Multiplication by 2

Multiplication by 2 is the simplest of the arithmetic tasks. Yet, it could be carried out in a number of ways. If you multiply by 2 in your head then it is often more convenient to multiply left-to-right and not right-to-left as we are all conditioned to do by the long multiplication algorithm. For example

and also

Note how useful here was the distributive law.

In the two examples above, we split a 4-digit number into four (decimal) pieces. There was no obligation to do so. For example, 1684×2 may be computed as

But here is another valid way: