Multiplying 1-digit numbers by multiples of 10, 100, and 1000 | Math | 4th grade | Khan Academy

Let's multiply 4 times 80.

So we can look at this a few ways. One way is to say 4 times we have the number 80. So we have the number 80 one time, two times, three times, four times. Four times we have the number eighty, and we could do this computation, add all of these, and get our solution.

But let's look at it another way. Let's try to stick with multiplication, and one way we can do that is to break up this 80. We know a pattern for multiplying by 10, so let's try to break up this 80 to get a 10. If we have 4 times and instead of 80, let's say 8 times 10, because 80 and 8 times 10 are equal; those are equivalent.

So we can replace our 80 with 8 times 10. Then we have this times 10 back here, which is super helpful because there's a nice, neat pattern in math that we can use to help us with the times 10 part.

So let's start to solve this. 4 times 8 is 32, and then we still have 32 times 10. We can use our pattern for multiplying by 10, which is that anytime we multiply a whole number times 10, we take that whole number—in this case, 32—and we add a zero to the end. So 32 times 10 is 320.

There's a reason that pattern works; we went into it in another video, but here just real quickly. 32 times 10 is 32 tens.

We can do a few examples. If we had, say, three times ten, that would be three tens or ten plus another ten plus another ten, which equals thirty—our whole number with a zero on the end. If we had something like 12 times 10, well, that would be 12 tens, and if we listed out 10, 12 times, and counted them up, there would be a hundred twenty.

It would add up to a hundred twenty, which again is our whole number with a zero on the end—our 12 with a zero on the end. So we can use that pattern here to see that 32 times 10 is 32 with a zero on the end.

Let's try another one. Let's do something like—let's say 300. This time we'll do hundreds instead of tens— times six. Well, 300 we can break up like we did with 80 in the last one, and we can say that 300 is 100 three times, or a hundred times three.

Then we still have our times six after that. So these two expressions, 1) 300 times 6 and 2) 100 times 3 times 6, are equivalent because we've replaced our 300 with a 100. From here we can multiply, and let's start with our one-digit numbers—let's multiply those first. 3 times 6 is 18, and then we still have 18 times 100, or 18 hundreds.

So we can write that as 18, and then to show hundreds, we'll put two zeros on the end, or eighteen hundred. Just like up here, just like we saw that 300 is equal to three times a hundred, or our three with two zeros on the end. Well, same thing here: eighteen times a hundred is eighteen with two zeros on the end, or eighteen hundreds.

So three hundred times six equals eighteen hundred. Let's try another one, but this time let's go even to another place value and try thousands—something like seven times seven thousand.

So, like in the previous ones, we're going to break up our thousands. Seven thousand is the same as seven times one thousand—one thousand seven times—and we still have our times seven in the front here to bring down. And again we can multiply our single digits first—our one-digit numbers.

Seven times seven is 49, and then 49 times a thousand is going to be 49,000, which we can write as 49. And this time, maybe the pattern's becoming clear; we're going to have three zeros on the end. So it'll be a 49 with three zeros, or 49,000.

Just like up here, seven times a thousand was a seven with three zeros; 49 times a thousand is a 49 with three zeros, or 49,000.

Let's look at this as a pattern. If we show this as a pattern, let's do something like 9 times 50, and then in another one, let's do 9 times 500, and one last one we can do is nine times five thousand.

I encourage you to pause here and see if you can work these out. See if you can come up with solutions for these three expressions.

Now we can work them out together. 9 times 50 will be the same as 9 times 5 times 10, because we broke up our 50 into a 5 times 10. Then if we multiply across, 9 times 5 is 45, and to the end, we're going to add 1 zero. The pattern for times ten is to add one zero.

We can keep going here; nine times five hundred will be nine, and then times five times one hundred. Five hundred is five hundreds, just like 50 was five tens.

Multiplying across, 9 times 5 still equals 45, but this time we will add two zeros to the end, or forty-five hundred. And finally, nine times five thousand will be nine times five times one thousand, because five thousand is five thousands, or a thousand five times.

Working across, 9 times 5 equals 45, and this time we add three zeros, so 45,000.

So, when we multiply each of these expressions, we can see the only thing that changed was the number of zeros on the end.

So the pattern—anytime we multiply a whole number times 10, we add 1 zero to the end of our number. Anytime we multiply a whole number times 100, we'll have two zeros, and times a thousand, we'll have three zeros.

Once we know that pattern, we can use it to help us with questions like this, where initially we don't see a 10, a 100, or a thousand, but we can get one. We can break up or decompose these numbers to get a 10, or 100, or thousand to help us solve the problem.