Question

I am an improper fraction whose numerator and denominator are made of odd digits only. In my simplest form, my representation as a mixed number is 2 1 3 . The sum of my numerator and denominator is 30. What fraction am I?

Answer 1

The fraction is =
`(21)/(9)`

Explanation:

In simplest form the fraction is represented in mixed number as
`2(1)/(3)`.

The fraction form of the mixed number can be given as :

`2(1)/(3)=(7)/(3)`

Let the fraction be =
`(7x)/(3x)` [As multiplying same numbers to numerator and denominator does not affect the proportion.

Sum of numerator and denominator is = 30

This, can be represented as:

`7x+3x=30`

Solving for
`x`.

`10x=30`

Dividing both sides by 10.

`(10x)/(10)=(30)/(10)`

`x=3`

So, the fraction will be =
`(7* 3)/(3* 3)`

⇒
`(21)/(9)`