Basic addition and subtraction
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Welcome to the video on basic subtraction. Let's do a little bit a review of basic addition first. If I said 4 plus 3, what did this mean? What did that equal? Well, there were a couple of ways we could have viewed this. We could have said I had 4 of something. Let's say I had 4 circles or I don't know, I had 4 lemons for breakfast. So 1, 2, 3, 4 lemons for breakfast. And let's say, I had another 3 lemons for lunch. 1, 2, 3, and so you could view 4 plus 3 as how many total lemons did I have? I'm adding 3 to 4. So how many total did I have? Well, it's 1, 2, 3, 4, 5, 6, 7. So I had a total of 7 lemons. Another way we could have viewed that is we could have drawn our number line. And I'll draw it in yellow because-- now that's not wide enough. I'll draw it in yellow because we're talking about lemons. So let's say that's our number line. And if I start at the number-- let me draw all of the numbers. 0, 1, 2, 3, 4, 5, 6, 7. So you could think about this as saying, well, we're on the number line. We start at the number 4. That's this number 4. And we're adding 3 to it. So we'll increase, along the number line by 3. So we'll go 1, 2, 3 and you end up at 7. So you could say if I have 4 and I get 3 more, I get 7. Or if I increase 4 by 3 I also get 7. So what's subtraction now? Because that's what this video is about. I shouldn't waste all of our time talking about addition. So let's take the example of 4 minus 3. What is that equal to? Let me switch colors just to keep things interesting. So what is 4 minus 3 equal to? Subtraction or minus is the opposite of addition. So in addition you're doing something more, you're adding. I don't want to use the word adding to define addition, but that's what you're doing. I had 4 lemons and then I had 3 more. In subtraction you're taking away. So this example, if I started with 4 lemons, let's say I had 4 lemons on a plate. If I'm subtracting 3, if I'm saying minus 3, instead of adding these 3 and getting 7, I'm going to take 3 away. So maybe I'm eating them or maybe I'm giving them to you in exchange for watching these videos. So to take away 3 from this 4, let's say this one goes away, this one goes away, and this one goes away. How many lemons would we have left? Well, this is the only one that I haven't crossed out. So we would have 1 lemon left. And this would be the lemon that's left. Didn't have to be that one, I could have crossed out any of the 3. Another way to view that, let's draw the same lemon colored number line. Let's say that this is the number line right here. And I'll draw all the same numbers. So that's 0, 1, 2, 3, 4, 5, 6, 7. Of course, the number line keeps going. There's no largest number. And you can imagine, any number that you can think of, I can think of one higher than that. So there is no largest number. So that's why we draw that arrow there. I could never draw the entire number line. But anyway, back to subtraction. So we're starting at 4 lemons, right? When we added 3-- plus 3-- we went to the right 4 spaces on the number line. And that's because the right is increasing value. So we went from 4 to 5. That was one more. 5 to 6 was two more, and 7 was 3 more. Now we're taking away from 4. So what do we do? What would you think we do? Well, since we're taking away we're going to decrease the total number of lemons we have. So we take away one, we get to 3. Take away two, get to 2. Take away three, we took away three, right? So we'll go back 1, 2, 3 along the number line and we'll end up at 1. And that's this 1 right here. So just to review, addition is you're doing more or something. Subtraction is you are taking away. If you think about it on the number line, addition is increasing along the number line by that amount. So in this case we increased along the number line by 3. And so we went from 4 to 7. In the subtraction case we decrease back on the number line. So we decrease by the amount that you're subtracting. So in this case we decreased by 3. We went back 1, 2, 3 and we had 1. And the other way to view it, if I have 4 of something. If I give 3 away or if I ate 3 of them or I don't know what I did to 3 of them. If I lost 3 of them I would have 1 left. Now let me show you some interesting things about subtraction. So we know that 4 minus 3 is equal to 1. Let me show you something else that's interesting. What is 4 minus 1? Well, we could use either example. Let's do the lemon example. Let's do apples now; I'm bored of the lemons. Let's say I 1, 2, 3, 4. I have a new pen, sometimes it doesn't draw right. Let's say I had 4 apples. This is the example we're dealing with. And I were to eat one of them. So one of them were to go away. How many apples would I have left? Well, 3-- 1, 2, 3. So 4 minus 1 is equal to 3. And if we did it on the number line, if we started at 4 and we subtracted 1-- we took 1 away. So we're going to become one smaller. We go back one, we get 3. Either way works. But isn't this interesting? 4 minus 3 is equal to 1 and 4 minus 1 is equal to 3. You might say, well, did I pick the numbers just so it worked? Well, it turns out that it's always true. Well, I don't want to get too technical, but we're already touching on something that you'll learn later, maybe in algebra one day. But actually I don't want to go into all that right now. So where does this come from? Well, this is also based on the fact that 3 plus 1-- I didn't want to confuse you. So I apologize if I did. But I'll show you another interesting thing. What is 3 plus 1? 3 plus 1 is equal to what? Well, that's easy. You know that from basic addition. You can start on the number line at 3 and add 1 do it. And where do you end up? You end up at 4. 3 plus 1 is equal to 4. Or you could have started at 1 on the number line and added 3. 1, 2, 3 and you would have also ended up at 4. So we also know that you could have switch this either way. Both of those are equal 4. What do you see here? Well, there's a bunch of things I've written here and they all kind of relate to each other. 1 plus 3 is equal to 4. 3 plus 1 is equal to 4. 4 minus 1 is 3. Essentially, 4 minus 1 and getting 3 is the exact same-- you're saying the same thing as 3 plus 1 is equal to 4. This statement says if I add 1 to 3 I get 4. This is saying if I take away 1 from 4 I get 3. So if I start at 4, move back, I get 3. This is saying if I start at 3, and I move up 1, I get 4. Hopefully that gives you a little bit of intuition about what subtraction is. In the next video I'll just do as many basic subtraction problems I can do in 10 minutes. And then you'll be ready to do the exercises. See you soon.