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Video:How to Multiply 3 Digit Numbers

with Zoya Popova

You can multiply 3-digit numbers with 2 different math methods. Learn the steps to multiplying 3-digit numbers with this helpful math lesson.See Transcript

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Transcript:How to Multiply 3 Digit Numbers

Hi, I'm Zoya Popova for About.com, and today I'm going to show you how to multiply 3-digit numbers.

Two Ways to Solve 3-Digit Multiplication Problems

There are actually 2 methods for multiplying 3-digit numbers. The first one is the traditional, universal method, and for that method, the first step is to multiply your top number by the number occupying the ones place of your bottom number.

So, to multiply 674x 132, you first have to multiply 674 by 2. And to do that, we'll be taking each of the numbers here in turn, from right to left, and we'll be multiplying them by 2. Starting with 4, 4x2=8.

Carry Over After Multiplying

Next, 7x2=14, and whenever your product is a 2-digit number, you only write down the last digit – in our case, 4. And the first digit, in our case, 1, is carried over to the next step, which is: 6x2=12.6 times 2 is 12, but we shouldn't forget the 1 that we carried over, so the result is not 12, it's actually 13.

The result of our first step is 1348.

Moving over to the next step, we will now multiply 674 by 3, and because 3 occupies the tens place in our bottom number, we will start off by writing a 0 here at the end of our product. Now, let's get on with our multiplication from right to left, just like in the previous step. The result is 20,220.

For our final step, we'll be multiplying our top number, 674, by 1, but because 1 occupies the hundreds place in our bottom number, we'll start by writing down 00 at the end of our product. The result of our third step is 67400.

The final result of our multiplication will be the sum of all these numbers, 1348+ 20220+ 67400------------ 88968.

Criss-Cross 3-Digit Multiplication Strategy

Now, there's another method for multiplying 3-digit numbers, and it's sort of a shortcut.

674x 132. Our first step is to multiply the 2 numbers on the right, 4 and 2.4x2=8, so we write 8 down as the extreme right number of our product.

Our second step is criss-cross multiplication of the numbers occupying the tens and ones places of 674 and 132,4x3+7x2=26. Their sum should be the second from the right digit of our product, but because 26 has two digits, just like in the method above, we only write down our second digit, 6, and we carry 2 over to our next step.

Our next step is three-way criss-cross multiplication: the left digit of the top number is multiplied by the right digit of the bottom number, plus the right digit of the top number is multiplied by the left digit of the bottom number, plus the middle digit of the top number is multiplied by the middle digit of the bottom number: 6x2+4x1+7x3=37. Plus the 2 we carried over, and the result is 39. We write down the 9 as the third from the right digit in our product, and we carry 3 over to the next step.

Continue to Criss-Cross Multiply the Digits

The next step is criss-cross multiplication of the numbers occupying the hundreds and the tens place of our top and bottom numbers: 6x3+7x1=25, plus the 3 we carried over. The result is 28, and we write down 8 as the next digit in our product, while carrying the 2 over to our next step.

The next, and final, step is multiplying the two numbers occupying the hundreds place in our top and bottom numbers: 6x1=6, plus the 2 we carried over. The result is 8, and that is the final digit in our product. As our digits line up, we get 88,968.

As you can see, we got the same result as in the previous method. And this is it for multiplying 3-digit numbers. Thank you for watching, and for more information, please visit us at About.com.

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