Question

The numerator of a fraction is '$4$‘ less than the denominator. If ’$1$‘ is added to both its numerator and denominator, it becomes ’$\frac{1}{2}$'.Find the fraction

Answer 1

Let the denominator be '$\mathrm{x}$'.

Here, it is given that, the numerator is $4$ less than the denominator, So, the numerator$=\mathrm{x}-4$

$\therefore$ The fraction$=\frac{\mathrm{x}-4}{\mathrm{x}}$

It is given that if '$1$‘ is added to both the numerator and denominator, it becomes equal to ’$\frac{1}{2}$'.

$\therefore$Adding '$1$' to the numerator and denominator, the new fraction becomes, $\frac{\mathrm{x}-4+1}{\mathrm{x}+1}=\frac{\mathrm{x}-3}{\mathrm{x}+1}$

$\therefore \frac{\mathrm{x}-3}{\mathrm{x}+1}=\frac{1}{2}$

$\begin{array}{rcl}2\left(\mathrm{x}-3\right)& =& \mathrm{x}+1\\ 2\mathrm{x}-6& =& \mathrm{x}+1\\ \mathrm{x}& =& 7\end{array}$

$\therefore \frac{\mathrm{x}-4}{\mathrm{x}}=\frac{3}{7}$

Therefore, the original fraction is '$\frac{3}{7}$'.