today I was sitting outside, chilling out and just as that I started to multiply numbers always adding one: 1*1=1 2*2=4 3*3=9 and so on. And I wondered, how far can this go without paper or calculator?
Well I finished with 100*100 without leaving single number and after a while I started to use this kind of fast and intuitive technique which in this post will be used only to multiply two same numbers smaller than 100.
Lets say you need to multiply 47*47. (40+7)*(40+7)
Fourty will be called “base number”. The first thing you need to do is to multiply base numbers to get your base. This is simple because 40*40 is the same as 4*4 plus two zeros which means 1600.
Base is quite easy to remember so you do not need to concentrate on that much. Now we need to combine base numbers with, lets call them “pariah numbers”.
In our case pariah number is 7. You multiply it with base number to get 40*7=280 or simply 4*7=28 (+ zero from base number). Because we have two same brackets we need to multiply this twice and add it which is the same as multiplying your result by 2.
Now just add this “double number” to your base which should be quite easy:
Repeat this one few times and then add the product of two pariah numbers to get the result:
Try this few times, and if you are sure in this simple case try any two digit numbers. It is quite nice way to warm up your brain 😉