How do you simplify #6 div 4/9 #?
When a number/variable is divided by another number, the result is the same as the former number/variable multiplied by the reciprocal of the other number.
This simplifies to
Dividing by a fraction is the same as multiplying by the reciprocal.
Cancelling like factors at this point makes it easier to find the answer, rather than simplifying with bigger numbers later.