Dividing by a two digit number

In this video, we're going to get a little bit of practice dividing by a two-digit number. So let's say that we have 4781 divided by 32. Pause this video and see if you can figure out what that's going to be and if there is a remainder, figure out what that remainder is going to be.

All right, now let's work on this together. So first, let me rewrite 4781, and this is going to be divided by 32. Now, whenever we divide by anything that has more than one digit, it's a little bit of an art. The way we're going to tackle it is a little trial and error using estimation. So we'll start by saying, "Hey, how many times does 32 go into 4?" Well, 32 doesn't go into 4 at all.

So then we'll move on. How many times does 32 go into 47? Well, it's pretty clear that 32 goes one time into 47, so I'll put the 1 right over there above the 7 in 47. If you're saying, "Hey, how did Sal know that?" Well, just remember, 2 times 32 would be 64. That's more than 47. So, 32 goes into 47 one time.

Now we multiply 1 times 32. 1 times 2 is 2; 1 times 3 is 3. You knew that 1 times 32 is 32. And then we subtract 32 from 47. Let's do that, and we get 7 minus 2 is 5 and 4 minus 3 is 1. The way you make sure that you did that step right is whatever we get over here should be less than 32. If whatever we have here is 32 or greater, that means we could have had a larger number up here.

But then our next step is we bring down the 8 and we say, "How many times does 32 go into 158?" Now this is a little bit tricky. If you were estimating how many times does 30 go into 150, you might say 5. Actually, this is for kicks; let's just try that out. Let's see if 5 works. So, let's see. 5 times 2 is 10. We'll put zero ones and then we will have one ten there, carry the one. 5 times 3 is fifteen plus one is sixteen. So that didn't work out. It almost worked out, but not quite. 160 is larger than 158, so 5 is too much there.

So we need to go down to 4. 4 times 2 is 8; 4 times 3 is 12. Now we subtract and 158 minus 128. Eight minus eight is zero; five tens minus two tens is three tens, and then we have no hundreds. And then this is right because thirty is less than thirty-two. Then we can bring down that one.

Now how many times does 32 go into 301? Well, we might be tempted to say, "Well, this is close to 30; this is close to 300, so maybe it's 10." But 10 times 32 would be 320, so that'd be too much. So I feel good about 9 as my estimate. 9 times 2 is 18, carry the 1. 9 times 3 is 27 plus 1 is 28.

And then we can subtract. We're actually going to do a little regrouping here. You might be able to do it in your head to go from 288 to 301. Let's say you would add 12 to get to 300 and then one more, 13. So you might be able to do it in your head that this is going to be 13, or you could regroup.

You could say, "All right, let's see. One is less than eight; can I regroup from the tens place?" No, I have nothing there, so I have to regroup from the hundreds place. I'm going to take one of those hundreds; I'm left with two hundreds, and then I'm going to have ten tens. Then I can take one of those tens, so I have nine tens left and give it to the ones place.

So now I have 11 ones, and 11 minus 8 is 3. Nine tens minus eight tens is 1 ten, and then the hundreds: 200 minus 200 is just a zero. And so there we have it: this is less than 32. We have nothing left to bring down, and so we're left with a remainder of 13.

So this is going to be equal to 149 with a remainder of 13. And we're done.