Strategies for dividing multiples of 10, 100 and 1000

We're going to do in this video is get some practice doing division with numbers that are multiples of 10, 100, 1000, things like that. So, let's say we wanted to compute what 2400 divided by 30 is. Pause this video and see if you can calculate it using whatever strategy makes sense to you.

All right, so let's think about this together, and I'm going to show you how my brain likes to handle this. We'll do this out on my little digital blackboard, but eventually, you'll be able to do things like this in your head. So, 2400, or 2400, divided by 30, that is the same thing as four hundred two thousand four hundred over thirty. So, this is just another way of saying two thousand four hundred divided by thirty.

Now, the reason why I wrote it this way is because you can now write each of these, the numerator and the denominators, as the product of some number and either 10 or 100 or a thousand. So, 2400, that's the same thing as 24 times 100, 24 times 100. And I knew that; I was like, "Okay, I've got these two zeros at the end," so you could view this literally as 24 hundreds. And then 30, you can view as we got one zero here, so it's three tens; the three is in the tens place, so three times ten.

Now, what's valuable about thinking of it this way is you can separately divide the 24 by the 3 and then the hundred by the ten. So, this is the same thing as, let me do this this way, as that times that. And so, we have 24 divided by 3 times 100 divided by 10. Now, 24 divided by 3, you might already know that is going to be eight; three times eight is twenty-four, so this is going to be equal to eight.

And what's a hundred divided by ten? Well, a hundred divided by ten is just going to be 10. So, our quotient, I guess you could say, is going to be 8 times 10, or it's going to be equal to, it's going to be equal to 80. And we're done. And you might notice something interesting here.

So, if I take my 24 and divide it by my 3, I'm going to get this 8. And then, if I take two zeros and if I take away another zero, I'm going to be left with one zero right over here, so you get 80. But why did that thing with the zeros work? Because you're really taking 24 hundreds divided by three tens. So, 100 divided by 10, well, you're going to lose a zero; that's going to be equal to 10, which has only one zero.

Let's do another example just to hit the point home and try to do this next example the way we just did it, maybe in your head or maybe on a piece of paper. So, let's say we wanted to calculate 3500, which you could also think of as 3500, and we want to divide that, we want to divide that by—let me write the division symbol a little bit nicer than that—we want to divide that by 700. Pause this video and see if you can compute that.

So, as we just did, we could view this as 3500 over 700. 3500, we can view as 35 times 100 over—this is going to be over, let me get the right color here—over 7 times 100. Now, the hundreds cancel out, and we're just left with 35 over 7. Now, what's 35 divided by 7? Well, that is going to be equal to 5.

And notice you could just say 35 divided by 7 is 5, and if you're saying how many zeros do I have left over, well, I have two zeros here, but since I'm dividing by something with two zeros, those two zeros are going to be cancelled out. Now, I don't want you to just memorize that; the reason why that happens is because as those two zeros here represent hundreds, 35 hundreds, these two zeros represent hundreds. So, if you divide 100 by hundreds, they're all going to cancel out.

So, you had two zeros before, but you're dividing by something with the two zeros, so you don't have any zeros after the five. Here, let me do one more example just to really hit that point home, but I want you to appreciate that it's not just some magical trick; it just makes sense out of things that you might already know.

So, if someone—and I'm gonna give this—I'm gonna give a crazy one. Let's say we had 42 million, 42 million divided by, let's say, 60,000. What is that going to be? Pause the video and see if you can think about it on your own. Well, using the notions that we just talked about, you could say, "All right, 42 divided by 6 is going to be seven," and then if I, let's see, over here I have six zeros, so we're talking about millions, and I'm going to draw, divide by four zeros right over here, which is ten thousand.

So, if you had six zeros but then you divide by—or if you have millions with six zeros and you divide by ten thousands with four zeros, six minus four is going to be two. So, your answer is going to have two zeros in it, so this is going to be equal to 700. Now, once again, not a magical trick; the way that we got this is that this is equal to 42 times a million, we got our six zeros right over there divided by, divided by six ten thousands, six times ten thousand.

So, our 42 divided by 6, that's where we get the seven from. And now, one way to think about it: if we divide the numerator and denominator by 10, we lose a zero. Then we do it again, we lose zeros; we do it again, we lose zeros; we do it again, we lose zeros.

And so this thing just all becomes one. Or another way to think about it: if we divide the numerator and the denominator by ten thousand, this becomes one, this thing loses four zeros, and you're left with 42 divided by 6 is seven hundreds because we have a one now in the denominator; hundred divided by one, so seven hundred.