Question

The numerator of rational number is 4 less than the denominator if 1 is added to both numerator and denominator that number becomes one by two . Find rational number

Answer 1

GIVEN :–

• The numerator of rational number is 4 less than the denominator.

• When 1 is added to both numerator and denominator that number becomes ½ .

TO FIND :–

• Rational number = ?

SOLUTION :–

• Let the denominator = x

• Then Numerator will be (x - 4).

• So that –

$\\ \implies \sf Rational \: \: number = \dfrac{x - 4}{x}$

• According to the question –

$\\ \implies \sf \dfrac{x - 4 + 1}{x + 1} = \dfrac{1}{2}$

$\\ \implies \sf \dfrac{x -3}{x + 1} = \dfrac{1}{2}$

$\\ \implies \sf 2(x - 3) = x + 1$

$\\ \implies \sf 2x - 6 = x + 1$

$\\ \implies \sf 2x - x= 6 + 1$

$\\ \implies \large{ \boxed{ \sf x=7}}$

• Now Rational number –

$\\ \implies \sf Rational \: \: number = \dfrac{7 - 4}{7}$

$\\ \implies{ \boxed { \sf Rational \: \: number = \dfrac{3}{7}}}$

• Hence, The Rational number is $= \dfrac{3}{7}$

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Numerator of rational number is 4 less than the denominator.
• If 1 is added to both numerator and denominator then number becomes 1/2.

${\bf{\blue{\underline{To\:Find:}}}}$

• Rational number =?

${\bf{\blue{\underline{Now:}}}}$

$\dagger \: \: \boxed{\sf{ Rational \: Number = \frac{ numerator}{denomerator} }}$

Numerator has relation with denominator,

$\star \: {\sf{ Let \: denomerator = x}}$

$\star \: {\sf{ let \: numerator = x-4}}$

$\star \: {\sf{ Rational \: number = \frac{x-4}{x } }}$

$\dagger \underline {\frak{ according \: to \: the \: question}}$

$: \implies{\sf{ \frac{n + 1}{d + 1} = \frac{1}{2} }}$

$: \implies{\sf{ \frac{x - 4 + 1}{x + 1} = \frac{1}{2} }}$

$: \implies{\sf{ \frac{x - 3 }{x + 1} = \frac{1}{2} }}$

$: \implies{\sf{ 2(x - 3) = x + 1}}$

$: \implies{\sf{ 2x - 6 = x + 1}}$

$: \implies{\sf{ 2x - x = 1 + 6}}$

$: \implies\boxed{\sf{ x = 7}}$

__________________________________

$: \implies{\sf{ Rational \: number= \frac{7 - 4}{7} }}$

$: \implies{\sf{ Rational \: number= \frac{3}{7} }}$

___________________________________

For checking,

$: \implies{\sf{ \frac{3 + 1}{7 + 1} = \frac{1}{2} }}$

$: \implies{\sf{ \frac{4}{8} = \frac{1}{2} }}$

$: \implies{\sf{ \frac{1}{2} = \frac{1}{2} }}$

Which is true.