Question

the numerator of a fraction is 6 less than the denominator . if 1 is added to both numerator and denominator.it become half ,then find the fraction
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Answer 1

Answer :- 5/11

Please refer to the attachment.

• Hope it helps!!!

Answer 2

Answer:

Let the denominator, D of the fraction be x. So, the numerator, N becomes (x - 6).

• Original fraction = ${\sf{ {\dfrac{N}{D}} = {\dfrac{x - 6}{x}}}}$

ATQ, After adding 1 to both numerator and denominator, the fraction equals to half, then the equation formed :

$\implies{\sf{ {\dfrac{x - 6 + 1}{x + 1}} = {\dfrac{1}{2}}}}$

$\implies{\sf{ {\dfrac{x - 5}{x + 1}} = {\dfrac{1}{2}}}}$

• Cross - multiplication

$\implies{\sf{ 2(x - 5) = 1(x + 1)}}$

$\implies{\sf{2x - 10 = x + 1}}$

$\implies{\sf{2x - x = 1 + 10}}$

$\implies{\sf{x = 11}}$

Now,

→ x - 6 = 11 - 6 = 5

Hence, the numerator and denominator are 5 and 11.

The fraction is ${\bf{{\dfrac{5}{11}}}}$.