1.

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»

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}}


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