Introduction to dividing by 2-digits

- [Instructor] What we're going to do in this video is start trying to divide by two-digit numbers. And 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 'cause it's a bit of an art. So let's just start by trying to compute what 186 divided by 31 is. And 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. And if I think about multiples of 30, well, those are just the multiples of three with an extra zero or the multiples of three times 10. So the multiples of 30 are 30, 60, 90. Instead of three times four is 12, 30 times four is 120, 150 instead of 15, 180 instead of 18 for 30 times six, and gee, this looks pretty close to 180. So this looks close to 30 times six. And if this is close to 30, well, maybe, maybe this is, maybe this is going to be six right over here. And I'm gonna put a question mark because then the natural thing to do is to actually try it out. Figure out what is six times 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 six, or let's multiple 31 times six. 31 times six, one times six is six, and then three times six, which is really 30 times six, is gonna 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 times six. And then you have 350, which would be 50 times seven, because five times seven is 35. And so let's think about this, and actually let me write these things down. If I were to say 50 times six, that's the same thing as, well, that's gonna be five times six times 10, which is 300. If I say 50 times seven, that's going to be 350. Five times seven is 35, and then you're multiplying 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. And what I would do is I would try out each of them. So let's try out 48 times six. So let's try that, this first candidate out. 48 times six, so eight times six is going to be 48. Four times six is 24, plus four 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 instead of squeezing, instead of being able to divide 6/48 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 times seven. 48 times seven, eight times seven is 56, four times seven is 28, plus three, 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 seven. This is what I meant, that it's a bit of an art.