Answer:

The fraction is 5/11.

Step-by-step explanation:

Let's assume the fraction as x/y, where x is the numerator and y is the denominator.

According to the given information:

The numerator is 6 > the denominator: x = y - 6.

When both the numerator and denominator are increased by 1, the fraction becomes [tex]1/2: (x + 1)/(y + 1) = 1/2.[/tex]

Now, we can use these two equations to find the values of x and y and then the fraction x/y.

Step 1: Substitute x = y - 6 into the second equation:

((y - 6) + 1)/(y + 1) = 1/2

(y - 5)/(y + 1) = 1/2

Step 2: Cross-multiply:

2(y - 5) = y + 1

Step 3: Expand and solve for y:

2y - 10 = y + 1

2y - y = 1 + 10

y = 11

Step 4: Now that we have the value of y, find the value of x using the first equation:

x = y - 6

x = 11 - 6

x = 5

Answer:

Let denominator =x

thus numerator =x−6

By condition  

x

x−6+3

​

=

3

2

​

3(x−3)=2x

3x−9=2x

x=9

So denominator =x=9

thus numerator ⇒x−6=9−6=3

Original fraction =

9

3

​