A is a proper fraction : False
B is smaller than A : True

Explanation :

A × 5/6 = B

So,

A × 5/6 ÷ A = B ÷ A

5/6 = B/A


This is as good as saying A is 6 units and B is 5 units.

A ⬛⬛⬛⬛⬛⬛
B ⬛⬛⬛⬛⬛

Ratio of A to B = 6 : 5


So A is definitely bigger than B, which means B is definitely smaller than A.

Next,

We can rewrite the equation as :

A = 6/5 × B

If B is an improper fraction bigger than 1, its numerator is bigger than its denominator.


Eg. B could be something like 6/5, 7/6, 100/89 , 35/23 , etc.

So since A is bigger than B, then A is also an improper fraction bigger than 1, but an even bigger value.



Eg. If B = 7/6 ,


Then A = 6/5 × 7/6 = 7/5


A can never be an proper fraction.

Alternatively,


If we assumed that A is a proper fraction to be true , then we are assuming that A is smaller than 1 or equal to 1.


Since A × 5/6 = B,


B would be an even smaller proper fraction than A, which means it is also smaller than 1.


Eg. If A = 3/4,

B = 3/4 × 5/6 = 1/4 × 5/2 = 5/8


Then this would contradict the given information that 'B is an improper fraction greater than 1'


So the assumption cannot be true.