# Is there a easier more efficient approach for the human brain to perform elementary mathematical computations (+-×÷) that differs from what is traditionally taught in school?

##### 1 Answer

It depends...

#### Explanation:

There are various tricks and techniques to make it easier to perform mental arithmetic, but many involve memorising more things first.

For example,

#17*19 = (18-1)(18+1) = 18^2-1^2 = 324 - 1 = 323#

So rather than memorise the whole "times table" you can memorise the 'diagonal' and use a little addition and subtraction instead.

You might use the formula:

#ab = ((a+b)/2)^2 - ((a-b)/2)^2#

This tends to work best if

For subtraction, you can use addition with

Other methods for multiplying numbers could use powers of

At a more advanced level, the standard Newton Raphson method for finding the square root of a number

#a_(i+1) = (a_i^2+n)/2#

This is all very well if you are using a four function calculator, but I prefer to work with rational approximations by separating the numerator and denominator of

#p_(i+1) = p_i^2+n q_i^2#

#q_(i+1) = 2 p_i q_i#

If the resulting numerator/denominator pair has a common factor, then divide both by that before the next iteration.

This allows me to work with integers instead of fractions. Once I think I have enough significant figures I then long divide