(i) Rearranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator

We have,

\(\frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}\)

\(\frac{2}{5}-\frac{4}{5}+\frac{7}{3}-\frac{1}{3}\) = \(\frac{-2}{5}+\frac{6}{3}\)

= \(\frac{-6}{15}+\frac{30}{15}\)

= \(\frac{24}{15}\)

= \(\frac{8}{5}\)

(ii) Rearranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator

We have,

\(\frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9}\)

\(\frac{3}{7}-\frac{11}{7}+\frac{7}{9}-\frac{4}{9}\) = \(\frac{-8}{7}+\frac{3}{9}\)

= \(\frac{-8}{7}+\frac{1}{3}\)

= \(\frac{-24}{21}+\frac{7}{21}\)

= \(\frac{-17}{21}\)

(iii) Rearranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator

We have,

\(\frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3}\)

\(\frac{2}{5}+\frac{4}{5}+\frac{8}{3}-\frac{2}{3}-\frac{11}{15}\) = \(\frac{6}{5}+\frac{8-2}{3}-\frac{11}{15}\)

= \(\frac{6}{5}+\frac{6}{3}+\frac{-11}{15}\)

= \(\frac{18}{15}+\frac{30}{15}-\frac{11}{15}\)

= \(\frac{18+30-11}{15}\)

= \(\frac{37}{15}\)

(iv) Rearranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator

We have,

\(\frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21}\)

\(\frac{4}{7}-\frac{13}{7}+0+\frac{-8}{9}+\frac{17}{21}\) = \(\frac{4-13}{7}+\frac{17}{21}-\frac{8}{9}\)

= \(\frac{-9}{7}+\frac{17}{21}-\frac{8}{9}\)

= \(\frac{-27+17}{21}-\frac{8}{9}\)

= \(\frac{-10\times9}{21\times 9}-\frac{8\times 21}{9\times 21}\)

= \(\frac{-90}{189}-\frac{168}{189}\)

= \(\frac{-258}{189}\)