Question

the numerator of a fraction is 5 less than the denominator if 2 is added to both its numerator and denominator it becomes 2/ 3 find the fraction​

Answer 1

Given:-

• Numerator of the fraction is 5 less tham its denomirator
• If 3 is added to Numerator and Denominator then, fraction becomes 2/3

To Find:-

• The original fraction

Explanation:-

Let,

• Denominator be x
• Numerator be x-5

After adding 3

• Numerator = x-2
• Denominator = x+3

Acc. to the question

$\dfrac{x-2}{x+3} = \dfrac{2}{3}$

$3(x-2) = 2(x+3)$

$3x-6 = 2x+6$

$3x -2x = 6+6$

$x = 12$

Now,

$= x-5$

$= 12-5$

$\bold{ = 7}$

Hence, the fraction is,

$\boxed{ \dfrac{x-5}{x} =\dfrac {7}{12}}$

Answer 2

Let the Denominator be x

So, Numerator is x-5.

Therefore, fraction form = (x-5)/x

After adding 2 both on numerator and denominator.

Then, Acoording to the question

$= > \frac{(x - 5) + 2}{x + 2} = \frac{2}{3} \\ = > \frac{x - 3}{x + 2} = \frac{2}{3} \\ = > 3(x - 3) = 2(x + 2) \\ = > 3x - 9 = 2x + 4 \\ = > 3x - 2x = 4 + 9 \\ = > x = 13$

So,

The fraction = (13-5)/13

= 8/13