Secrets of the Mathematical Ninja: multiplying numbers that are close together
This is a fairly specific trick, but it comes up often enough that you can dazzle people once in a while by multiplying numbers that are close together. You need to know how to square numbers (check back to this series of posts).
Here’s the trick: say you need to work out
The reason it works is called the ‘difference of two squares’ – to multiply the numbers, what I did was find the number midway between them (60) and square it (3600); then find the difference from the midway number to either of the originals (3) and square it (9); and simply take them away (3591).
That always works. Obviously, though, some numbers are easier to square than others: to do
Why does multiplying like this work?
Well, my little chickadee, I’m afraid that needs a little bit of algebra. What I worked out at the top there was actually
It works just the same way with anything you pick: let the middle number be
Footnotes:
1. Some people use a table, some FOIL, some a smiley face – there are several methods that do the same thing