Question

If is added to both numerator and denominator of a fraction,the fraction become 1/2 if 8 is added to both, the fraction become 2/3 what is the fraction

Answer 1

Answer:

The fraction is  $\frac{6}{13} .$

Step-by-step explanation:

There is a data missing in the question so the complete question is below:

If 1 is added to both numerator and denominator of a fraction,the fraction become 1/2 if 8 is added to both, the fraction become 2/3 what is the fraction?

Now, to find the fraction.

Let the fraction be $\frac{x}{y} .$

If 1 is added to both numerator and denominator of a fraction,the fraction become 1/2.

$\frac{x+1}{y+1}=\frac{1}{2}$

By cross multiplying we get:

$2x+2=y+1$

Subtracting both sides by $1$ we get:

$2x+1=y$

$y=2x+1$    ......(1)

Now, if 8 is added to both, the fraction become 2/3:

$\frac{x+8}{y+8} =\frac{2}{3}$

By cross multiplying we get:

$3x+24=2y+16$

Subtracting both sides by 16 we get:

$3x+8=2y$

Substituting the value of $y$ from equation (1) we get:

$3x+8=2(2x+1)$

$3x+8=4x+2$

Adding both sides by 2 we get:

$3x+6=4x$

Subtracting both sides by 3$x$ we get:

$6=x$

$x=6.$

Now, substituting the value of $x$ in equation (1):

$y=2x+1\\y=2\times 6+1\\y=12+1\\y=13.$

Therefore, the fraction is  $\frac{6}{13} .$