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# Division with partial quotients (remainder)

CCSS.Math:

## Video transcript

let's say we want to figure out what 473 divided by five is and like always want you pause this video and try to work through it and if you're familiar with the idea of division with partial quotients I encourage you to try it out that way all right now let's work on this together and so let me just rewrite this in a format that makes it a little bit easier for me to do my division with partial quotients and so I'm just going to write four hundred and seventy three divided by five and what's neat about division with partial quotients is that there's a lot of flexibility in how you do it there's no exactly one right way and so you could say all right how many times can 5 go into 473 without going over 473 you might be tempted someone might say oh maybe you can go a hundred times but you could quickly see that if you said a hundred times and then say how much do I have left over you do a hundred times five you'd get 500 and you'd say oh wait I overshot 473 so 100 is too high so then you would back up a little bit and then you could say all right I'm gonna I'm gonna go for low numbers and just slowly chip away out of it so you might say that 5 goes into 4 inch 73 you know it goes more than 20 times so let's just start with 20 well what is 20 times 5 20 times 5 is 100 and let me be very clear what that is that is 20 times our 5 right over there and so clearly we did not overshoot it but how much how many more times can 5 going to 473 than 20 to figure that out we figure out how much more we have left over to go so we subtract the hundred from 473 and we have 373 so how many times can 5 go into 373 well if 20 times 5 was a hundred well gee this is three hundred here so maybe we can go another 60 times so let me put a 60 right over there and so what is 60 times five well six tens times five would be 30 tens which is three and so how much further do we have to go so we still have 73 left 373 - 300 is 73 so how many times does 5 go into 73 well let's see I know 5 times 12 is 60 so let me try 12 so I will put a 12 over here and so 12 times 5 is 60 so how much further do we have to go let's see 73 minus 60 is 13 and 5 can go into 13 so we can get a little a few more fives in there just to be clear what we're doing we've already said hey we can go 20 times and then another 60 and then another 12 times and if we go into 4 and 73 all of those times we still have 13 left over so we could go into we can even fit a few more fives in there now how many times does 5 go into 13 well 5 times 2 is 10 5 times 3 would be too much so we could say 2 times so that gets us 2 times 5 is 10 and so there what we have a left over is a 3 and then we can't fit any more fives in we can't divide 5 into 3 so that's going to give us our remainder so how many times does 5 go into 473 well we were able to get it in there 20 times and then another 60 times and then another 12 times and then another 2 times so what we can do is we can add all of these together and what do we get 2 plus 12 is 14 plus 60 is 74 + 20 is 94 and then we have a remainder of 3 so this is equal to 94 and then I'll write this in red with a remainder of 3 did I do that right 2 plus 14 let's see 2 plus 12 is 1474 94 now let me just show you that there's more than one way to do this and I will draw a little line here so we don't get it too confused we could have done something like this we could have said what is 473 divided by five and we might have immediately recognized that all right 5 goes into 40 eight times so five would go into 480 times at least probably more times than that but let's just start with 80 and so how close does that get us to 473 well to figure that out we multiply 80 times 5 to get 400 and so can we fit any more fives into the difference so let's figure out the difference so we will subtract and just to be very clear this was 80 times 5 the reason why we did that who see how close did we get to 473 and now we want to figure out how much do we have left over how many more fives can we fit in and so you subtract 400 from 473 and we are going to get 73 well we can for sure fit more fives into 73 we might say hey maybe let's try to fit another 10 5s in there so let's take another 10 fives in there now how close are we well 10 times 5 is 50 and to be clear what we just did here is we multiplied 10 times 5 and now can we fit any more fives in well to figure that out we would need to subtract and figure out what what we have left so 73 minus 52 23 and we can for sure fit more fives into 23 we know that 5 times 4 is equal to 20 so let's put 4 more fives in there so 4 times 5 is going to be 20 let's see how close we are now and to be very clear that is 4 times our 5 and so what do we get to what do we have left and can we fit any more fives in let's see 23 minus 20 is just 3 and that's less than 5 so we can't fit any more fives in so there we have it we were able to get eighty fives in to 473 we saw that we still had some leftover we were able to fit another 10 into that leftover and then we still saw that we had some leftover they were able to fit another fought for into that leftover and then we had a leftover 3 and we weren't able to fit any more fives in and so in total we were able to fit 94 5 to 473 and then we had three left over which is exactly what we had there