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## Multi-digit division (remainders)

# Dividing by 2-digits: 6250÷25

## Video transcript

Welcome to the presentation
on level 4 division. So what makes level 4 division
harder than level 3 division is instead of having a one-digit
number being divided into a multi-digit number, we're now
going to have a two-addition number divided into a
multi-digit number. So let's get started with
some practice problems. So let's start with what I
would say is a relatively straightforward example. The level 4 problems
you'll see are actually a little harder than this. But let's say I had
25 goes into 6,250. So the best way to think about
this is you say, OK, I have 25. Does 25 go into 6? Well, no. Clearly 6 is smaller than 25,
so 25 does not go into 6. So then ask yourself, well,
then if 25 doesn't go into 6, does 25 go into 62? Well, sure. 62 is larger than 25,
so 25 will go into 62? Well, let's think about it. 25 times 1 is 25. 25 times 2 is 50. So it goes into 62
at least two times. And 25 times 3 is 75. So that's too much. So 25 goes into 62 two times. And there's really no
mechanical way to go about figuring this out. You have to kind of think
about, OK, how many times do I think 25 will go into 62? And sometimes you get it wrong. Sometimes you'll
put a number here. Say if I didn't know, I
would've put a 3 up here and then I would've said 3 times
25 and I would've gotten a 75 here. And then that would have been
too large of a number, so I would have gone back
and changed it to a 2. Likewise, if I had done a 1 and
I had done 1 tmes 25, when I subtracted it out, the
difference I would've gotten would be larger than 25. And then I would know
that, OK, 1 is too small. I have to increase it to 2. I hope I didn't
confuse you too much. I just want you to know that
you shouldn't get nervous if you're like, boy, every time I
go through the step it's kind of like- I kind of have to
guess what the numbers is as opposed to kind of a method. And that's true; everyone
has to do that. So anyway, so 25 goes
into 62 two times. Now let's multiply 2 times 25. Well, 2 times 5 is 10. And then 2 times 2 plus 1 is 5. And we know that 25
times 2 is 50 anyway. Then we subtract. 2 minus 0 is 2. 6 minus 5 is 1. And now we bring down the 5. So the rest of the mechanics
are pretty much just like a level 3 division problem. Now we ask ourselves, how many
times does 25 go into 125? Well, the way I think about it
is 25-- it goes into 100 about four times, so it will go
into 125 one more time. It goes into it five times. If you weren't sure you could
try 4 and then you would see that you would have
too much left over. Or if you tried 6 you would see
that you would actually get 6 times 25 is a number
larger than 125. So you can't use 6. So if we say 25 goes into 125
five times then we just multiply 5 times 5 is 25. 5 times 2 is 10 plus 2, 125. So it goes in exact. So 125 minus 125 is clearly 0. Then we bring down this 0. And 25 goes into 0 zero times. 0 times 25 is 0. Remainder is 0. So we see that 25 goes into
6,250 exactly 250 times. Let's do another problem. Let's say I had-- let me
pick an interesting number. Let's say I had 15 and I
want to know how many times it goes into 2,265. Well, we just do the same
thing we did before. We say OK, does 15 go into 2? No. So does 15 go into 22? Sure. 15 goes into 22 one time. Notice we wrote the
1 above the 22. If it go had gone into 2 we
would've written the 1 here. But 15 goes into 22 one time. 1 times 15 is 15. 22 minus 15-- we could do the
whole carrying thing-- 1, 12. 12 minus 5 is 7. 1 minus 1 is 0. 22 minus 15 is 7. Bring down the 6. OK, now how many times
does 15 go into 76? Once again, there isn't a real
easy mechanical way to do it. You can kind of eyeball
it and estimate. Well, 15 times 2 is 30. 15 times 4 is 60. 15 times 5 is 75. That's pretty close, so let's
say 15 goes into 76 five times. So 5 times 5 once again, I
already figured it out in my head, but I'll
just do it again. 5 times 1 is 5. Plus 7. Oh, sorry. 5 times 5 is 25. 5 times 1 is 5. Plus 2 is 7. Now we just subtract. 76 minus 75 is clearly 1. Bring down that 5. Well, 15 goes into 15
exactly one time. 1 times 15 is 15. Subtract it and we get
a remainder of 0. So 15 goes into 2,265
exactly 151 times. So just think about what we're
doing here and why it's a little bit harder than when you
have a one-digit number here. Is that you have to kind of
think about, well, how many times does this two-digit
number go into this larger number? And since you don't know
two-digit multiplication tables-- very few people do--
you have to do a little bit of guesswork. Sometimes you can look at this
first digit and look at the first digit here and
make an estimate. But sometimes it's
trial and error. You'll try and when you
multiply it out you might get it wrong on the first try. Let's do another problem. And actually, I'm going to pick
numbers at random, so it might not have an easy remainder. But I think you'll
get the point. I won't teach you decimals
now, so I'll just leave the remainder if there is one. Let's say I had 67
going into 5,978. So I just picked these numbers
randomly out of my head, so I'll show you that I also
sometimes have to do a little bit of guesswork to figure out
how many times one of these two-digit numbers go
into a larger number. So 67 goes into 5 zero times. 67 goes into 59 zero times. 67 goes into 597--
so let's see. 67 is almost 70 and
597 is almost 600. So if it was 70 goes
into-- 70 times 9 to 630. Because 7 times 9 is 63. So I'm going to just
eyball approximate. I'm going to say that it
goes into it eight times. I might be wrong. And you can always check, but
well, we're going to actually check in this step essentially. 8 times 7-- well that's 56. And then 8 times 6 is 48. Plus 2 is 53. 7 minus 6 is 1. 9 minus 9 is 6. 5 minus 5 is 0. 61. So good. I got it right because if I got
a number here that was larger than-- 67 or larger, than that
means that this number up here wasn't large enough. But here, I got a number
that's positive because 536 is less than 597. And it's less than 67, so
I did that step right. So now we bring down this 8. Now this one might be a little
bit trickier this time. Once again, we have almost 70
and here we have almost 630. So maybe it will go
into it 9 times. Well, let's give it a
try and see if it does. 9 times 7 is 63. 9 times 6 is 54. Plus 6 is 60. Good. So it did actually go into
it nine times because 603 is less than 618. 8 minus 3 is 5. 1 minus 0 is 1. And 6 minus 6 is 0. We have a remainder of 15,
which is smaller than 67. So I'm not going to teach you
decimals right now, so we can just leave that remainder. So what we could say is that
67 goes into 5,978 89 times. And when it goes into it 89
times, you're left with a remainder of 15. hopefully you're ready
now to try some level 4 division problems. Have fun.