Example multiplying multi digit numbers

In this video, we're going to try to compute 6742 times 23.

So like always, pause this video and try to compute it for yourself.

All right, now let's work on this together, and I'm going to do it using what's often known as the standard algorithm. Algorithm's just a fancy word for a series of steps, a process for doing something.

So we have 6742 times 23, and so I'm going to write the 23 in the same place values. So that's 20 and 3. I'm going to write it under the four tens over there, and then three ones I'll write it under the two ones.

It's important to realize this isn't the only way to multiply numbers. In fact, we've studied other methods for doing it in other videos, and it's important to realize what's really going on and how these different methods are all, on some level, doing the same thing—maybe just writing them different or doing them in different orders.

So the way that we would tackle it using the standard algorithm, probably the way that your parents first learned to multiply multi-digit numbers like this, is we'll take all of the numbers in 6742, all the various places, and multiply it by three. Then we're going to multiply it times two tens, and then we're going to add everything up.

So let's first multiply it times three. So we have two times three; that is six. Then we have four times three, and what people often say is four times three is twelve—write the two and then carry the one. But what really just happened is you said four tens times three is twelve tens. Twelve tens can be written as two tens plus one hundred.

Then we say seven times three is twenty-one, and then you'll say, "Oh, I have to add that other one," so I get 22. But once again, what just happened? We said seven hundreds times three is twenty-one hundred plus another hundred is twenty-two hundreds, which can be expressed as two hundreds and two thousands.

And then last but not least, six times three is eighteen plus two is twenty. But remember we're talking about thousands, so this is twenty thousands.

So then we will move on to the two tens right over here. So two times two tens is four tens. Now some folks might be tempted to put the four over there, but that's not four tens. Four tens would be right over here, and so it's common practice as you move to the next place value over, as you get to this 2, that people will just put a 0 here just so they don't make that mistake.

All right, now let's keep going. What is four times two? Well, that's 8. We'll just write the 8 right over there. Why did that work? Well, we're having four tens times two tens. Well, that's going to be 8 times 10 times 10, which equals 800.

And then we say, what is seven times two? That is 14, which of course we can write the 4 and then we can carry the 1, so to speak, and I'll cross these out so I don't get confused. And then six times two is going to be equal to 12 plus this one that we had carried is 13.

So there we go, and then we just have to add everything up.

We're going to get six plus zero ones is six. Two tens plus four tens is six tens. Two hundreds plus eight hundreds is ten hundreds, which you could use zero hundreds and one thousand.

One thousand plus zero thousands plus four thousands is five thousands. Two ten thousands plus three ten thousands is going to be five ten thousands, and then we just have one hundred thousand right over there.

So we've got a hundred fifty-five thousand and six, and we are done.