Multiplication as equal groups
- [Instructor] Our squirrel friend here likes to collect acorns, because, really, that's how he is able to live. And let's say everyday, he collects exactly three acorns. And so what I'm curious about is how many acorns will he have after doing this for five days? So one way to think about it is every day he is able to collect a group of three acorns. So you could view this as maybe what he's able to collect in day one. And then in day two, he's able to collect a second group of three acorns. In day three, he's able to collect another group of three acorns. And every day it's a equal number of acorns that he's collecting. On the fourth day, another three. On the fifth day, another three. And so if you were curious how many total acorns he's collected, well, you could just count them up, or you could think about, well, he's got five groups of three acorns. Five equal groups of three acorns. So you could say five groups of three acorns, three acorns. And so the total amount would be five, we could view this as five threes. Now, five threes, you could view this as five threes added together. Three plus three, plus three, plus three, plus three. And if you wanted to calculate this, you could skip count by three. So this would be three, six, nine, 12, 15, because we add three, we get to six, we add another three, we get to nine, we add another three, we get to 12, we add another three, we get to 15. And so this would be a way of recognizing that you have 15 acorns, but we're starting to touch on one of the most fundamental ideas in all of mathematics. In fact, we actually are applying it, we just haven't used the world, and that's, we are multiplying. We are using multiplication. All multiplication is is this notion of multiple equal groups of something. So, here, one way to express what we just did, is we just, when we said five threes, that's the same thing as five, and I'm going to introduce a new symbol to you, five times three. So all of these things are equivalent. You're already used to seeing equal groups and multiple equal groups, and you're used to adding something multiple times, and you're used to skip counting, and all of that is, in some way shape or form, you have been doing multiplication. So when someone says five times three, you could view that is five groups of three, or you could view that as five threes, or you could view that as three plus three, plus three, plus three, or you could view that as 15. I'll leave ya there. There's a lot of practice on Khan Academy to work through this and make sure you get the underlying idea. But as you'll see, this is perhaps one of the most useful concepts that you might learn in your entire lives.