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The numerator of a fraction is 7 less than the denominator. If 3 is added to the...

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carman222 | eNotes Newbie

Posted June 30, 2013 at 11:31 AM via web

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The numerator of a fraction is 7 less than the denominator. If 3 is added to the numerator, the value of the fraction becomes 2/3. Find the original fraction.

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llltkl | College Teacher | Valedictorian

Posted June 30, 2013 at 11:56 AM (Answer #1)

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Let the denominator of the fraction be x. The numerator is (x-7). Hence the original fraction is `(x-7)/x.`

According to the given condition:

`((x-7)+3)/x=2/3`

`rArr (x-4)/x=2/3`

Cross multiplying we get:

`3x-12=2x`

`rArr` ` x=12`

Hence the numerator of the original fraction is (12-7)=5 and its denominator =12.

Therefore the original fraction is `5/12.`

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