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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?

User Naomi
by
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2 Answers

2 votes

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)

User FrioneL
by
8.0k points
5 votes

Answer:

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

User Ishrat
by
7.6k points

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