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:

Original fraction is 12/48

Step-by-step 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

Answer 2

Answer: $\frac{12}{48}$

Step-by-step explanation:

You know that the ratio of the numerator to the denominator of the fraction is 1:4. This can be written as $\frac{1}{4}$. Then you can write the following expression

$\frac{n}{4n}=\frac{1}{4}$

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 $\frac{1}{3}$:

$\frac{n+3}{4n-3}=\frac{1}{3}$

Then, you must solve for n, as following:

\$\frac{n+3}{4n-3}=\frac{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:

$\frac{12}{48}$