Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to \[\frac{2}{3}\]. What is the original fraction equal to?

Answer 1

Let the denominator of the fraction be x . 
Therefore, the numerator will be ( x - 6) .
\[ \therefore\text{ Fraction }= \frac{x - 6}{x}\]
According to the question, 
\[\frac{x - 6 + 3}{x} = \frac{2}{3}\]
or\[ \frac{x - 3}{x} = \frac{2}{3}\]
or 3x - 9 = 2x [After cross multiplication]
or 3x - 2x = 9
or x = 9
\[\text{ Thus, the original fraction }= \frac{9 - 6}{9} = \frac{1}{3}\]