Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and the denominator, it becomes 1/2 . Find the fraction

Answer 1

`(3)/(7)`

Explanation:

let x be the value of the denominator , then fraction is

`(x-4)/(x)`

adding 1 to numerator and denominator , gives

`(x-4+1)/(x+1)` =
`(1)/(2)`

`(x-3)/(x+1)` =
`(1)/(2)` ( cross- multiply )

2(x - 3) = x + 1

2x - 6 = x + 1 ( subtract x from both sides )

x - 6 = 1 ( add 6 to both sides )

x = 7

then original fraction

=
`(7-4)/(7)` =
`(3)/(7)`