Question

The denominator of a fraction is greater than its numerator by 11.If 8 is added to both its numerator and denominator, it reduces to 1/3 Find the fraction..

Answer 1

Fraction = -5/17



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Answer 2

Answer:

Concept:

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

Step-by-step explanation:

Given:

The denominator of a fraction is greater than its numerator by 11.

If 8 is added to both its numerator and denominator, it reduces to 1/3.

Find:

Find the fraction

Solution:

Let us assume the Numerator $=x$

Denominator $=x+11$

If 8 is added to both, the fraction becomes $\frac{1}{3}$

       $\frac{x+8}{x+11+8}=\frac{1}{3}$

      $\begin{aligned}3(x+8) &=x+19 \\3 x+24 &=x+19 \\3 x-x &=19-24 \\2 x & \Rightarrow-5 \\x &=\frac{-5}{2}=-2.5\end{aligned}$

        Denominator $=-2.5+11$

                               =  8.5

        $\begin{aligned} \text { fraction } &=\frac{x}{x+11} \Rightarrow \frac{-2.5}{8.5} \\\\ & \Rightarrow\frac{-25}{85} \quad \Rightarrow-\frac{5}{17} \end{aligned}$

           $Fraction=-\frac{5}{17}$

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