Question

In a rational number, the numerator is 3 less than the denominator. When 2 is subtracted from both the
numerator and the denominator, the rational number in its simplest form is 5/6. What is the rational number?​

Answer 1

5/6-2/2

=3/4

3/4-3 or3/4-3/1=2/4

Answer =2/4

Am I correct

Answer 2

$\begin{gathered} \begin{gathered}\begin{gathered}\\\;\underbrace{\underline{\sf{Let's \; understand \; the \; Question:-}}}\end{gathered}\end{gathered} \end{gathered}$

we have to find a rational number

In which

• the numerator is 3 less than the denominator

• When 2 is subtracted from both the numerator and the denominator = the rational number in its simplest form is 5/6

Let's solve it -

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$\begin{gathered} \begin{gathered}\begin{gathered}\\\;\underbrace{\underline{\sf{Answer:-}}}\end{gathered}\end{gathered} \end{gathered}$

$\Longrightarrow \sf\dfrac{ 17}{20 }$

________________________________________

$\begin{gathered} \begin{gathered}\begin{gathered}\\\;\underbrace{\underline{\sf{Given:-}}}\end{gathered}\end{gathered} \end{gathered}$

★ the numerator is 3 less than the denominator

★ When 2 is subtracted from both the numerator and the denominator = the rational number in its simplest form is 5/6

________________________________________

$\begin{gathered} \begin{gathered}\begin{gathered}\\\;\underbrace{\underline{\sf{To \; find :-}}}\end{gathered}\end{gathered} \end{gathered}$

★ rational number

________________________________________

$\begin{gathered} \begin{gathered}\begin{gathered}\\\;\underbrace{\underline{\sf{Solution:-}}}\end{gathered}\end{gathered} \end{gathered}$

let -

denominator be x

Therefore , Numerator = x - 3

and When 2 is subtracted from both the numerator and the denominator = the rational number in its simplest form is 5/6

$\longrightarrow \sf\dfrac{x - 3 - 2}{x - 2} = \dfrac{5}{6}$

$\longrightarrow \sf\dfrac{x - 5}{x - 2} = \dfrac{5}{6}$

After cross multiply

$\longrightarrow \sf 6 (x-5) = 5(x-2)$

$\longrightarrow \sf 6 x- 30 = 5x - 10$

$\longrightarrow \sf 6 x- 30 = 5x - 10$

$\longrightarrow \sf 6 x- 5x = - 10 + 30$

$\Longrightarrow \sf x = 20$

therefore ,

$\longrightarrow \sf\dfrac{x - 3}{x }$

write 20 in the place of x

$\longrightarrow \sf\dfrac{20 - 3}{20 }$

$\Longrightarrow \sf\dfrac{ 17 }{ 20}$