grammaticality - Divide two into four and Divide two by four

Why does "divide two into four" equal two, and "divide two by four" equal one half?

Correct if I am wrong, but this what I have learned recently.

Answer

OP's confusion arises because "divide 2 into 4" is an idiomatic usage meaning perform a division operation, using 2 as the divisor, and 4 as the dividend.

symbolically...
4/2 = 2

clearest verbal form...
divide 4 by 2, giving the answer 2

idiomatic alternative...
divide 2 into 4, giving the answer 2

It's not the same usage as dividing a pizza into 4 [pieces], where you'd probably get 1/4 (a quarter) of a pizza as your share!