Numerator and Denominator in Fractions

Question

The numerator of a certain fraction is one less than the denominator. If the numerator is halved, and the denominator is decreased by two, the value of the resulting fraction is three fifths. What was the original fraction?

Answer 1

Let x be the numerator of the fraction, then the fraction is x/(x+1)

If the numerator is halved, and the denominator is decreased by two,

the value of the resulting fraction is three fifths

⇒ (x/2)/[(x+1)-2] = 3/5

⇒ 5(x/2) = 3 (x-1)

⇒ x = 6

 

So the original fraction was 6/7.