Estimating when subtracting large numbers

Let’s say that you have a jar of jelly beans, and you know that there are exactly 282 jelly beans in that jar of jelly beans. Then, the next day you come, and you see there are fewer. You say, “What happened?” Let’s say someone who lives with you or your friend says, “Oh yeah, I counted exactly, and I ate 59 of those jelly beans.”

So, you started with 282, 59 are taken out, and you don't need to know exactly how many jelly beans are left, but you want to estimate roughly how many jelly beans are left. That's why, as the title of this video says, we're going to estimate when subtracting large numbers. We can debate how large is large, but these aren't reasonably large.

So, let's do that. Let's see if we can estimate what 282 minus 59 is. Sometimes when we're estimating, we will use this squiggly equal sign. This means approximately, which is just a fancy way of saying roughly what is this equal to.

The way that I would approach this is to say, “Hey, are these close to numbers that are easier to subtract with?” For example, 282. I would say, "You know what? Maybe I can round to the nearest 10 here." So, I could round it down to 280. If I round down to the nearest 10, if I round it up, it would go to 290. But 282 is closer to 280 than it is to 290, so I would round this when I'm estimating to 280.

And then what about 59? If I were to round to the nearest 10, what would I round that to? Pause the video and think about that. Well, 59, if I round down to the nearest 10, it would be 50, and if I round up to the nearest 10, it would be 60. Five-nine is definitely closer to 60, so I would say that this is roughly, if I'm rounding, I could say, “Hey, I'm going to round that to 60.”

So I could say that 282 minus 59 is roughly going to be 280 minus 60. And now what is this? You might be able to do this in your head. You could view this as 28 tens minus 6 tens. If you have 28 of something minus 6 of it, you're going to be left with 22 of that something. So you could say that this is going to be 22 tens.

Twenty-two tens or another way to think about it: you have two hundreds and then eight tens, and then you're going to take six tens away from it. So then you'll be left with two hundreds and two tens, just like we have here.

So the whole point here is this is not exactly what 282 minus 59 is, but if you just said, “Hey, ballpark, do I want to know if I have roughly how many jelly beans do I have?” Well, this could be useful. You'll see later in life this is actually a very, very useful skill where you might have these numbers that get a lot larger than this, but you'll round to the nearest 10 or you'll round to other places so that you can do that computation in your head.