Question

The ratio of the numerator to the denomintor of a certain fraction is one to four. If three is added to the numerator and subtracted from the denominator, the new fraction reduces to one-third. What is the original fraction?

Answer 1

Answer:
`(12)/(48)`

Explanation:

You know that the ratio of the numerator to the denominator of the fraction is 1:4. This can be written as
`(1)/(4)`. Then you can write the following expression

`(n)/(4n)=(1)/(4)`

Where the denumerator is 4 times the numerator.

You also know that if you add three to the numerator and subtracted from the denominator, the new fraction reduces to
`(1)/(3)`:

`(n+3)/(4n-3)=(1)/(3)`

Then, you must solve for n, as following:

\
`(n+3)/(4n-3)=(1)/(3)\\\\3(n+3)=4n-3\\3n+9=4n-3\\n=12`

Then the denominator is:

`d=4n\\d=4(12)\\d=48`

The original fraction is:

`(12)/(48)`

Answer 2

Original fraction is 12/48

Explanation:

The original fraction is 12/48 which is equivalent to 1/4

If three is added to the numerator and subtracted from the denominator;

we get; (12+3)/(48-3) = 15/45,

15/45 is equivalent to 1/3