Estimating with multiplication

In this video, we're going to get a little bit of practice estimating with multiplication. So over here, it says question mark is, and you have the squiggly equal sign. You could view that squiggly equal sign as being, "What is this roughly equal to?" It doesn't have to be exactly right.

So what is roughly equal to 58 times 6? Which of these choices would you pick? Pause the video and see if you can answer that.

So, once again, we don't have to get this exactly; we just need to estimate what 58 times 6 is. The way that I would tackle it is, "Hey, can I rewrite 58 as a number that’s easy to multiply by 6, or easy to multiply in general?" The easiest thing I can think of is 58 is awfully close to 60.

If you say that that is close to 60, if we're just estimating it, well, what would 60 times 6 be? Well, 60 times 6 is the same thing as—actually, let me just write it this way—you could do 60 times 6 as 6 times 10 times 6, which you could also view as 6 times 6 times 10.

And what's 6 times 6? That's 36. Then 36 times 10 is 360. So I would go with that choice right over there. Notice these other choices aren't even close to that, so we feel pretty good about our estimation.

Let's do another example. So here's where I asked, "What's three times 2890? What's that roughly equal to?" How would you estimate this? Pause the video and see if you can figure that out.

All right, so 2890 is not an easy thing to maybe multiply in our heads, but I can say, "Hey, that’s kind of close to three thousand." So I'm going to say that this is going to be approximately equal to—or roughly equal to—three times three thousand.

Now what's 3 times 3? That's 9, so 3 times 3,000? Well, it's going to be 9 thousands, and so it would be this choice right over there. Here, what I just did was a little bit confusing. You could view 3 times 3,000 as three times three times a thousand. This part right over there is three thousand.

Three times three is the 9, and you have nine thousands, nine thousand. Let’s do one more example. This is going to involve fairly large numbers. So what is, if you had to estimate 5,111 times 9, which of these would you pick? Pause the video and answer that.

All right, so I would view this—this is roughly—I would estimate it as five thousand times 9. So five thousand times 9, that’s the same thing as five times a thousand times 9, which is the same thing as five times 9 times a thousand.

Five times 9 is forty-five, so it's going to be forty-five thousands or forty-five thousand, which is this choice right over there.