Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the
numerator, the fraction is equal to 2/3. What is the original fraction equal to?​

Answer 1

Answer:

$\sf{Original\:fraction = \dfrac{3}{9}}$

Step-by-step explanation:

Let,

The denominator of fraction = x

The numerator of fraction = x - 6

If 3 is added to the numerator = x - 6 + 3

⇒ x - 3

So,

⇒ $\sf{\dfrac{x - 3}{x} = \dfrac{2}{3}}$

⇒ 3 (x-3) = 2 (x)

⇒ 3x - 9 = 2x

⇒ 3x - 2x = 9

⇒ x = 9

The denominator of fraction = 9

The numerator of fraction = x - 6

⇒ 9 - 6

⇒ 3

Therefore,

$\sf{Original\:fraction = \dfrac{3}{9}}$

Answer 2

AnsWer :

3 / 9.

SolutioN :

Let's,

• Numerator be ' N '
• And, Denominator be ' D '

♢ Condition :

• N = D - 6.

☛ Case 1.

• The numerator of a fraction is 6 less than the denominator.

→ D - 6 / D ______ ( 1 )

$\rule{120}2$

☛ Case 2.

• If 3 is added to the numerator, the fraction is equal to 2/3.

→ D - 6 + 3 / D = 2 / 3. [ From Equation ( 1 ) ]

→ D - 3 / D = 2 / 3.

→ 3( D - 3 ) = 2D.

→ 3D - 9 = 2D.

→ D = 9.

› Now, Let's Find the numerator.

→ N = D - 6.

→ N = 9 - 6.

→ N = 3. [ from Equation ( 1 ) ]

So, Our Fraction become N / D → 3 / 9.

✡ Therefore, the original fraction equal to 3 / 9.