(i) The denominator of given rational numbers are 4 and 8 respectively

The L.C.M. of 4 and 8 is 8

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{3\times 2}{4\times 2} = \frac{6}{8}\) and \(\frac{-5}{8}\)

Therefore,

\(\frac{6}{8}\, -\, \frac{5}{8}\, =\, \frac{6-5}{8}\)

\(= \frac{1}{8}\)

(ii) The denominator of given rational numbers are 9 and 3 respectively

The L.C.M of 9 and 3 is 9

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{-5\times 1}{9\times 1} = \frac{-5}{9} \) and \(\frac{7\times 3}{3\times 3} = \frac{21}{9}\)

Therefore,

\(\frac{-5}{9} + \frac{21}{9} = \frac{-5+21}{9}\)

\(= \frac{16}{9}\)

(iii) The denominator of given rational numbers are 1 and 5 respectively 

The L.C.M of 1 and 5 is 5 

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{-3\times 5}{1\times 5} = \frac{-3\times 5}{5}\) and \(\frac{3}{5}\)

Therefore,

\(\frac{-15}{5} + \frac{3}{5} = \frac{3-15}{5}\)

\(= \frac{-12}{5}\)

(iv) The denominator of given rational numbers are 27 and 18 respectively

The L.C.M of 27 and 18 is 54

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{-7}{27} = \frac{-7\times 2}{27\times 2}\)

= \(\frac{-14}{54}\)

And,

\(\frac{11}{18} = \frac{11\times 3}{18\times 3}\)

= \(\frac{33}{54}\)

Therefore,

\((\frac{-7\times2}{27\times 2}) + \frac{33}{54}\)

= \(\frac{33}{54} - \frac{14}{54}\)

= \(\frac{33-14}{54}\)

= \(\frac{19}{54}\)

(v) The denominator of given rational numbers are -4 and 8 respectively

The L.C.M of -4 and 8 is 8

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{31}{4} = \frac{31\times 2}{-4\times 2}\)

= \(\frac{-62}{8}\)

And,

\(\frac{5}{8}\)

Therefore,

\((\frac{-31\times 2}{4\times 2}) + \frac{-5}{8}\)

= \(\frac{-62}{8} - \frac{5}{8}\)

= \(\frac{-67}{8}\)

(vi) The denominator of given rational numbers are 36 and 12 respectively 

The L.C.M of 36 and 12 is 36 

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{-7\times3}{12\times 3} = \frac{-21}{36}\)

And,

\(\frac{5}{36}\)

Therefore,

\(\frac{5}{36} - \frac{21}{36}\)

= \(\frac{-16}{36}\)

= \(\frac{-4}{9}\)

(vii) The denominator of given rational numbers are 16 and 24 respectively 

The L.C.M of 16 and 24 is 48 

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{-5}{16} = \frac{-5\times 3}{16\times 3}\)

= \(\frac{-15}{48}\)

And,

\(\frac{7}{24} = \frac{7\times 2}{24\times 2}\)

= \(\frac{14}{48}\)

Therefore,

\(\frac{-5}{16} + \frac{7}{24}\)

= \(\frac{-15}{48} + \frac{14}{48}\)

= \(\frac{-1}{48}\)

(viii) The denominator of given rational numbers are -4 and 8 respectively

The L.C.M of 18 and 27 is 54

Now, we rewrite the given rational numbers into forms in which both of them have the same denominator

\(\frac{7}{-18} = \frac{7\times 3}{-18\times 3}\)

= \(\frac{-21}{54}\)

And,

\(\frac{8\times 2}{27\times 2}\) = \(\frac{16}{54}\)

Therefore,

\(\frac{-21}{54} + \frac{16}{54}\)

= \(\frac{16-21}{54}\)

= \(\frac{-5}{54}\)