Question

find two fraction F1 and F 2 with same denominator equal to 6 such that F1+ F2 =1 and F1-F2=2/3​

Answer 1

Answer:

 Fractions are 5 / 6 and 1 / 6

Step-by-step explanation:

Let x / 6 and y / 6 are fractions

Then according to first condition

              x / 6 + y / 6 = 1  ...........(1)

and according to second condition

             x / 6 -  y / 6 = 2 / 3  .............(2)

NOW

From equation (1)

             x / 6 + y / 6 = 1  

Multiplying by 6 on both sides we get

                       x + y = 6

⇒                          y = 6 - x        .........(3)

Putting "y = 6 - x" in equation (1) we get

                     x / 6 -  ( 6 - x ) / 6 = 2 / 3  

Multiplying by 6 both sides we get

               x  -  ( 6 - x )  = 4

⇒                  x - 6 + x = 4  

⇒                           2x = 4 +6

⇒                           2x = 10

⇒                              x = 5      

Putting "x = 5" in equation (3) we get

                               y = 6 - 5 = 1  

⇒                            y = 1

So

Fractions are 5 / 6 and 1 / 6

Checking:

5 / 6 + 1 / 6 = (1+5) / 6 = 6 / 6 = 1

5 / 6 - 1 / 6 = (5-1) / 6 = 4 / 6 = 2 / 3

Hence our solution is correct.