# Mental Maths Workbook - multiplication by 11 trick

### Class Room

Multiplication by 11 is simple - once you know the trick!

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Let us suppose that we had to multiply 42 and 11. Note, in this example, 42 is called the multiplicand and 11 is the multiplier.

Here is the trick.

Simply write down 4 and 2 and leave a space between them, like 4_2. Next, add the two digits of the multiplicand, that is 4 + 2 and write the sum (that is 6) into the space. That is, the final answer is 462. You can check that with your calculator. Wasn't that quick?

You would wonder, how does it work ?

Here is how you would do it using long multiplication:

If you look closely, in effect, what we did was to copy the first digit and the last digit down and added the two digits and wrote the number in the middle.

You might wonder, is it always this simple? Well, it works, but there is a slight twist. What if the adding the two digits generate a carry?

Consider multiplying 83 by 11. If we follow the steps given above, we would write down 8_3 and then write 8+3, i.e. 11 into the space. However, the correct answer is not 8113!

If adding the two digits of the multiplicand generates a carry, we add the carry to the first number we copied down. In this case, 8 + 3 = 11, so, we write the 1 as the middle number and add the carry to the first digit (i.e. 8) to arrive at the correct answer 913, as shown here:

You can apply the same prinicples to any number. For instance, to multiply a 3 digit number by 11:

That is,

• the result always begins and ends with the first and the last digit of the multiplicand.
• The middle digits are the sum of the consecitive digits. For instance, in the above example, we the middle digits are 6+2 and 2+1.