Introduction to multiplication

Our squirrel friend here likes to collect acorns because, really, that's how he is able to live. Let's say every day he collects exactly three acorns. So, what I'm curious about is how many acorns will he have after doing this for five days?

One way to think about it is every day he is able to collect a group of three acorns. You could view this as maybe what he's able to collect in day one. 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. Every day is the equal number of acorns that he's collecting. On the fourth day, another three; on the fifth day, another three.

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. 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. If you wanted to calculate this, you could skip count by three. So this would be 3, 6, 9, 12, 15, because we add 3, we get to 6, we add another 3, we get to 9, 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 word. 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. You're used to adding something multiple times, and you're used to skip counting. All of that is, in some way, shape, or form, you have been doing multiplication. So when someone says 5 times 3, you could view that as 5 groups of 3, or you could view that as five threes, or you could do that as three plus three plus three plus three, or you could view that as fifteen.

I'll leave you 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.