Subtraction by breaking apart

We're told that Lindy isn't sure how to subtract 853. We are told Lindy isn't sure how to subtract 853 minus 283. Help Lindy by choosing an expression that is the same as 853 minus 283. So pause this video and see if you can answer it on your own before we work through it together.

All right, now when we look at all the choices, they all start with 853. Now this first choice, they subtract out 200. That makes sense because we have 200s right over there. Then they subtract out 50 and then they subtract out 3. So the 200 and the 3 make sense. You can view 853 minus 283 as 853 minus two hundreds minus 80, 8 tens right here minus 3. But that's not what they wrote over here. Instead of putting an 80 here, they put a 50. So we can rule that out.

Here we have 253 minus 20 minus 800 minus 3. Well, this is a little bit strange because we don't have two tens; we have two hundreds. And we don't have eight hundreds; we have eight tens. So this is also incorrect. Now it's probably going to be this one, but let's just make sure we feel comfortable with this.

So this one has 853 minus 200 minus 50 minus 30. Does that make sense? Well, let's think about it. What they're doing is that they're subtracting out first the 200, so that's this part right over here. So that makes sense; they're subtracting out first that, and then they're subtracting out 53 and then subtracting out 30. Well, that is the same thing as subtracting out 83 because subtracting 83 is the same thing as subtracting out 53 and then subtracting 30. 53 plus 30 is 83.

Now you might be wondering, why would they even do it this way? Well, it's easier to do in your head. 853 minus 200 is 653. You take away 53 from that, so you take away 53 from that and you're going to be left with 600. And then 600 minus 30, you might recognize that you could use this as 60 tens minus three tens. That's going to be 57 tens, or you might be able to do it in your head: 600 minus 30 is 570.

So that's why they broke up the 83. Instead of just breaking it up into 80 and 3, they broke it up into 53 and 30 to match this 53 over here, and so it was easier to work out the result.

Let's do another example. So here we're asked to fill in the blank. They say 143 minus 79 is the same as blank minus 80. So pause this video and see if you can figure this out.

So the key here is to realize is that when you have a difference, here, as long as you add or subtract the same amount to both of these, the difference will be the same. So it looks like they tried to turn the 79 into, it looks like they turned the 79 into an 80 by adding one. And so if we want the difference to be the same, we would add one to the 143 as well. So 143 plus 1 is 144. If we add 1 to both of these numbers, the difference would be the same, and we're done. So it's 144 minus 80.