The numerator of a rational number is 3 less than the denominator. If 5 is added to denominator and 2 is added to numerator, it becomes 1/2 Find the rational number.
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QUESTION:
The numerator of a rational number is 3 less than the denominator. If 5 is added to denominator and 2 is added to numerator, it becomes 1/2 Find the rational number.
ANSWER:
Le the denominator be x and the numerator be (x – 3)
By using the formula
Fraction = numerator/denominator
= (x – 3)/x
So, when numerator is increased by 2 and Denominator is increased by 5, then fraction is 1/2
(x – 3 + 2)/(x + 5) = 1/2
(x – 1)/(x + 5) = 1/2
By using cross-multiplication, we get
2(x – 1) = x + 5
2x – 2 = x + 5
2x – x = 2 + 5
x = 7
∴ Denominator is x = 7, numerator is (x – 3) = 7 – 3 = 4
And the fraction = numerator/denominator = 4/7
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