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# Introduction to division with partial quotients (no remainder)

CCSS.Math:

## Video transcript

in this video we want to compute what 833 divided by 7 is so I encourage you to pause this video and see if you can figure that out on your own alright now let's work through it together and you might have appreciated this is a little bit more difficult than things that we've done in the past and in this video I'm going to show you a method that your parents have probably not seen but you'll see that it's kind of fun and it's called division with partial quotients which is a very fancy word but as I said it'll be fun so the first thing I will do is I will rewrite this as 833 divided by divided by 7 so you can view these as the same expression the reason why we do it this way it formats it so it's a little bit easier to do our division with partial quotients so way the way that division with partial quotients work and once again it's not the way that your parents probably learn how to do it is you just say hey how many times can 7 go into 833 I don't have to get it exactly I just want to go under 833 and so my brain immediately thinks well 700 s is less than 833 so we're going to go into 833 at least a hundred times and so what we would do is we would write that hundred up here we want to be very careful about our place value you could view this column as the hundreds column this is the tens column this is the ones column and then we want to see how much do we have left over how close did 7 times a hundred get us so what we do is we multiply 100 times seven to get seven hundred and then we can subtract that seven hundred from 833 to figure out how much more we have left and so in our 33 minus seven hundred is 133 and so we could then say all right we still have another 133 to go so how many more times can seven go into this well 7 goes into 133 you don't once again you don't have to have it exactly if you know C seven times 10 is equal to 70 actually let's go with that we know we go at least 10 times so let's write that up here we're going at least 10 times and to figure out how much more we have left let's multiply 10 times 7 to get 70 and then we can subtract and we see that we have let's see 3 minus 0 is 3 13 tens minus 7 tens is 6 tens so we have 63 left so 7 definitely can go into 63 we're gonna keep doing this until we have a number less than 7 over here so let's see 7 how many times does 7 go into 63 you might know from your multiplication tables that 7 times 9 is 63 so you could get it exactly so you could just write that up here we have 9 more times to go into the number and then you would say 9 times 7 is 63 and you could say hey we got exactly there we have nothing left over and as long as this number is less than 7 you know that you can't divide 7 any more into our original number and so you're done and so how many times does 7 go into 833 well we said it went a hundred times and then we were able to go another 10 times and then we were able to go another 9 times and so what we want to do is add these numbers so you want to add 100 plus 10 plus 9 when you add up all of them what do you get you get 9 ones 110 100 you get 119 so this is equal to 119 all I did is I added these up now I want to be very clear that you could do division with partial quotients and not do it exactly like this that's kind of why it's fun so let's read let's do it another way so let's say we want to figure out again how many times does 7 go into 833 833 we could have said maybe it goes 150 times so what you could have said is you could have said alright my current guess or estimate is 150 times then I could multiply 150 times 7 how would I do that let's see 0 times 7 is 0 5 times 7 is 35 you can carry the 3 so to speak 5 times sorry 1 seven is seven plus that three is going to be ten and so that gets us to 10:50 well over here we just finished overshooting it doesn't go 150 times there's nothing left over so 150 is too high so we would want to backtrack that and then you could go well maybe I could go to a hundred and ten so let's try that out so 110 and now let's multiply 0 times 7 is 0 1 times 7 is 7 1 times 7 is 7 so 110 times 7 is 770 so that works it's less than 833 but let's see what we have left so we subtract we get a 3 here and then let's see 83 tens minus 77 tens that's 6 tens and actually that got us there a lot faster so then you could just know that hey 7 goes into 63 nine times but let's say we didn't know that we could say all right let's say I'm gonna estimate it goes 8 times so you would put an 8 up here and then you say how much do we have left over 8 times 7 is 56 you subtract and then 63 minus 56 is exactly 7 and say okay look I can go one more time so I'd write that up there and so one times seven is seven and then you see we have nothing left over so we are done so how many times did it go in 1 plus 8 is 9 plus 110 is 119 so hopefully you find that interesting and I really want you to think about why this is working we're just trying to see how many times can we go in without overshooting it and then what's left over so how many more times can we go in and then what's left over then how many more times can we go in until what we have left over is less than seven so that we can't go into it any more times