Estimating quotients

We are told to use estimation to tell whether each estimated quotient is reasonable or unreasonable. So we have a bunch of estimated quotients here. Someone is estimating that 2419 divided by 3 is roughly equal to 7500. We have to figure out is that reasonable or unreasonable.

Then we have two more quotients to figure out if they're unreasonable or reasonable. So pause this video and see if you can figure it out on your own before we work through it together.

All right, now let's work through it together. The way that I'd like to tackle this is just to try to do the estimation myself. So I'll start with this first one: 2419 divided by 3. Well, one way to estimate is to try to think about what numbers these are close to that are a little bit easier to compute with, or some people would say they're a little bit friendlier, so to speak.

Well, three is already a pretty simple number, a pretty friendly number. 2419, well, it's a little bit more complicated, but I could try to think of—is there a multiple of three that's close to 2419 that is a fairly friendly number? Well, I do know that 3 times 8 is 24. So if I had something like 2400, which is the same thing as 2400, that'd be easy to divide by 3.

So I could say that this is roughly equal to 2400 divided by 3. All I did is I said, "Hey, 2419, for estimation purposes, let's just say it's roughly equal to 2400." Then 2400 is fairly straightforward to divide by 3. This over here, 24 divided by 3 is 8. So 2400 divided by 3 is 800. So this is going to be 800.

Therefore, 2419 divided by 3 should be roughly around 800. Now they're saying that it's roughly 7500. That's a lot more than 800. If they said 750, then I'd say, "Hey, that's pretty reasonable." But they're saying 7500; that's almost 10 times more than 800, so this I would say is unreasonable.

All right, now let's think about this next one, and again pause the video and see if you can have a go at it.

All right, so I'm just going to try to estimate again. So 435 divided by 5, let's say that's roughly equal to—an easy multiple of 5 that's close to 435. If I want to think of a friendly number, it might be 400. So I'll say that's roughly equal to 400 divided by 5.

Now we know that 40 divided by 5 is 8. So for 40 tens divided by 5 is 8 tens. So this is going to be equal to 80. And you could think about it the other way; five times eight tens is going to be 40 tens, which is the same thing as 400. So this thing should be roughly equal to 80.

Well, that's exactly what we estimated, so that feels very reasonable.

All right, this last one, so pause the video again and see if you can have a go at that.

All right, so we have 6202, and they're saying divided by 2. Now we could say that's approximately equal to—or roughly equal to. Well, if I just want to do it very roughly, I could say, "Hey, 6202, let's just go to 6000 just to make things really easy," divided by 2.

So this is going to be six thousands divided by two, which would be three thousands or three thousand. But here they have 300; that's one-tenth of what I have over here, so this is unreasonable. And we're done.