Question

the denominator of a rational number is greater than its numerator by 6 if the numerator is decreased by 1 and the denominator is increased by 1 the number is obtain is 2/3 find the rational number​

Answer 1

2/3 itself is a rational number

Answer 2

Answer:

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

$:\implies\sf \dfrac{Numerator-1}{Denominator+1}=\dfrac{1}{3}\\\\\\:\implies\sf \dfrac{a-1}{(a+6)+1}=\dfrac{1}{3}\\\\\\:\implies\sf \dfrac{a-1}{a+7}=\dfrac{1}{3}\\\\\\:\implies\sf 3(a - 1) = 1(a + 7)\\\\\\:\implies\sf 3a - 3 = a + 7\\\\\\:\implies\sf 3a -a = 7 + 3\\\\\\:\implies\sf 2a= 10\\\\\\:\implies\sf a = \dfrac{10}{2}\\\\\\:\implies\sf a = 5$

⠀

$\dag\:\underline{\boxed{\sf Original\:Fraction=\dfrac{a}{a + 6} = \dfrac{5}{(5 + 6)} = \dfrac{5}{11} }}$