Question

The denominator of a rational number is 5 less than the numerator. If 9 is subtracted

from the numerator and 1 is added to the denominator, the number becomes 7/2Find

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Answer 1

EXPLANATION.

Let the numerator of the fraction be = x

Let the denominator of the fraction be = x - 5

If 9 is subtracted from the numerator

and 1 is added to the denominator

Fraction become = 7/2.

=> x - 9 / x - 5 + 1 = 7/2

=> x - 9 / x - 4 = 7/2

=> 2 ( x - 9 ) = 7 ( x - 4 )

=> 2x - 18 = 7x - 28

=> - 18 + 28 = 7x - 2x

=> 10 = 5x

=> x = 2

Fraction become = x / x - 5 = 2 / 2 - 5 = 2 / -3

Fraction become = -2/3.

Answer 2

Answer:

Let the Numerator be n and Denominator be (n - 5) of the Fraction.

If 9 is subtracted from the numerator and 1 is added to the denominator, the number becomes 7/2

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{Numerator-9}{Denominator+1}=\dfrac{7}{2}\\\\\\:\implies\sf \dfrac{n-9}{(n - 5)+1}=\dfrac{7}{2}\\\\\\:\implies\sf \dfrac{n-9}{n - 4}=\dfrac{7}{2}\\\\\\:\implies\sf 2(n - 9) = 7(n - 4)\\\\\\:\implies\sf 2n - 18 = 7n - 28\\\\\\:\implies\sf 28 - 18 = 7n - 2n\\\\\\:\implies\sf 10 = 5n\\\\\\:\implies\sf \dfrac{10}{5} = n\\\\\\:\implies\sf n = 2$

⠀

$\dag\:\underline{\boxed{\sf Original\:Fraction=\dfrac{n}{n-5} = \dfrac{2}{ - \:3} = \dfrac{ - \:2}{3} }}$