Introduction to dividing by 2 digits

What we're going to do in this video is start trying to divide by two-digit numbers. As we'll see, this is a super important skill that a lot of the rest of mathematics will build off of. But it's also interesting because it's a bit of an art. So let's just start by trying to compute what 186 divided by 31 is. Of course, we could also write this as 186 divided by 31. Pause the video and see if you can figure it out.

All right, now let's work through this together. I assumed you've given it a go at it. So, I don't have my 31 times tables memorized, so I can't just immediately tell you the answer. But my brain tries to approximate these numbers so that my times tables knowledge does come in handy. For example, 31 is close to 30, and this is why I'm saying it's a bit of an art. But I'm saying, hey look, this is pretty close to 30.

If I think about multiples of 30, well, those are just the multiples of three with an extra zero, or the multiples of 3 * 10. So the multiples of 30 are 30, 60, 90. Instead of 3 * 4 is 12, 30 * 4 is 120, 150, instead of 15, 180 instead of 18 for 30 * 6. And gee, this looks pretty close to 180, so this looks close to 30 * 6.

If this is close to 30, well, maybe, maybe this is going to be six right over here, and I'm going to put a question mark because then the natural thing to do is to actually try it out. Figure out what is 6 * 31? I'll put the question mark here again: Is this equal to six? Well, the art part is you've made a good—or we've made a good guess here. Now let's try to verify that maybe it is six, maybe it isn't.

So let's multiply 6, or let's multiply 31 * 6. 31 * 6: 1 * 6 is 6, and then 3 * 6, which is really 30 * 6, is going to be 180 right over here. So this is 186, so it all works out. 186 divided by 31 is indeed six. We can get rid of this question mark here.

Let's do another example. So let me delete, let me delete that as well. Let's say we want to figure out what 336 divided by 48 is equal to. So pause this video and see if you can figure it out.

So the way I would think about it, this thing right over here is close to 50—close to 50—and this thing, well, if you think about the multiples of 50, you have things like 300, which would be 50 * 6, and then you have 350, which would be 50 * 7 because 5 * 7 is 35.

So let's think about this and actually let me write those things down. If I were to say 50 * 6, that's the same thing as well. That's going to be 5 * 6 * 10, which is 300. If I say 50 * 7, that's going to be 350. 5 * 7 is 35, and then you multiply that by 10. But this number is someplace in between 300 and 350, so my candidates for what this is going to be—well, I'm saying, hey, maybe this is six, maybe this is seven.

What I would do is I would try out each of them. So let's try out 48 * 6. So let's try that, this first candidate out: 48 * 6. So 8 * 6 is going to be 48, and 4 * 6 is 24 + 4 is 288. So that actually seems a good bit lower than this. It actually seems almost exactly 48 lower, so I could probably—I'm feeling pretty confident that I can squeeze another 48 into this.

So I'm going to get instead of squeezing four— instead of being able to divide 6 48s into this, I'm feeling pretty good that maybe seven is the answer. But let me try it out. So this—so six is not going to be my answer; I tried it out. Let me try 48 * 7.

48 * 7: 8 * 7 is 56, 4 * 7 is 28 + 3, 336—that's exactly right. So there you have it. With a little bit of trial and error, but it was an informed trial and error, we got 336 divided by 48 is equal to 7. This is what I meant—that it's a bit of an art.