Explain why it is correct to claim that A/B<B/A is true.

Question

 I know it is true if you multiply both sides by AB. Once you multiply and take the square root the answer is true.

Answer 1

As written with no further qualifiers, your statement is not true.

 

If  A/B = 4/3

Then B/A = 3/4

If A/B < B/A then 4/3 < 3/4   which is not true.

Thus, your assumption is not valid

 

If you rule that the fraction must not be improper and A≠B, and thus have

value A/B<1 then this is true for positive values (i.e. A and B are both positive

or A and B are both negative)

 

Example:  3/4 < 4/3  is true

               -3/4 < -4/3  is not true

               -3/(-4) = 3/4 < 4/3  is true