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?

Given :

The numerator of a fraction is 6 less than the denominator.

 If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$.

To find : 

We have to find the original fraction.

Solution :

Let the Denominator of the fraction be $'x'.$

The numerator of a fraction is 6 less than the denominator.

So, Numerator $= x - 6$

The Original fraction is $\frac{x -6}{x}$

If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$

So, $\frac{x -6 + 3}{x} = \frac{2}{3}$

$\frac{x - 3}{x} = \frac{2}{3}$

Cross multiply,

$3 \times (x - 3) = 2 \times x$

$3 x - 9 = 2 x$

$3 x - 2 x = 9$

$x = 9$

Substitute $x = 9$ in the original fraction ,

$\frac{9 - 6}{9} = \frac{3}{9}$

The original fraction is $\frac{3}{9}$.

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Updated on: 10-Oct-2022

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