Fractions

Choose the Correct Answer

Correct Answer : Option a

Explanation
Let the original proper fraction be:
a/b, where 0 < a < b
Now subtract a positive number k from both numerator and denominator
(i.e., k > 0 and a > k, b > k
New fraction = (a − k) / (b − k) ​
Let’s compare
(a − k) / (b – k)​ with a/b
We want to know if:
(a − k) / (b – k) < a/b ​
Cross-multiplying:
(a – k) * b < a * (b − k)
ab – kb < ab – ak
−kb < −ak
kb > ak
b > a
Which is true, since a < b (because it's a proper fraction).
Therefore, the new fraction is always less than the original.
Hence, option a is correct.