How to Multiply by 11
Question
If you multiply a single-digit number by 11, the result will be the same number
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Hi, I'm Zoya Popova for About.com, and today I'm going to show you how to multiply by 11. When we multiply by 11, we can see some interesting patterns.For instance, if you multiply a single-digit number by 11, we can always say that the result will be the same number written down twice: 9x11=99.When we multiply 2-digit numbers by 11, the pattern is a little bit more complex, but still pretty easy to understand.Take the example of 54x11. Let's write down our numbers one under the other: 54x 11. If you're familiar with the criss-cross method of multiplication of 2-digit numbers, you know that it takes three steps.Our first step is to multiply the numbers occupying the ones places of our top and bottom numbers, and write the result down as the ones digit of our product:4x1=4.Our next step is criss-cross multiplication of the numbers occupying the ones and the tens place of our top and bottom numbers:5x1+4x1=9,and this is be the tens digit in our product.And our final step is the multiplication of the numbers occupying the tens places in our top and bottom number: 5x1=5,and this is the hundreds digit in our product.And the pattern that you see here is that in our product, the left and the right digits, 5 and 4, are the same as in our top factor, 54. And the middle number is the sum of 5 and 4.To multiply 31 by 11, take the first and the last digit of 31 and write them down, leaving a small gap between them. In that gap we will insert the sum of those two numbers: 3+1=4.So 31x11=341.To multiply 75 by 11, we write down the first and the last digits, 7 and 5, and then we realize that the sum of these two numbers is 12, a 2-digit number. So we write down the 2 as our middle digit, and the 1 is carried over to the preceding digit, 7. As a result of carrying over, 7 must be increased to 8, so 75x11=825.Similar patterns also work when multiplying 3-digit numbers by 11. To multiply 231 by 11, first, write down the extreme left and extreme right digits of 231, 2 and 1. Now, in between those digits, there will be sandwiched not one, but two digits. The digit occupying the tens place of our product will be the sum of the numbers occupying the last two positions of 231:3+1=4.TThe digit occupying the hundreds place of our product will be the sum of the numbers occupying the hundreds and the tens places of 231:2+3=5.So, the product of 231x11 is 2541.When multiplying 3-digit numbers by 11, you will also sometimes need to carry digits over. In the example of 738x11, we start by writing down 7 and 8 as our two extreme digits. Now, the number occupying the tens place of our product should be the sum of 3 and 8:3+8=11. Because 11 is a 2-digit number, we write down its last digit, 1, as the tens digit of our product, but we carry the other 1 over to our preceding digit.The hundreds digit of our product should be 7+3=10, plus the 1 we carried over. We have another 11. We write down 1 as the hundreds digit in our product, and we carry the other 1 over to the preceding digit, 7. When 7 is increased by 1 due to the 1 we carried over, our final answer is:738x11=8118.And this is how you multiply by 11. Thank you for watching, and for more information, please visit us at About.com.