Question

. The sum of the numerator and the denominator
of a fraction is 9. If one is added to the numerator
and one is subtracted from the denominator, it
1
reduces to Find the fraction.
2
0 - -​

Answer 1

Correct Question :

The sum of the numerator and the denominator  of a fraction is 9. If one is added to the numerator  and one is subtracted from the denominator, it reduces to 1/2. Find the fraction.

Answer :

The required fraction is 2/7

Step-by-step explanation :

Given :

• The sum of the numerator and the denominator  of a fraction is 9
• If one is added to the numerator  and one is subtracted from the denominator, it reduces to 1/2

To find :

the fraction

Solution :

Let the numerator of the fraction be x and denominator of the fraction be y.

$\boxed{\sf fraction=\dfrac{numerator}{denominator}}$

The required fraction = x/y

The first condition : The sum of the numerator and the denominator  of a fraction is 9

  x + y = 9 ➙[1]

The second condition : If one is added to the numerator  and one is subtracted from the denominator, it reduces to 1/2.

 $\sf \dfrac{x+1}{y-1}=\dfrac{1}{2}$

2(x + 1) = 1(y - 1)

2x + 2 = y - 1

y - 2x = 2 + 1

y - 2x = 3 ➙[2]

Subtract equation [2] from equation [1],

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

x + y - y + 2x = 6

  3x = 6

   x = 6/3

   x = 2

➙ x + y = 9

   2 + y = 9

    y = 9 - 2

    y = 7

Therefore,

numerator = 2

denominator = 7

The required fraction is 2/7