Question

What should be added to twice the rational number `(-7)/3 "to get" 3/7`?

Answer 1

Twice the rational number `((-7)/3)  "is"  2 xx ((-7)/3) = (-14)/3`.

Suppose x added to this number gives `3/7`; i.e.,

`x + ((-14)/3) = 3/7`

or `x - 14/3 = 3/7`

or `x = 3/7 + 14/3`         .......(transposing `14/3` to RHS)

or `x= ((3 xx 3) + (14 xx 7))/21`

or `x = (9 + 98)/21`

or `x = 107/21`.

Thus, `107/21 "should be added to" 2 xx ((-7)/3) "to give" 3/7.`