How to Multiply by 11 in One's Head

Most students learn multiplication tables from 1 through 10 by middle school, but then are forced to resort to using a pencil and paper or a calculator to multiply larger numbers. However, it's easy to multiply any two-digit number by 11 without using a pencil or calculator.

Instructions

Difficulty: Easy

1. Run quickly through the single digit numbers (1 through 9) multiplied by 11 in your head. Simply put that same number beside the first - 1 becomes 11, 2 becomes 22, 3 becomes 33 and so on.
2. Choose a two-digit number you want to multiply by 11.
3. Imagine that the number is the first and third digit of a 3-digit number, and you want to find the second digit. It may be easier to imagine that there is a hole in the middle of a 3-digit number and you want to find the number that goes in the hole. For instance, if you're multiplying 21 by 11, your number with a hole in the middle would be 2_1.
4. Add the first and third digit. The sum is the second digit (it goes in the hole)or the number in Step 3, it'd be a "3", which would make the three-digit number 231. If the sum is a 2-digit number, the second digit of the sum is the second digit (it goes in the hole) and then you increase the first digit by one.

Tips & Warnings

• Multiply several numbers by 11 on paper to prove to yourself that the above steps work.
• Some numbers can be multiplied by 11 without using these steps. For instance, you can multiply 12 by 11 by first multiplying 12 by 10 and then adding 12 to the result. (Notice that the steps provide the same answer.)