Strategies for multiplying multiples of 10, 100 and 1000

Do in this video is think about multiplying our strategies for multiplying numbers that are expressed in terms of hundreds or thousands or tens. So we see an example right over here: we have 800 times 400.

Now, like always, I encourage you to pause this video and see if you can work this out on your own. Now let's work this through together, and I'm going to work it out in a way that at least my head likes to tackle it. Once you get enough practice, you might even be able to do these types of multiplication problems without even needing to use paper.

So the key realization here is to say, well look, this is eight hundreds. So that's the same thing as eight times one hundred. And this over here is four hundreds, so this is four times one hundred. And so it's eight times one hundred times four times one hundred. If you're multiplying a bunch of numbers like this, you can switch the order in which you're doing the multiplication.

So you can view this as 8 times 4 times 100 times 100. Now, why is this easier? Well, what is 8 times 4 going to be? Well, 8 times 4, if we know our times tables, is 32. So it's going to be 32 times what's a hundred times a hundred going to be?

Now, there's multiple ways that you could think about this, and I want you to really think it through. But we'll soon see that there's a fairly fast way of making sure we got it right. But one way to think about it is: well, let me do it over here. 10 times 100 is equal to a thousand. So a hundred times a hundred is going to be ten times that, or it's going to be equal to ten thousand.

So this stuff right over here is equal to 32 times 10,000. Now you might notice something interesting here: I have two zeros and then another two zeros, so I have a total of four zeros. And then I have four zeros here because every time you multiply by 10, you're going to add another zero. So if you're multiplying by 100, you're going to add two zeros. If you're multiplying by a thousand, you're going to add three zeros. And you see that here.

So you have 32 times 10,000, which is going to be... cut b? Well, let's see. 32 times a thousand would be 32,000, but this is 32 times 10,000. So it's going to be 320,000. Now, you might already notice an interesting pattern here: 32 times 1 followed by four zeros is 32 followed by four zeros. This is 32 ten thousands, which is three hundred and twenty thousand.

Now, another way you could have thought about it is eight times four gives us our thirty-two, and then we have two zeros there, two zeros there for a total of four zeros. We have our four zeros right over there. Now, I don't want you to just memorize that it works because this is eight hundreds times four hundreds. Eight times four gives us the 32, and then the 100 times the hundreds—that's where these four zeros come from.

Let's do another example. So let's do... let me delete this, and let us do... let me get my pen back. So let's do 30 times 70... or let's do 30 times 700. Pause the video and see if you can figure this out.

We can do it like we did before: 30 is 3 times 10, and 700 is 7 times 100. So if you say 3 times 7 is going to be 21 times 10 times 100, it's going to be a thousand. So what's 21 times a thousand? Well, that's going to be 21,000.

Now just like we saw before, once you get a hang of it, I always want you to understand where it's coming from: 3 times 7 is the 21, and then you're going to multiply that times 10 and then 100. So you have one, two, three zeros; one, two, three zeros.

Let's do one more of these. So let's say we wanted to multiply two thousand times eight thousand. Pause the video and see if you can figure out what this is. Maybe in your head, try to do this one in your head or on paper. Don't feel bad if you need to use paper; that's always prudent.

Well, you might get the hang of it now. You might be able to do this quite quickly. You might be able to say, "Hey, 2 times 8, well that's going to be equal to 16," and then I have three plus three zeros, so that's going to be six zeros: one, two, three, four, five, six, which gives me 16 million, and you would absolutely be correct.

Now, I want to reinforce what you're doing when you're just counting zeros like that. What you're doing is you're saying, "Hey, this is the same thing as two times one thousand times eight times one thousand." Eight times one thousand, and then you're just changing the order of multiplication.

You're saying, "Hey, let me multiply the two and the eight." You multiply the two times the eight, and you get sixteen. And then you multiply times a thousand times a thousand—so times a thousand, times a thousand.

And a thousand to thousands, that's one million; this is one million right over here. And notice—you see it there too—a thousand times a thousand, you have three zeros, three zeros; you get six zeros. A thousand thousands is a million; sixteen times a million is sixteen million.

So hopefully that helps and makes you a little bit more comfortable multiplying these numbers that are multiples of ten, hundred, thousands, even millions.