Question

The denominator of a fraction is one more than the numerator. If 3 is subtracted to

the numerator and to the denominator, the resulting fraction is equivalent to 1 . What is the 2
original fraction?

Answer 1

`(4)/(5)`

Explanation:

let the original fraction be

`(n)/(n+1)` ( with denominator 1 more than numerator )

Subtracting 3 from numerator/ denominator gives

`(n-3)/(n+1-3)` =
`(n-3)/(n-2)`

Given that the fraction is now equivalent to
`(1)/(2)` , then

`(n-3)/(n-2)` =
`(1)/(2)` ( cross- multiply )

2(n - 3) = n - 2, distribute left side

2n - 6 = n - 2 ( subtract n from both sides )

n - 6 = - 2 ( add 6 to both sides )

n = 4

and n + 1 = 4 + 1 = 5

Thus original fraction is
`(4)/(5)`