Question

The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2. Find the rational number.

Answer 1

Let the denominator is x

Numerator is x - 3

Fraction = \(\frac{Numetator}{Denominator}=\frac{x-3}x\)

According to the question:

Numerator is increased by 2 and Denominator is increased by 5, then fraction is 1/2

On cross multiplication, we get 

2(x - 1) = x + 52x - 2 = x + 52x - x = 2 + 5x = 7

Therefore Denominator = 7

Numerator = x - 3 = 7 - 3 = 4

Therefore fraction = 4/7