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

Let us assume the original factor is x/y

Given:

x = y – 6 ----------1

Also given

(x + 3) / y = 2/3

3x + 9 = 2y ---------------2

Substitute the value of x from equation 1 in equation 2

3 (y – 6) + 9 = 2y

3y – 18 + 9 = 2y

y = 9

Therefore, x = y – 6 = 9 – 6 = 3

Therefore, the  original fraction = x / y = 3/9 

Answer 2

Let the denominator be 'x'

If the denominator is 'x' than numerator will be 'x-6'

Now we have to find the value of 'x'.

According to the question,

$\implies(x-6)+\dfrac{3}x=\dfrac{2}{3}\\\\\\\implies\dfrac{x-6+3}{x}=\dfrac{2}{3}\\\\\\\implies\dfrac{x-3}{x}=\dfrac{2}{3}$

Now we have to do cross multiplication

we get

$\implies3\:(x-3)=2x\\\\\implies3x-9=2x\\\\\implies3x-2x=9\\\\\implies x=9\:(Denominator)$

Let us verify that our answer is correct,

to verify our answers we have to put the value of 'x' which is '9'.

Lets do it,

$\implies\:(9-6)+\dfrac{3}{9}=\dfrac{2}{3}\\\\\\\implies\dfrac{(9-6+3)}{9}=\dfrac{2}{3}\\\\\\\implies\dfrac{6}{9}=\dfrac{2}{3}\\\\\\\implies\dfrac{2}{3}=\dfrac{2}{3}$

LHS=RHS

Hence it is verified.

Numerator = x-6 = 9-6 =3

Denominator = x = 9

The fraction = 3/9 answer