Question

The numerator of a rational number is8less than its denominator. If the numinator increased by 2 and the denominator is decreased by 1 the number obtained is 1/2 . Find the number

Answer 1

Hey mate!

Here is your answer > >

Let the denominator of a rational number be x

numerator of rational number=x-8

Rational number=x-8/x

According to question

x-8+2/x-1=1/2

x-6/x-1=1/2

(x-6)×2=x-1

2x-12=x-1

2x-x=-1+12

x=11

Numerator=11-8=3

Denominator=11

Rational number=3/11

Hope it helps!

Thankyou ☆ ☆

Answer 2

let x be the denominator.

so, numerator = x - 8

if ,

numerator = x - 8 + 2 = x - 6

and , denominator = x - 1

number obtained = $\bf{\frac{1}{2}}$

$\therefore$ According to the question ,

$\bf{\frac{x-6}{x-1}}$ = $\bf{\frac{1}{2}}$

solve by cross multiplication method,

=> $\bf{2(x-6)}$ = $\bf{1(x-1)}$

Multiply the terms ,

=> $\bf{2x-12}$ = $\bf{x-1}$

Take the like terms at one side :-

=> $\bf{2x - x}$ = $\bf{12 - 1}$

=> $\bf{x\: =\: 11}$

thus ,

numerator = x - 8 = 11 - 8 = 3

and, denominator = x = 11

hence , fraction = $\frac{3}{11}$