Question

a fraction has denominator 4 more than its numerator. If 6 is added to the numerator and 6 is subtracted from the denominator the fraction is
$\frac{11}{3}$
Find the fraction.
Fast answer please ​

Answer 1

Answer

Let the numerator be x.

Let the denominator be x + 4.

Numerator of the fraction :

According to the question,

${\sf \dashrightarrow \dfrac{x + 6}{(x + 4) - 6} = \dfrac{11}{3}}$

Cross multiply the numbers.

${\sf \dashrightarrow 3 (x + 6) = 11 (x + 4 - 6)}$

${\sf \dashrightarrow 3x + 18 = 11x + 44 - 66}$

${\sf \dashrightarrow 3x - 11x = 44 - 66 - 18}$

${\sf \dashrightarrow -8x = -22 - 18}$

${\sf \dashrightarrow -8x = -40}$

${\sf \dashrightarrow x = \dfrac{-40}{-8}}$

${\sf \dashrightarrow x = 5}$

Now, we can find the denominator of the fraction.

Denominator of the fraction :

${\sf \dashrightarrow x + 4}$

${\sf \dashrightarrow 5 + 4 = 9}$

So, the fraction is,

${\sf \dashrightarrow \dfrac{5}{9}}$

Hence, the fraction is $\sf \dfrac{5}{9}$

Verification

${\sf \dashrightarrow \dfrac{x + 6}{(x + 4) - 6} = \dfrac{11}{3}}$

${\sf \dashrightarrow \dfrac{5 + 6}{(5 + 4) - 6} = \dfrac{11}{3}}$

${\sf \dashrightarrow \dfrac{11}{9 - 6} = \dfrac{11}{3}}$

${\sf \dashrightarrow \dfrac{11}{3} = \dfrac{11}{3}}$

${\sf \dashrightarrow LHS = RHS}$