Add and express the sum as a mixed fraction: `(-12)/5` and `(43)/(10)` (ii) `(24)/7` and `(-11)/4`

Explanation

(i) The denominators of the given rational numbers `5` and `10` respectively.
The L.C.M of `5` and `10` is `10`
Now,
We write the given rational numbers into forms in which both of them have the same denominator
`(-12xx2)/(5xx2)=-24/10`
And ,
`(43xx1)/(10xx1)=(43/10)`
Therefore
`(-24/10)+(43/10)=((-24+43)/10)`
`(10/10)`
`1 (9/10)`
(ii) The denominators of the given rational numbers 7 and 4 respectively.
The L.C.M of 7 and 4 is 28
Now,
We write the given rational numbers into forms in which both of them have the same denominator
`(24xx4)/(7xx4)=(96/28)`
And
`(-11xx7)/(4xx7)=(-77/28)`
Therefore
`(96/28)+(-77/28)`
`((96-77)/(28))`
`(19/28)`