Question

A fraction equivalent to 4/5 is given. The sum of the numerator and the denominator of the equivalent fraction is 135 what is the equivalent fraction?

Answer 1

`4+5=9`

`135/9=15`

`15 xx 4= 60`
`15 xx 5=75`

`60+75=135`

`60/75`

Answer 2

The equivalent fraction is: `60/75`

Explanation:

From the problem, we get that the proportion of the numerator `n` over the denominator `d` is `4/5`:
`n/d = 4/5`

which means:
`n=4/5d`

In addition, the problem states that:
`n+d=135`

So we have a system of 2 equations.
By substitution:
`4/5d+d=135`

`9/5d=135`

`d=135*5/9 = 75`

`n = 4/5d = 4/5*75= 60`

So, the equivalent fraction: `n/d = 60/75`