(i) \(\frac{2}{3}-\frac{3}{5}\)

= \(\frac{2\times 5-3\times 3}{15}\)

= \(\frac{10-9}{15}\)

= \(\frac{1}{15}\)

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

= \(\frac{-4\times 3+2\times 7}{21}\)

= \(\frac{-12+14}{21}\)

= \(\frac{2}{21}\)

(iii) \(\frac{4}{7}-\frac{5}{7}\)

= \(\frac{4\times 1-5\times 1}{7}\)

= \(\frac{4-5}{7}\)

= \(\frac{-1}{7}\)

(iv) \(-2-\frac{5}{9}\)

= \(\frac{-2\times 9-5\times 1}{9}\)

= \(\frac{-18-5}{9}\)

= \(\frac{-23}{9}\)

(v) \(\frac{3}{8}+\frac{2}{7}\)

= \(\frac{3\times 7+2\times 8}{56}\)

= \(\frac{21+16}{56}\)

= \(\frac{37}{56}\)

(vi) \(\frac{-4}{13}+\frac{5}{26}\)

= \(\frac{-4\times 2+5\times 1}{26}\)

= \(\frac{-8+5}{26}\)

= \(\frac{-3}{26}\)

(vii) \(\frac{-5}{14}+\frac{2}{7}\)

= \(\frac{-5\times 1+2\times 2}{14}\)

= \(\frac{-5+4}{14}\)

= \(\frac{-1}{14}\)

(viii) \(\frac{13}{15}-\frac{12}{25}\)

= \(\frac{13\times 5-12\times 3}{75}\)

= \(\frac{65-36}{75}\)

= \(\frac{29}{75}\)

(ix) \(\frac{-6}{13}+\frac{7}{13}\)

= \(\frac{-6\times 1+7\times 1}{13}\)

= \(\frac{-6+7}{13}\)

= \(\frac{1}{13}\)

(x) \(\frac{7}{24}-\frac{19}{36}\)

= \(\frac{7\times 3-19\times 2}{72}\)

= \(\frac{21-38}{72}\)

= \(\frac{-17}{72}\)

(xi) \(\frac{5}{63}+\frac{8}{21}\)

= \(\frac{5\times 1+8\times 3}{63}\)

= \(\frac{5+24}{63}\)

= \(\frac{29}{63}\)