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Welcome to the presentation on level 4 division.

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So what makes level 4 division harder than level 3 division is

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instead of having a one-digit number being divided into a

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multi-digit number, we're now going to have a two-addition

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number divided into a multi-digit number.

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So let's get started with some practice problems.

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So let's start with what I would say is a relatively

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straightforward example.

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The level 4 problems you'll see are actually a

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little harder than this.

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But let's say I had 25 goes into 6,250.

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So the best way to think about this is you say, OK, I have 25.

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Does 25 go into 6?

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Well, no.

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Clearly 6 is smaller than 25, so 25 does not go into 6.

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So then ask yourself, well, then if 25 doesn't go into

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6, does 25 go into 62?

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Well, sure.

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62 is larger than 25, so 25 will go into 62?

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Well, let's think about it.

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25 times 1 is 25.

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25 times 2 is 50.

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So it goes into 62 at least two times.

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And 25 times 3 is 75.

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So that's too much.

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So 25 goes into 62 two times.

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And there's really no mechanical way to go

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about figuring this out.

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You have to kind of think about, OK, how many times do

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I think 25 will go into 62?

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And sometimes you get it wrong.

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Sometimes you'll put a number here.

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Say if I didn't know, I would've put a 3 up here and

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then I would've said 3 times 25 and I would've

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gotten a 75 here.

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And then that would have been too large of a number, so

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I would have gone back and changed it to a 2.

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Likewise, if I had done a 1 and I had done 1 tmes 25, when I

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subtracted it out, the difference I would've gotten

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would be larger than 25.

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And then I would know that, OK, 1 is too small.

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I have to increase it to 2.

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I hope I didn't confuse you too much.

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I just want you to know that you shouldn't get nervous if

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you're like, boy, every time I go through the step it's kind

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of like- I kind of have to guess what the numbers is as

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opposed to kind of a method.

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And that's true; everyone has to do that.

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So anyway, so 25 goes into 62 two times.

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Now let's multiply 2 times 25.

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Well, 2 times 5 is 10.

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And then 2 times 2 plus 1 is 5.

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And we know that 25 times 2 is 50 anyway.

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Then we subtract.

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2 minus 0 is 2.

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6 minus 5 is 1.

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And now we bring down the 5.

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So the rest of the mechanics are pretty much just like a

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level 3 division problem.

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Now we ask ourselves, how many times does 25 go into 125?

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Well, the way I think about it is 25-- it goes into 100 about

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four times, so it will go into 125 one more time.

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It goes into it five times.

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If you weren't sure you could try 4 and then you would see

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that you would have too much left over.

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Or if you tried 6 you would see that you would actually get 6

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times 25 is a number larger than 125.

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So you can't use 6.

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So if we say 25 goes into 125 five times then we just

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multiply 5 times 5 is 25.

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5 times 2 is 10 plus 2, 125.

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So it goes in exact.

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So 125 minus 125 is clearly 0.

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Then we bring down this 0.

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And 25 goes into 0 zero times.

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0 times 25 is 0.

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Remainder is 0.

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So we see that 25 goes into 6,250 exactly 250 times.

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Let's do another problem.

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Let's say I had-- let me pick an interesting number.

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Let's say I had 15 and I want to know how many

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times it goes into 2,265.

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Well, we just do the same thing we did before.

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We say OK, does 15 go into 2?

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No.

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So does 15 go into 22?

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Sure.

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15 goes into 22 one time.

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Notice we wrote the 1 above the 22.

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If it go had gone into 2 we would've written the 1 here.

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But 15 goes into 22 one time.

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1 times 15 is 15.

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22 minus 15-- we could do the whole carrying thing-- 1, 12.

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12 minus 5 is 7.

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1 minus 1 is 0.

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22 minus 15 is 7.

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Bring down the 6.

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OK, now how many times does 15 go into 76?

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Once again, there isn't a real easy mechanical way to do it.

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You can kind of eyeball it and estimate.

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Well, 15 times 2 is 30.

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15 times 4 is 60.

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15 times 5 is 75.

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That's pretty close, so let's say 15 goes into 76 five times.

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So 5 times 5 once again, I already figured it out in

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my head, but I'll just do it again.

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5 times 1 is 5.

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Plus 7.

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Oh, sorry.

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5 times 5 is 25.

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5 times 1 is 5.

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Plus 2 is 7.

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Now we just subtract.

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76 minus 75 is clearly 1.

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Bring down that 5.

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Well, 15 goes into 15 exactly one time.

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1 times 15 is 15.

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Subtract it and we get a remainder of 0.

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So 15 goes into 2,265 exactly 151 times.

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So just think about what we're doing here and why it's a

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little bit harder than when you have a one-digit number here.

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Is that you have to kind of think about, well, how many

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times does this two-digit number go into this

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larger number?

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And since you don't know two-digit multiplication

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tables-- very few people do-- you have to do a little

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bit of guesswork.

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Sometimes you can look at this first digit and look at the

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first digit here and make an estimate.

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But sometimes it's trial and error.

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You'll try and when you multiply it out you might get

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it wrong on the first try.

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Let's do another problem.

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And actually, I'm going to pick numbers at random, so it might

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not have an easy remainder.

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But I think you'll get the point.

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I won't teach you decimals now, so I'll just leave the

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remainder if there is one.

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Let's say I had 67 going into 5,978.

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So I just picked these numbers randomly out of my head, so

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I'll show you that I also sometimes have to do a little

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bit of guesswork to figure out how many times one of these

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two-digit numbers go into a larger number.

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So 67 goes into 5 zero times.

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67 goes into 59 zero times.

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67 goes into 597-- so let's see.

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67 is almost 70 and 597 is almost 600.

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So if it was 70 goes into-- 70 times 9 to 630.

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Because 7 times 9 is 63.

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So I'm going to just eyball approximate.

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I'm going to say that it goes into it eight times.

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I might be wrong.

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And you can always check, but well, we're going to actually

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check in this step essentially.

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8 times 7-- well that's 56.

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And then 8 times 6 is 48.

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Plus 2 is 53.

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7 minus 6 is 1.

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9 minus 9 is 6.

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5 minus 5 is 0.

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61.

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So good.

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I got it right because if I got a number here that was larger

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than-- 67 or larger, than that means that this number up

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here wasn't large enough.

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But here, I got a number that's positive because

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536 is less than 597.

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And it's less than 67, so I did that step right.

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So now we bring down this 8.

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Now this one might be a little bit trickier this time.

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Once again, we have almost 70 and here we have almost 630.

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So maybe it will go into it 9 times.

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Well, let's give it a try and see if it does.

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9 times 7 is 63.

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9 times 6 is 54.

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Plus 6 is 60.

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Good.

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So it did actually go into it nine times because

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603 is less than 618.

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8 minus 3 is 5.

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1 minus 0 is 1.

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And 6 minus 6 is 0.

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We have a remainder of 15, which is smaller than 67.

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So I'm not going to teach you decimals right now, so we can

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just leave that remainder.

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So what we could say is that 67 goes into 5,978 89 times.

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And when it goes into it 89 times, you're left with

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a remainder of 15.

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hopefully you're ready now to try some level

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4 division problems.

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Have fun.

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