I've been interested on this for a few days so I thought of looking for a name.

What is the name of the branch of maths (if there is any) that deals with looking for shortcuts?

For instance, (99)(68) = 6732, 67 being (68-1), 32 being (99-68)

for the sake of mathematicality,

it is:

_{2}Φ_{99}= 10(χ-1)+(99-χ)

Let:

χ be the multiplicand

_{2}Φ_{11}= 10(χ+ β)+ α

Where:

χ is the multiplicand

α is the ones digit of the multiplicand

β is the tens digit of the multiplicand

and

_{2}Φ_{12}= 10[χ+(2α + γ)] + δ

Where:

χ is the multiplicand

α is the ones digit of the multiplicand

γ is 1 if β≥5, 0 if β≤4

δ is the last digit of 2α

there will be more after our semester break...