Question

The numerator of a fraction is 6 less than the
denominator. If 3 is added to the numesator,
the fraction becomes 2/3
find the odiginal fection
.​

Answer 1

Correct question:

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction becomes 2/3 to find the original fraction.

Answer:

• The original fraction is 3/9

Step-by-step explanation:

Given:

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

Let the denominator be x

So, the numerator is = (x - 6)

Now,

According to the question,

When 3 is added to the numerator the fraction becomes 2/3.

• The equation formed is

$\implies \boxed{\frac{(x-6)\red{+3} }{x}=\frac{2}{3}}$

⇒ (x - 3)/x = 2/3

⇒ 3(x - 3) = 2(x)

[By doing cross multiplication]

⇒ 3x - 9 = 2x

⇒ 3x - 2x = 9

[By transporting (2x) to LHS and (-9) to RHS]

⇒ x = 9

Therefore,

• The value of denominator = x = 9
• The value of numerator is = (x - 6) = (9 - 6) = 3

Hence,

The original fraction is 3/9