Multiplying 2-digit by 1-digit

Let's try to calculate 3 times 32. And I like to rewrite it, and this is one way of doing it. I like to rewrite it where I have a larger number on top. So in this case it's 32. And I write the smaller number right below it. And since the smaller number is only one digit, it's only a ones digit, I put that below the ones place on the larger number. So I'll put the 3 right over here. And of course, we can't forget our multiplication symbol. And this is essentially a way of saying the same thing. You could read this as 32 times 3. But 32 times 3 is the exact same value as 3 times 32. It doesn't matter what order you multiply in. Now let's try to compute it. And once again, this is only one way of doing it. There's many ways of doing it. And I want you to think about why this works. We'll start with this 3 down here, and we're going to multiply it times each of the digits in 32. So we'll start with 3 times 2. Well, 3 times 2 from our multiplication tables, and you can figure it out even if you didn't know your multiplication tables, is 6. So 3 times 2, I'll write 6 right over here in the ones place. Now we're going to figure out what 3 times 3 is. Well, once again, we know that 3 times 3 is 9. And since I'm multiplying times the tens place right over here, I'm going to put it in the tens place right like this. So we're done. We got 32 times 3 is 96. And I really encourage you to think about why this worked. And I'll give you a little bit of a hint here. I'll give you a little bit of a hint about why this worked. Remember, 3 times 32 is the same thing as 3 times 30 plus 3 times 2. And if you look at it that way, that's essentially what this process did. We did 3 times 2 is 6. 3 times 30 is 90. You add them together, you get 90 plus 6 is 96.