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

The fraction is
`(6)/(13) .`

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
`(x)/(y) .`

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

`(x+1)/(y+1)=(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:

`(x+8)/(y+8) =(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* 6+1\\y=12+1\\y=13.`

Therefore, the fraction is
`(6)/(13) .`