Question

30. If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both ,the rational number in its simplest form is 1/2 . What is the rational number. I want the whole calculation.

Answer 1

Answer:

$\sf{The \: rational \: number \: = \: \dfrac{3}{5}}$

Step-by-step explanation:

Let,

• The denominator of rational number = x

• The numerator of rational number = x - 2

• When 1 is subtracted from both numerator and denominator:

The denominator x - 1

The numerator is x - 2 - 1

⇒ x - 3

⇒ $\frac{x - 3}{x - 1} = \frac{1}{2}$

⇒ 2 (x - 3) = 1 (x - 1)

⇒ 2x - 6 = 1x - 1

⇒ 2x - x = - 1 + 6

⇒ x = 5

Denominator of rational number = 5

Numerator of rational number = x - 2

⇒ 5 - 2

⇒ 3

Numerator of rational number is = 3

Therefore,

The rational number =

$\sf{The \: rational \: number \: = \dfrac{3}{5}}$

Answer 2

$\LARGE{\textbf{\textsf{ANSWER}}$

$\texttt {Let the denomiator be \textbf{x} and numerator be \textbf{(x-2)}.}$

$\textsf{According to the question , }$

$\Huge{\textt{{\frac{x-2-1}{x-1} = \frac{1}{2}}}}$

$\Longrightarrow\rm \frac{x-3}{x-1} =\frac{1}{2}$

$\Longrightarrow \rm 2 (x - 3) = 1 (x - 1)$

$\Longrightarrow \rm 2x - 6 = x - 1$

$\Longrightarrow \rm 2x - x = - 1 + 6$

$\Longrightarrow\underline{ x = 5}$

$\texttt{DENOMINATOR = 5}$

$\texttt{NUMERATOR = 3}$

${ \rm{FRACTION =\frac{3}{5}}}$

HOPE IT HELPS U ......