Question

the numerator of a fraction is 6 less than the denominator. if one is added to both the numerator and denominator,the fraction becomes 1/2 find the fraction

Answer 1

$\sf{The \: fraction \: is \: \: \dfrac{5}{11}}$

Step-by-step explanation:

Given :

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

• If one is added to both the numerator and denominator, the fraction becomes 1/2

To find :

• The fraction

Solution :

Let,

The denominator of fraction = x

The numerator of a fraction = x - 6

If 1 is added to both the numerator and denominator :

The denominator of fraction = x + 1

The numerator of a fraction = x - 6 + 1

x + 5

According to question:

⇒ $\sf{\dfrac{x \: - \: 5}{x \: + \: 1} \: = \: \dfrac{1}{2}}$

⇒ 2 (x - 5) = 1 (x + 1)

⇒ 2x - 10 = x + 1

⇒ 2x - x = 1 + 10

⇒ x = 11

The denominator of fraction = 11

The numerator of fraction = x - 6

⇒ 11 - 6

⇒ 5

The numerator of fraction = 5

Therefore,$\sf{The \: fraction \: is \: \: \dfrac{5}{11}}$

Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:$

$\:$

$\footnotesize{\text{ Let,\: the \: denominator \: be \: x}}$

$\:$

$\footnotesize{ \dfrac{(x - 6) + 1}{x + 1} = \dfrac{1}{2}}$

$\footnotesize{\implies \dfrac{x - 5}{x + 1} = \dfrac{1}{2}}$

$\footnotesize{\implies \dfrac{x - 5}{x + 1} \times 2 = 1}$

$\footnotesize{\implies \dfrac{2x - 10}{x + 1} = 1}$

$\footnotesize{\implies 2x - 10 = 1 \times (x + 1)}$

$\footnotesize{\implies 2x - 10 = x + 1}$

$\footnotesize{\implies 2x - x = 10 + 1}$

$\footnotesize{\implies x = 11}$

$\:$

___________________________

$\:$

$\footnotesize{Fraction = \dfrac{x - 6}{x }}$

$\footnotesize{\implies Fraction = \dfrac{11 - 6}{11 }}$

$\footnotesize{\implies Fraction = \dfrac{5}{11 }}$

$\:$

$\bold{ Answer = \dfrac{5}{11 }}$