About this video
Starting with apples, the video shows that adding or subtracting the same kind of thing is just counting. Writing apples as the letter a gives 4a + 2a = 6a, and the same thinking with a variable gives 5x - 2x = 3x.
You'll be able to
- combine terms with the same variable by adding or subtracting the numbers in front.
- explain 4a + 2a = 6a by writing it as a + a + a + a + a + a.
- simplify subtraction of like terms, such as 5x - 2x.
Key words
- variable
- A letter, like a or x, that stands for something or some number.
- like terms
- Terms with the same letter, like 4a and 2a, which can be combined.
Transcript
Let's say that you started off with 3 apples. And then I were to give you another 7, another 7 apples. So my question to you-- and this might be very obvious-- is how many apples do you now have? And I'll give you a second to think about that. Well, this is fairly basic.
You had 3 apples. Now, I'm going to give you 7 more. You now have 3 plus 7. You now have 10 apples. But let's say I want to do the same type of thinking, but I'm too lazy to write the word "apples." Let's say instead of writing the word "apples," I just use the letter a.
And let's say this is, say, a different scenario. You start off with 4 apples. And to that, I add another 2 apples. How many apples do you now have? Instead of writing apples, I'm just going to write a's here. So how many of these a's do you now have? And once again, I'll give you a few seconds to think about that.
This also might be a little bit of common sense for you. If you had 4 of these apples or whatever these a's represented, if you had 4 of them and then you add 2 more of them, you're now going to have 6 of these apples. But once again, we started off assuming that a's represent apples.
But they could have represented anything. If you have 4 of whatever a represents, and then you have another 2 of whatever a represents, you'll now have 6 of whatever a represents. Or if you just think of it if I have 4 a's, and then I add another 2 a's, I'm going to have 6 a's.
You can literally think of 4 a's as a plus a plus a plus a. And if to that, I add another 2 a's-- so plus a plus a, that's 2 a's right over there-- how many a's do I now have? Well, that's 1, 2, 3, 4, 5, 6. I now have 6 a's. So thinking of it that way, let's get a little bit more abstract.
Let's say that I have 5 x's, whatever x represents. x could be some number. So I have 5 of whatever that number is. And from that, I subtract 2 of whatever that number is. What would this evaluate to? How many of these x's would I now have? So it's essentially 5x minus 2x is going to be what times x?
Once again, I'll give you a few seconds to think about it. Well, if I have 5 of something and I subtract 2 of those away, I'm going to have 3 of that something left. So this is going to be equal to 3x. 5x minus 2x is equal to 3x. And if you really think about what that means, five x's are just x plus x plus x plus x plus x.
And then we're going to take away two of those x's. So take away one x, take away two x's. You are going to be left with three x's.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.