Maths with Fun

The Miracle of 11

Here’s an easy way to multiply any two digit number by 11, provided the sum of the digits in less than 10.

Let’s say you wish to multiply 45 by 11. What you need to do is add 4 and 5. Your answer is 9. Now put 9 between 4 and 5 and you get 495, which is 45 x 11.

What should you do if the sum of the digits of the number you want to multiply with 11 is 10 or greater than 10? Simple.

Let’s say your number is 58.

5 + 8 = 13.

Now place the 3 of 13 between 5 and 8 and add 1 to 5. Thus, 58 x 11 = 638.

Follow this method to multiply any large number by 11. Let’s say you want to multiply 123454321 by 11.

Place the two ones of 11 at either ends of your answer. Then starting from the right, add each number with the number on its left. Example, add 1 to 2. Place the answer 3 as the second digit from the right (the first is 1). Then add 2 to 3 and place your answer 5 as the third digit. The fourth digit will be 3+4 =7, the fifth 4+5=9, the sixth 5+4=9, the seventh 4+3=7, the eighth 3+2=5 and the ninth will be 2+1=3.

Thus 123454321 x 11 = 1357997531.

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