# How can you multiply quickly in your head?

##### 1 Answer

A few ideas...

#### Explanation:

There are many ways to compute exact or approximate products. I find myself using different methods in different combinations according to what numbers are involved.

I am not a competitive mental arithmetic practitioner, so here are just a few simple ideas:

**Product as a difference of squares**

Note that:

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

This is easiest when

For example:

#33 * 37 = 35^2 - 2^2 = 1225 - 4 = 1221#

So you find the average of the two numbers, square it and subtract the square of half the difference.

This method really relies on having memorised square numbers. It's as if you only need to remember the diagonal of the times table.

**Powers of #2#**

If you have memorised some powers of two, then multiplying or dividing by them is as easy as doubling a few times or halving a few times.

For example to multiply by

To multiply by

**Percentage tweaks for approximations**

If one of the factors is inconvenient, but close to an easier number, then calculate the product using the easier number, then tweak by a percentage.

For example, to multiply by

**Fibonacci factors**

If you are wanting to convert quickly and roughly between miles and kilometres, then Fibonacci numbers can help.

The Fibonacci sequence starts:

#0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89#

The ratio between successive terms tends towards

So for a quick approximation note that