Thursday, 24 July 2008

Trick on Multiplying "Y" by 11

Although multiplication can be tedious at times, understanding some basic principles can actually hasten the process.

This is so when numbers are multiplied by eleven.

For x 11, the process revolves round the fact that "any number" x 1 = "the same number".

Let me explain.

Y x 11 = Y x (10 + 1) = 10Y + Y.

Example:
25 x 11 = 25 x (10 + 1) = 250 + 25 = 275

Now, look carefully!

The final multiplied result of 275 has its digit "2" taken from the 10-th digit of the original "25", and the digit 5 of the multiplied (product) result is taken from the 1-th digit of the original 25.

What then is in the centre digit of the multiplied result (275)?
It is the maths addition of the 2 end digits of the original 25 , which is "2 + 5" = 7!

Got the picture?

This is due to the fact that the "x10" shifts the 25 left by one digit. Thus retaining the number 2 on its leftmost digit at the multiplied end product.

To summarise:
Multiplying 25 x 11 = a three digit number. This three digit number is obtained by inserting into the centre of the final product result, the addition of the two numbers 2 and 5 (the original 25). OK?

New Example:
3
2 x 11 ==> 3, (3 + 2), 2 ==> 352 (answer).

Maths is fun and interesting if you understand the underlining tricks !