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# Dividing a whole number by a decimal

CCSS.Math:

## Video transcript

let's divide 518 by so let's going to divide it by 0.7 0.7 so we're dividing this whole number by a decimal so we could also write this as 518 518 divided let me write a little bit bigger than that since we have to do some work with it 518 divided by 2 the division sign in white divided by 0.7 0.7 so the first thing we do since we have this decimal you were dividing by decimals to try to turn this into a whole number somehow well the best way to turn this into a whole number is to multiply this by 10 which is essentially multiplying shifting the decimal point over to the right so this would become a 7 but we can't just do that only for what we're dividing by we also have to do that to the 518 so that a value does not change so we need to multiply both of these times 10 so if we move the decimal over to the right with the 0.72 turn into a 7 we also need to move the decimal over the right for 518 now you're probably saying I don't see a decimal in 518 well there is one you just didn't have to write it because it's 518 point to the 0 zero and we can add as many zeros as we want so we if we move the decimal to the right it becomes 5,180 so really what we're saying is 518 divided by 0.7 is the same thing is the same thing as five thousand five thousand one hundred and eighty five thousand one hundred and eighty divided by divided by seven notice all we did by moving the decimal one place to the right is we multiplied both of these numbers by 10 which is not going to change the actual value of the decimal one other way of thinking about this if you wanted to write this as a fraction this is the same thing this is the same thing as 518 over zero point seven over zero point seven you multiply both the numerator and the denominator by 10:00 you will get 5,180 you will get 5,180 / 7 / 7 so let's clean this up a little bit just so we remember what we did so we move the decimal over to the right one so now this is just a 7 the decimal is there in fact we really don't have to write the decimal anymore just a 7 point you can imagine seven point two zero so we can just write this as a seven and then the 518 the decimal is now out here so this is 580 and let's increase increase this sign right over here now this is just a straight up long division problem how many times does 7 go into 5 well it goes 0 times 0 times 7 actually let's just let's just cut to the chase 7 doesn't go into 5 it does go into 51 7 times 7 is 49 so it goes 7 times 7 times 7 is 49 subtract 51 - 49 is 2 and now we can bring down we can bring down this 8 7 goes into 28 4 times 4 times 7 is 28 subtract you get a 0 now we can bring down another 0 we want to at least get to the decimal place so bring down another 0 right over here when I say get to the decimal place we can put the decimal place up here - just to make sure we're keeping track of the right place values or that we have the decimal in the right place so notice I'm very particular when I'm doing 7 goes into 51 I put the 7 right above the 1 in the 50 ones place when I'm saying 7 it goes into 28 I'm putting the 4 right above the 8 in this ones place when we're doing the division so now we say how many times does 7 go into 0 well it goes 0 times 0 times 7 is 0 subtract you have no remainder so we could keep going and we'll just keep getting zeroes like this but we see that this is equal to 740 740