Question

The numerator of a friction is 6 less than the denominator.If 3 is added to the numerator,the fraction is equal to 2/3 ,find the original fraction​

Answer 1

$\bf{\huge{\underline{\underline {\red{\rm{Answer}}}}}}$

Let the denominator of a fraction be x.

Fraction formed will be in the form $\bf\huge\frac{x}{y}$

According to the first part,

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

Numerator = x - 6

According to the second part,

If 3 is added to the numerator of the fraction, the fraction becomes $\bf{2}{3}$

$\bf\huge\frac{x - 6 + 3}{x}$ = $\bf\frac{2}{3}$

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

$\bf\huge<strong> </strong>{<strong>3 </strong><strong>(</strong><strong> </strong><strong>x </strong><strong>-</strong><strong> </strong><strong>3</strong><strong>) </strong><strong> </strong><strong>=</strong><strong> </strong><strong>2x</strong>}$$\bf\underbrace{cross\:multiplying \:the\:terms}$

$\implies$ $\bf\huge{<strong> </strong><strong>3x </strong><strong>-</strong><strong> </strong><strong>9 </strong><strong>=</strong><strong> </strong><strong>2x</strong><strong> </strong>}$

$\implies$ $\bf\huge{<strong> </strong><strong>3x </strong><strong>-</strong><strong> </strong><strong>2x </strong><strong>=</strong><strong> </strong><strong>9</strong>}$

$\implies{\bf{\huge{\boxed{\underline{x = 9}}}}}$

$\bf\boxed{ <strong>Denominator</strong><strong>,</strong><strong> </strong><strong>x </strong><strong>=</strong><strong> </strong><strong>9</strong>}$

Numerator, x - 6 = 9 - 6

$\bf\boxed{<strong> </strong><strong>Numerator </strong><strong>=</strong><strong>3</strong>}$

Fraction = $\bf\huge\dfrac{3}{9}$