For arithmetic question like this
(3*4)/2
2 can divide 3, 3/2 and multiple 4 or
2 can divide 4, 4/2, and multiply by 3
But not
3/2 * 4/2 ,
Could someone explain why this is not possible ? Is there a name why the denominator can not be shared with the numerators?
In evaluating Algebraic expressions, we must follow rules of Algebra. Those rules come for a reason.
In your question, the two expressions have different 'real life' meanings. Say you have a big piece of rectangular cake cut into $3$x$4$ pieces.
If you have $2$ kids, each kid can take $(3*4)/2=6$ pieces.
Now, say you want to give equal number of pieces to $4$ kids, in this case each kid can have $(3*4)/4=(3/2)(4/2)=3$ pieces.
In the first case, each kid's share is $2$ pieces but in case $2$, each kid's share is $3$ pieces only. This is why the two expressions produce different results. Each expression answers a different question.