Question

if numerator is 2 less than denominator of a rational number and with when 1 is subtracted from numerator and denominator both the rational number in its simplest form is 1/2. what is the raitonal number solution​

Answer 1

Given

If numerator is 2 less than denominator of a rational number and with when 1 is subtracted from numerator and denominator both the rational number in its simplest form is 1/2.

To find

what is the rational number ?

Solution

★ Let the denominator be x and numerator be (x - 2).

**According to the given condition**

when 1 is subtracted from numerator and denominator both the rational number in its simplest form is 1/2

→ x - 2 - 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 = 5

Rational number

→ numerator/denominator

→ x - 2/x

→ 5 - 2/5 = 3/5

Hence, the required rational number is 3/5

Answer 2

Answer:

Let the Denominator be n and Numerator be (n – 2) of the Fraction respectively.

⠀

Given : When 1 is subtracted from numerator and denominator both the rational number in its simplest form is ½

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{Numerator-1}{Denominator-1}=\dfrac{1}{2}\\\\\\:\implies\sf \dfrac{(n - 2) - 1}{n - 1} = \dfrac{1}{2}\\\\\\:\implies\sf \dfrac{n - 3}{n - 1} = \dfrac{1}{2}\\\\\\:\implies\sf (n - 3)2 = 1(n - 1)\\\\\\:\implies\sf 2n - 6 = n - 1\\\\\\:\implies\sf 2n - n = 6 - 1\\\\\\:\implies\sf n = 5$

$\rule{140}{1.5}$

$\bf{\dag}\:\boxed{\sf Fraction=\dfrac{Numerator}{Denominator} = \dfrac{(n-2)}{n} = \dfrac{\textsf{\textbf{3}}}{\textsf{\textbf{5}}}}$