Question

the numerator of a fraction is 4 less than the denominator 1 is added to both its numerator and denominator it becomes 1/2 . find the fraction.​

Answer 1

As per the data given in the question,

We have to determine the value of the fraction.

Let the fraction be $\frac{\mathrm{a}}{\mathrm{b}}$

So, from the question,

We have,

Numerator= denominator - 4

$a=b-4 \\\Rightarrow b-a=4$

As, When 1 added to both numerator and denumerator of the fraction, then the value of the fraction will be,

$\frac{a+1}{b+1} = \frac{1}{2}\\=> \frac{a+1}{a+4+1}=\frac{1}{2}\\=>2a+2=a+5\\=>a=3\\=> b = a+4 = 3+4 = 7$

Hence, the required fraction will be $\frac{3}{7}$.

Answer 2

• As per the given data in the question, We have to find the fraction.
• Let the numerator and denominator be x and y.
• then the fraction will be $\frac{x}{y}$

        According to the question,

        Numerator=  denominator-4

        So, $\Rightarrow x=y-4$

        In the fraction, one is added to both its numerator and denominator    

         it becomes 1/2.

         $\Rightarrow \frac{x+1}{y+1}=\frac{1}{2}$ equation 1.  

         $\Rightarrow 2x+2=y+1$

         $\Rightarrow 2x-y=1-2$

         $\Rightarrow 2x-y=-1$

         Putting the value of $x$ in equation 1. we will get it,

         $\Rightarrow 2(y-4)-y=-1$

         $\Rightarrow 2y-8-y=-1$

         $\Rightarrow y-8=-1$

         $\Rightarrow y=-1+8$

         $\Rightarrow y=7$

         So, $x=y-4$

          $\Rightarrow x=7-4$

          $\Rightarrow x=3$.

         Hence, The fraction will be $\frac{3}{7}$