe can subtract. 30 minus 25, well,that's just 5. I mean, we can do all thisborrowing business, or regrouping. This can become a 10. This becomes a 2. 10 minus 5 is 5. 2 minus 2 is nothing. But anyway, 30 minus 25 is 5. Now we can bring down this 7. 25 goes into 57 twotimes, right? 25 times 2 is 50. 25 goes into 57 two times. 2 times 25 is 50. And now we subtract again. 57 minus 50 is 7. And now we're almost done. We bring down that 5right over there. 25 goes into 75 three times. 3 times 25 is 75. 3 times 5 is 15. Regroup the 1. We can ignore that. That was from before. 3 times 2 is 6, plus 1 is 7. So you can see that. And then we subtract, and thenwe have no remainder. So 25 goes into 103.075 exactly4.123 times, which makes sense, because 25 goesinto 100 about four times. This is a little bit larger than100, so it's going to be a little bit morethan four times. And that's going to be theexact same answer as the number of times that 0.25goes into 1.03075. This will also be 4.123. So this fraction, or thisexpression, is the exact same thing as 4.123. And we're done!
