Question

Write a pair of fractions whose sum is 7/11and difference is 3/11

Answer 1

`(5)/(11)` and
`(2)/(11)`

Explanation:

let the 2 fractions be x and y , x > y , then

x + y =
`(7)/(11)` → (1)

x - y =
`(3)/(11)` → (2)

add the 2 equations term by term to eliminate y

2x + 0 =
`(10)/(11)`

2x =
`(10)/(11)` ( divide both sides by 2 )

x =
`(5)/(11)`

substitute x =
`(5)/(11)` into (1) and solve for y

`(5)/(11)` + y =
`(7)/(11)` ( subtract
`(5)/(11)` from both sides )

y =
`(2)/(11)`

the pair of fractions are
`(5)/(11)` and
`(2)/(11)`

Answer 2

If;

• 
  `(x)/(11)=a` and
• 
  `(y)/(11) =b`

then these variables must meet the following conditions below;

• 
  `a+b=(7)/(11)`
• 
  `a-b=(3)/(11)`

In rational expressions (fractional numbers), if the denominators are equal, arithmetic operations are performed with the numerators. Therefore;

• 
  `x+y=7`
• 
  `x-y=3`

If we add both equations at the same time, we get the following result;

• 
  `x+y+x-y=7+3`
• 
  `2x=10`
• 
  `x=5`

Now that we have found the unknown x, we can find the unknown y.

• 
  `x+y=7`
• 
  `5+y=7`
• 
  `y=2`

Now let's write our fraction pairs.

• 
  `((5)/(11),(2)/(11) )`