(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

\(\frac{-12\times2}{5\times2}=\frac{-24}{10}\)

And,

\(\frac{43\times1}{10\times1}=\frac{43}{10}\)

Therefore,

\(\frac{-24}{10}+\frac{43}{10}=\frac{-24+43}{10}\)

= \(\frac{19}{10}\)

= \(1\frac{9}{10}\)

(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

\(\frac{24\times4}{7\times4}=\frac{96}{28}\)

And,

\(\frac{-11\times7}{4\times7}=\frac{-77}{28}\)

Therefore,

\(\frac{96}{28}-\frac{77}{28}=\frac{96-77}{28}\)

= \(\frac{19}{28}\)

= \(1\frac{9}{10}\)

(iii) The denominators of the given rational numbers 6 and 8 respectively.

The L.C.M of 6 and 8 is 24

Now,

We write the given rational numbers into forms in which both of them have the same denominator

\(\frac{-31\times4}{6\times4}=\frac{-124}{24}\)

And,

\(\frac{-27\times3}{8\times3}=\frac{-81}{24}\)

Therefore,

\(\frac{-124}{24}-\frac{81}{24}=\frac{-124-81}{24}\)

= \(\frac{-205}{24}\)

 \(-8\frac{13}{24}\)

(iv) The denominators of the given rational numbers 6 and 8 respectively.

The L.C.M of 6 and 8 is 24

Now,

We write the given rational numbers into forms in which both of them have the same denominator

\(\frac{101\times4}{6\times4}=\frac{404}{24}\)

And,

\(\frac{7\times3}{8\times3}=\frac{21}{24}\)

Therefore,

\(\frac{404}{24}+\frac{21}{24}=\frac{404+21}{24}\)

= \(\frac{425}{24}\)

= \(17\frac{17}{24}\)