Question

Write a pair of fractions whose sum is `7/11` and difference is `2/11`.

Answer 1

Let a and b be the pair of fractions whose sum is `7/11` and difference is `2/11`, then 

a + b = `7/11`  .....(i)

And a – b = `2/11`  .....(ii)

On adding equations (i) and (ii), we get

(a + b) + (a – b) = `7/11 + 2/11`

⇒ a + b + a – b = `(7 + 2)/11`

⇒ 2a = `9/11`

⇒ a = `9/(11 xx 2) = 9/22`

On substituting the value of a in equation (i), we get

`9/22 + b = 7/11` 

⇒ b = `(7 xx 2)/(11 xx 2) - 9/22`  .....`[(because  "LCM of 11 and 22 is 22, so covert each"),("of the given fraction to an equivalent"),("fraction with denominator"  22.)]`

⇒ b = `14/22 - 9/22`

⇒ b = `(14 - 9)/22 = 5/22`

So, `9/22` and `5/22` is a pair of fractions, whose sum is `7/11` and difference is `2/11.`