# Fastest Methods At Mental Math And Your Personal Timings

#1

Hello everyone! I am looking forward to know what you guys think the fastest method for the following is (along with your personal best timings).

2 vs 2
3 vs 3

Subtraction
2 vs 2
3 vs 3

Multiplication (Direct only)
2 vs 2
3 vs 3

Division (upto 2 decimal units)
2 vs 2
3 vs 3

Square Roots (Direct only)
2 digit numbers
3 digit numbers
4 digit numbers

Squares (Direct only)
2 digit numbers
3 digit numbers

The reason I am asking you this is to know what methods work the best individually for these systems. I have already practised quite a bit of these (for example, the Tratchenberg system except direct multiplication). Sorry for my poor English.

Additionally, I have never practised the Soroban, and hence I am eagerly looking forward to replies from Soroban maestros as well.

#2

No personal timings I’m afraid:

The fastest methods for addition that I have seen to date are visual ( anzan - mental soroban )
I would assume this would apply equally for subtraction.

Multiplication - Strong Numeracy including a good grasp of difference of squares and decomposition. For 2x2 I am mentally comfortable. rote memorization of a large number of base elements to work with really helps. Know your squares. Often the real time wasted in mental multiplication for me is actually subtraction and i tend to avoid it because I am weak. For 3x3 you should find that an obscenely strong 2x2 should provide a very good basis up to 6x6 with cross multiplication and or simplification.

I think the challenge as the numbers go up is to have a quick grasp of a major system for storing your interim terms. ( I don’t)

## Division and Roots -> no idea for me here lies dragons - logarithms may actually be your friend here I suspect. plus a bunch of tricks I haven’t memorized around common fractions.

Squares of 2 digit number a^2 + b^2 + 2ab is your friend although I tend to vote for memorization of 2 digit squares

Squares of 2 digit numbers a^2 + b^2 + 2ab works very nicely with up to 4 digits if you have you 2 digit squares and multiplication nailed.