Subtraction by breaking apart

- [Instructor] We're told that Linde isn't sure how to subtract 853. We are told Linde isn't sure how to subtract 853 minus 283. Help Linde 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 of the choices, they all start with 853. Now, this first choice, they subtract out 200. That makes sense 'cause we have 200s right over there. Then they subtract out 50 and then they subtract out three. So the 200 and the three make sense. You can view 853 minus 283 as 853 minus 200s minus 80, eight 10s right here, minus three. But that's not what they wrote in here. Instead of putting an 80 here, they put a 50, so we can rule that out. Here we have 853 minus 20 minus 800 minus three. Well, this is a little bit strange because we don't have two 10s, we have 200s, and we don't have 800s, we have eight 10s, 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 they're subtracting out 30. Well, that is the same thing as subtracting out 83 'cause 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? What'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 the 60 10s minus three 10s, this is gonna be 57 10s or you might be able to do it in your head, 600 minus 30 is 570. So that's why they broke out, they broke up the 83. Instead of just breaking it up into 80 and three, 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 one is 144. If we add one to both of these numbers, the difference would be the same. And we're done. So, it's 144 minus 80.