Missing numbers in addition and subtraction

- Let's say someone walks up to you on the street and says, "Quick! "73 plus blank is equal to 57." What would blank be? Well, there's a couple of ways to think about it. Blank is essentially what you have to add to 57 to get to 73. It's the difference between 57 and 73. And so you could think about it as, "Well, let me start with 57..." And this is actually how I would do it in my head. I would start with 57, and I would add numbers that get me to nice round numbers until I get to 73. So I'd start with 57, and I would say, "Let's see. I could get to 60 pretty easily by adding three." So that's going to get me to 60. And from 60 to 73, well, I can imagine I'm gonna add 13. That's easy for my brain to compute. Or I could say I'm gonna add 10 to get to 70. And then I could add another three. But my brain can say 60 plus 13. Yeah, that's gonna be 73. So now this whole thing is 73. So what did I add to 57 to actually bridge the gap? I added three plus 13. So I added 16. So 16 plus 57 is equal to 73. Now there's other ways that you could try to tackle it. You could say, "Look! This blank is the difference between 73 and 57." So you could write this as 73 minus 57 is equal to blank. And this would get you the same value. It would get you 16. And there's multiple ways to compute this. But this is the way that I would actually try to tackle this in my brain. Let's do a few more examples. This is strangely, strangely fun. So let's say that someone, another person walks up to you on the street and says, "Quick! "94 minus blank "is equal to 57." So this is saying, "What do I have to subtract from 94 "to get to 57?" Well, I could do it in the similar way, I'm subtracting this time, where I could keep subtracting numbers that make the math easy in my head until I get to 57. And this is actually how I would do it in my head. I would start at 94. And then I would subtract four to get to 90. So that's 90 right over there. And let's see. Then I could subtract 20 to get to 60. I don't want to get lower than 57. So I'm going to subtract 20, 90 minus 20. Oh, sorry, I could subtract 30 to get to 60. So I could subtract 30 now. So 90 minus 30, this is going to be equal to 60. And then to go from 60 to 57, pretty straightforward. I just have to subtract another three. 60 minus three, this is going to be 57. So how much did I subtract? I subtracted four, 30, and three. So let's see. I subtracted, this is 34, 37. I subtracted 37, just like that. Now another way you could have done it, you could have said, "Look! "37 is the difference between 94 and 57." So you could have thought about it. Well, if I start at 57, what do I have to add to get to 94? And you could have tackled it exactly the way that we did the last problem, where you could, here I'm gonna add three. If I add three, I get to 60; then if I add 30, I get to 90. And then if I add another four, I get to 94. So I added 37. Now there are clearly other ways to do this, especially if you have paper around. But this is actually how my brain would tackle it if someone walked up to me in the street and asked me to solve these problems. Now let's do one more. Let's do one more of these. Let's see where I have a clear space. So let's say that someone asks, "You have 36 is equal to blank "minus 41." So the way I think about this is, they're saying that 36 is the difference between blank and 41. Or another way to think about it is 36 plus 41 is going to be equal to blank. You could draw this on a number line. If these two statements being the same doesn't make full sense, you do a number line right over here. And then they're saying, "OK, "we're gonna start at some mystery number. "We're starting at some mystery number. "That's our blank. "We're gonna subtract 41. "We're subtracting 41, "and we're getting to 36." So this is the exact same thing as saying, "If we start at 36, and if we were to add 41, "we get back to our blank right over here." So what's 36 plus 41? Well, let's add our ones first. So we have six ones plus one one. That is seven ones. And then we have three tens plus four tens, which is seven tens, 77. So this is 77. And we're done.