Whats best method to calculate multiplication mentally?

Question

I would like to know which method is better for mentally multiplication calculation between

a) Cross-Multiplication

and b) Left-to-Right Multiplication

Thank you!

Answer 1

Probably neither, unless all you know is single digit multiplication. Then it comes down to which one you find quickest.

$$1225\cdot 1225=1500625$$ can be done as $$12^2\cdot100^2+2\cdot 12\cdot 25\cdot 100+25^2$$ if you know two digit multiples, and a bit of algebra ( See Karatsuba multiplication).

If you know about friendly numbers ( nearby numbers with easy multiples), then you can do more steps, but do them quicker.

Almost all multiplication of same parity except prime squares, can be don't using differences of squares, by averaging, subtracting, and subtraction of squares. a few more adds can deal with opposite parity multiplication.

In conclusion which is quickest like in computing, comes down to your relative speeds of operations.