Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to both itsnumerator and denominator , it becomes 1/2, Find the fraction.

Answer 1

Let the fraction be (x - 4) / x .

$\frac{x - 4 + 1}{x + 1} = \frac{1}{2} \\ \\ = \frac{x - 3}{x + 1} = \frac{1}{2} \\ \\ \\ 2(x - 3) = 1(x + 1) \\ \\ = 2x - 6 = x + 1 \\ \\ \\ 2x - x = 6 + 1 \\ \\ = x = 7 \\ \\ \\ x - 4 = 7 - 4 = 3$

∴ The answer is 3/7.

$\frac{3}{7} \to \frac{3 + 1}{7 + 1} = \frac{4}{8} = \frac{1}{2}$

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the denominator of the required fraction be x.

Then, its numerator = (x - 4)

∴ (x - 4) + 1/ x + 1 = 1/2

⇒ x - 3/x + 1 = 1/2

⇒ 2(x - 3) = x + 1

⇒ 2x - 6 = x +1

⇒ 2x - x = 6 + 1

⇒ x = 7.

∴ Denominator = 7 and Numerator = (7 - 4) = 3.

Hence, the required fraction is 3/7.