Question

The numerator of a fraction is 4 less than its denominator.If 2 is added to the numerator then the fraction becomes 5/7 the fraction

Answer 1

`(3)/(7)` is the original fraction

let the denominator of the original fraction be n, then

`(n-4)/(n)` is the original fraction

adding 2 to the numerator gives

`(n-4+2)/(n)` =
`(5)/(7)`, hence

`(n-2)/(n)` =
`(5)/(7)` ( cross- multiply )

7(n - 2) = 5n

7n - 14 = 5n ( subtract 5n from both sides )

2n - 14 = 0 ( add 14 to both sides )

2n = 14 ( divide both sides by 2 )

n = 7

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