Question

Why is 1/2 not useful as a benchmark to compare 5/8 and 9/10?

Answer 1

1/2 would not be a useful benchmark to compare these 2 fractions because both of them are greater than half. The benchmark fraction 1/2 is most useful when one fraction is less than half and the other more than 1/2. 5/8 is more than 4/8(1/2), and 9/10 is more than 5/10(1/2).

Answer 2

Solution:

1/2 is not a useful benchmark to compare 5/8 and 9/10 because if we observe closely we found that

$\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} =\frac{1}{8}$

and

$\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times\frac{1}{2}=\frac{1}{10}$

In the first case 1/2 comes four times and in the second case 1/2 comes 5 times in multiplication so logically the second number 9/10 should be smaller than the first number 5/8.

But 9 is greater than 5 it mean second number should be greater than the first number.

Both the above two conclusions are contradictory to each other.

Hence we can not use 1/2 as a benchmark to compare 5/8 and 9/10.