## Tuesday, 5 August 2008

### Mental Multiplication of 2 close-by Numbers

There is another set of special numbers that can be esaily handled by the mental mind. They are the "close-by" numbers.

What is meant by "close-by" numbers?

Example: 22 and 25, 34 and 38, numbers that differs by a few ones away.

Mental multiplication of these number can be performed with a special technique.

The "trick" is to use the Special product in quadratic equation,

(a + b) ( a - b) = a2 - b2.

How to get the "a" of above and also the "b"?

Let's take an example.

Example: 23 x 27

a is the average of 23 and 27, that is, (23 + 27) / 2 = 25
b is the difference from a to the 2 numbers to be multiplied (27 - 23 ) / 2 = 2

Thus 23 x 27 can be modified to (25 - 2)(25 + 2) which is easier to mentally manage.

(25 - 2)(25 + 2) = 252 - 22 = 25(20 + 5) - 4 = 625 - 4 = 621.

The conversion from multiplication of 2 different numbers (23, 27) to squaring a number (25) is the catch to handling the multiplication mentally easier.

Therefore, as long as you know the trick to manipulate numbers with simple algebra, you can do mental maths with ease.

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