Topic A: Multiplication and the meaning of the factors
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- [Instructor] So as some of you already know, I really enjoy eating a good avocado, which, despite its appearance that it looks like a vegetable, but it's actually a fruit. And let's say that I eat two avocados per day, and I eat two avocados per day for six days. Now, there's a couple of ways that I could think about how many avocados did I eat? I could say, hey, I eat two a day, and I'm going to do that for six days, so I'm gonna add six twos together. So it'll be two, plus two, plus two, plus two, plus two, plus two, I have six twos right over there. And then I can add them together. And we could say two plus two is four. You add another two, you get to six. You add another two, you get to eight. Yet another two to get to 10. Yet another two, you get to 12. And that all is fine, but there's an easier way to express this repeated addition. One way is to view it as multiplication. Instead of just writing out six twos and adding them together, mathematicians have come up with a neater way of writing that. Let's say, okay, we're going to add up a bunch of twos. How many twos are we going to add up? We're going to have six of those twos, and we need to come up with some type of a symbol for it. So we will use this X-looking thing. And so, six times two can be viewed as repeated addition in exactly this same way. So six times two would be equal to 12. And we could go the other way around. If someone were to ask you, what is four times three? Pause this video and see if you can write it out as repeated addition, like we saw up here. Well, one way to interpret this is to say, this is four threes, so we could say this is equal to three, plus three, plus three, plus three. And three plus three is six, six plus three is nine, nine plus three is equal to 12. You might be familiar with skip counting, and you would say three, six, nine, 12. Just out of curiosity, what do you think three times four is going to be? Pause this video and try to represent it as repeated addition, and then see what you come up with. Well, we can interpret this as three fours. And so, we could say this is going to be four, plus four, plus four. And if we skip count fours, we'd have four, eight, 12, (chuckles) I was about to go to 16, four, eight, 12. So this is going to be 12. So this is interesting, at least for this example, for these two examples, I got to the same thing. Four times three got me the same result as three times four, interesting. I wonder if that's always true. But anyway, big picture from this video is that you can view multiplication as repeated addition.