Question

The numerator of a fraction is 5 less than the denominator. If 9 is added to both the numerator and denominator, it becomes 2/3 .Find the rational number.

Answer 1

Answer:

let the denominator be x

so the numerator =x-5

if 9 us added to both numerator and denominator

numerator =x-5+9

=x+4

denominator =x+9

now, according to question

x+4/x+9=2/3

3(x+4)=2(x+9)

3x+12=2x+18

3x-2x=18-12

x=6

denominator=6

then numerator = x-5

6-5=1

then fraction =1/6

Answer 2

Answer:

The rational number is $\sf{\dfrac{1}{6}}$

Step-by-step explanation:

Given :

The numerator of a fraction is 5 less than the denominator

If 9 is added to both the numerator and denominator, it becomes 2/3

To find :

The rational number

Solution :

Let the -

• Numerator = (y)
• Denominator = (y + 5)

⇒ $\sf{\dfrac{y + 9}{(y + 5) + 9} = \dfrac{2}{3}}$

⇒ 3(y + 9) = 2(y + 5 + 9)

⇒ 3y + 27 = 2(y + 14)

⇒ 3y + 27 = 2y + 28

⇒ 3y - 2y = 28 - 27

⇒ y = 1

Numerator = 1

$\rule{300}{1.5}$

★ Denominator =

⇒ y + 1

⇒ 6

The rational number formed = $\sf{\dfrac{1}{6}}$

$\therefore$ The rational number is $\sf{\dfrac{1}{6}}$