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