Question

The numerator of a fraction is $3$ less than the denominator.If numerator is added to the denominator then the fraction becomes $\frac{2}{7}$.Find the fraction.

Answer 1

Let the numerator of the fraction be $x$.

Then denominator$=x+3$

Fraction$=\frac{x}{x+3}$

If the numerator is added to the denominator

the new fraction$=\frac{Numerator}{Denominator+Numerator}$

$\Rightarrow \frac{x}{(x+3)+x}=\frac{2}{7}$

$\Rightarrow \frac{x}{2x+3}=\frac{2}{7}$

$\Rightarrow 7x=4x+6$

$\Rightarrow 7x-4x=6$

$\Rightarrow 3x=6$ or $x=\frac{6}{3}=2$

Numerator$=x=2$

Denominator$=x+3=2+3=5$

Fraction$=\frac{2}{5}$