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:

1/6

Step-by-step explanation:

Let the denominator be X

and numerator be x-5

ATQ,

(x-5)+9/X+9= 2/3

3(x-5+9)= 2(x+9)

3x-15+27=2x+18

3x+12=2x+18

3x-2x=18-12

X=6

denominator be X=6

and numerator be x-5 = 6-5 =1

Then, rational number will be 1/6

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Answer 2

AnswEr:-

Rational number = 1/6

Step-by-step-explanation :-

Let the numerator be N and denominator be D.

•°• Fraction or rational number = N/D

✏ ATQ:-

➩ N = D - 5 ................(Eq.1)

2nd case:-

➩ (N + 9)/(D + 9) = 2/3

• Putting value from (Eq.1):-

➩ (D - 5 + 9)/(D + 9) = 2/3

➩ (D + 4)/(D + 9) = 2/3

➩ 3(D + 4) = 2(D + 9)

➩ 3D + 12 = 2D + 18

➩ 3D - 2D = 18 - 12

➩ D = 6

$\therefore\underline{\textsf{Denominator \: of \: fraction = {\textbf{6 }}}}$

• Putting value of D in (Eq.1) :-

➩ N = 6 - 5

➩ N = 1

$\therefore\underline{\textsf{Numerator \: of \: fraction = {\textbf{ 1 }}}}$

$\rule{200}{1}$

✏ Fraction or rational number:-

⇒ Fraction = N/D

⇒Fraction or rational number= 1/6

$\therefore\underbrace{\textsf{Rational \: number = {\textbf{ \dfrac{1}{6} }}}}$