The numerator of a fraction is 2 less than the denominator. If 1 is added to its denominator, it becomes ½. Find the fraction.

Solution

Let the denominator of the fraction be x.

∴ Numerator = x - 2

∴           The fraction = $fraction numerator straight x minus 2 over denominator straight x end fraction$
    Since, it becomes $1 half$ when 1 is added to its denominator
i.e.             $fraction numerator straight x minus 2 over denominator straight x plus 1 end fraction equals 1 half$
   By cross multiplication, we have

                     2(x - 2) = x + 1
$rightwards double arrow$                    2x - 4 = x + 1
$rightwards double arrow$                   2x - x = 1 + 4
$rightwards double arrow$                            x = 5