Question

The numerator of a fraction is 3 less than its denominator. If 3 is subtracted from both the numerator and the denominator the fraction becomes 4.
Find the fraction.

Answer 1

Answer :-

The fraction is - 1/2.

Solution :-

Let the denominator of a fraction be x

Numerator of a fraction = 3 less than x = (x - 3)

According to the question :

⇒ {(x - 3) - 3}/{x - 3} = 4

⇒ (x - 3 - 3)/(x - 3) = 4

⇒ (x - 6)/(x - 3) = 4

⇒ x - 6 = 4(x - 3)

⇒ x - 6 = 4x - 12

⇒ - 6 + 12 = 4x - x

⇒ 6 = 3x

⇒ 6/3 = x

⇒ 2 = x

⇒ x = 2

i.e Denominator of the fraction = 2

Numerator of the fraction = (x - 3) = (2 - 3) = - 1

Fraction = Numerator/Denominator = - 1/2

Therefore the fraction is - 1/2.

Answer 2

Answer:-

-1/2 is the fraction

Further Explanation

Let (x) be the denominator of a fraction

x = (x - 3)

Here the fractions numerator is 3 less

According to the given question:-

$= > \frac{(x - 3) -3}{(x \: \times - 3)} = 4$

$= > \frac{(x - 3 - 3)}{(x - 3)} = 4$

$= > \frac{(x - 6)}{(x - 3)} = 4 \\ </p><p> = > x - 6 = 4.....(x - 3) \\ </p><p> = > x - 6 = 4x - 12$

$= > (- 6 + 12 = 4x - x) \\ </p><p> = > (6 = 3x) \\ </p><p> = > ( \frac{6}{3}= x) \\ </p><p> = > ( 2 = x) \\ </p><p> = > (x = 2)$

Hence,2 is the fraction's denominator

$= > (x - 3) = > (2 - 3) = - 1$

Formula:-

$Fraction = \frac{(Numerator)}{(Denominator = - \frac{1}{2}) }$

Hence, - 1/2 is the fraction