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# Dividing by a multi-digit decimal

## Thuyết minh video

we nee divided 0.25 into one point zero three zero seven five now the first thing you want to do when your devise or the number that you're dividing into the other number is a decimal is to multiply it by ten enough times so that it becomes a whole number so you can shift the decimal to the right so every time you multiply something by ten you're shifting the decimal over to the right once so in this case we want to shift it over to the right once and twice 0.25 times ten twice is the same thing as 0.25 times 100 and we'll turn the point two five into 25 now if you do that with the devise or you also have to do that with the dividend the number that you're dividing into so we also have to multiply this by 10 twice or another way of viewing it is shift the decimal over to the right twice so we shift it over once twice it will sit right over here and to see why that makes sense you just have to realize that this expression right here this division problem is the exact same thing as having 0.25 is the exact same thing let me make it is the exact same thing as having one point zero three zero seven five divided by divided by 0.25 and so we're multiplying the 0.25 by 10 twice we're essentially multiplying it by 100 let me do that in a different color we're multiplying it by a hundred in the denominator this is the divisor or we're multiplying it by 100 so we also have to do the same thing to the numerator if we don't want to change this expression we don't change the number so we also have to multiply that by 100 and when you do that this becomes 25 and this becomes a hundred and three point zero seven five now let me just rewrite this sometimes if you're doing this in a workbook or something you don't have to rewrite as long as you remember where the decimal is but I'm going to rewrite it just so it's a little bit neater so we multiplied both the divisor and the dividend by a hundred this problem becomes 25 25 divided into divided into 100 three point zero seven five these are going to result in the exact same quotient they're the exact same fraction if you want to view it that way we've just multiplied both the numerator and the denominator by a hundred to shift the decimal over to the right twice now that we've done that we're ready to divide so the first thing we have 25 here and there's always a little bit of an art to dividing something by a multiple digit number so we'll see how well we can do so 25 does not go into 125 does not go into 10 25 does go into 103 we know that 4 times 25 is 100 so 25 goes into 100 3 4 times 4 times 5 is 20 4 times 2 is 8 plus 2 is 100 we knew that 4 times 4 quarters is a dollar it's a hundred cents and now we subtract 100 3 minus 100 is going to be 3 and now we can bring down we can bring down this 0 so we bring down that zero there 25 goes into 30 one time and if we want we can immediately put this decimal here we don't have to wait until the end of the problem this decimal sits right in that place so we could always have that decimal sitting right there in our quotient or in our answer or our quotient so anyway we were at 25 goes into 30 one time one times 25 one times 25 is 25 and then we can subtract 30 minus 25 well that's just 5 I'm going to do all of this borrowing 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 bring down now we can bring down this 7 25 goes into 57 2 times right 25 times 2 is 50 25 goes into 57 2 times 2 times 25 is 50 and now we subtract again 57 minus 50 is 7 and now we're almost done we can bring down this 5 we bring down that 5 right over there there 25 goes into 75 3 times 3 times 3 times 25 is 75 we say 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 then we have we have no remainder so 25 goes into 100 3.07 5 exactly 4 point 1 2 3 times which makes sense because 25 goes into 100 about 4 times this is a little bit larger than 100 it's going to be a little bit more than 4 times and that's going to be the exact same answer as the number of times that 0.25 goes into 1 point 0 3 0 7 5 this will also be this will also be 4 point 1 2 3 so this fraction or this expression is the exact same thing as 4 point 1 2 3 and we're done