Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:
(i)`2/5+8/3+(-11)/(15)+4/5+(-2)/3`
(ii) `4/7+\ 0+(-8)/9+(-13)/7+(17)/(21)`

Explanation

(i)`2/5+8/3+(-11)/(15)+4/5+(-2)/3`
`=(2+4)/(5)+(8-2)/(3)-11/15`
`=6/5+6/3-11/15`
Taking `15` as LCM of `3,5,15`.
`=(6xx3+6xx5-11xx1)/(15)`
`=(18+30-11)/(15)`
`=37/15`

(ii) `4/7+\ 0+(-8)/9+(-13)/7+(17)/(21)`
`=(4-13)/7-8/9+17/21`
`=-9/7-8/9+17/21`
Taking `63` as LCM of `7,9,21`.
`=(-9xx9-8xx7+17xx3)/(63)`
`=(-81-56+51)/(63)`
`=-86/63`