Approximating multi digit division

What we want to do in this video is get some practice estimating multi-digit division problems. So here we're asked to estimate 794 divided by 18. Now, if you wanted to get the exact answer, you'd probably have to do—in fact, you would have to do—some long division or maybe use a calculator. But the whole point here is to get some practice estimating. So pause this video and try to see if you can figure this out without even using any pencil or paper.

All right, so now let's do this together. So I'll tell you what my brain does. My brain says that look, 794 is awfully close to 800, and then 18 is close to 20. And so I would say this is going to be roughly the same thing as 800; it's going to be roughly equal to 800 divided by 20. It's going to be exactly equal? No, but these are the numbers closest to the numbers there that it's easy for me to divide in my head.

So for example, I could—I would then say if I was just doing this purely in my head, I would say, well, 100 divided by 20 is 5. So 800 divided by 20 is equal to 40. Or another way to think about it: 800 over 20, if we divide the numerator and denominator by 10, it's the same thing as 80 over 2, which is equal to 40. So 794 divided by 18 definitely isn't exactly 40, but it's going to be close to 40.

And especially of these choices right over here, it's definitely going to be much closer to 40 than 84 or definitely 400. So we're gonna go with that. Let's give—get another example here, make sure we get enough practice.

So once again, we are asked to estimate 722 divided by 68. And so why don't you have a go at it? Pause the video and try to see if you can figure out what it is and try to do it in your head. Well, what I would do in my head, I would say, well look, 722, this is awfully close to 700, and 68 is awfully close to 70.

And then this is quite straightforward to do in your head. 700 divided by 70 is going to be equal to 10. And good for us, there is a choice here that is awfully close to what we approximated. Now, if you don't find your exact answer here, that's okay, because remember it's an approximation. You should find the answer that is closest to what you estimated.

But whoever wrote this question had a very similar thought process. They said, okay, 722 pretty close to 700, and 68 pretty close to 70, and so it's going to be approximately equal to 700 divided by 70.