# Q.1 Find the sum: (i) $$\frac{5}{4}$$ +( $$\frac{-11}{4}$$) (ii) $$\frac{5}{3}$$ + $$\frac{3}{5}$$ (iii) $$\frac{-9}{10}$$ + $$\frac{22}{15}$$ (iv) $$\frac{-3}{-11}$$ + $$\frac{5}{9}$$ (v) $$\frac{-8}{-19}$$ + $$\frac{(-2)}{57}$$ (vi) $$\frac{-2}{3}$$ + 0 (vii) $$-2\frac{1}{3}$$ + $$4\frac{3}{5}$$

(i) $$\frac{5}{4}$$ +( $$\frac{-11}{4}$$) =$$\frac{5}{4}$$ -$$\frac{11}{4}$$ = $$\frac{5-11}{4}$$= $$\frac{-6}{4}$$
(ii) $$\frac{5}{3}$$ + $$\frac{3}{5}$$ = $$\frac{5×5}{3×5}$$ + $$\frac{3×3}{5×3}$$
= $$\frac{25}{15}$$ + $$\frac{9}{15}$$ = $$\frac{25+9}{15}$$ =$$\frac{25+9}{15}$$ =$$\frac{34 }{15}$$ = $$2\frac{4}{15}$$
(iii) $$\frac{-9}{10}$$ + $$\frac{22}{15}$$ = $$\frac{-9×3}{10×3}$$ + $$\frac{22×2}{15×2}$$=$$\frac{-27}{30}$$ + $$\frac{44}{30}$$ = $$\frac{-27+44}{30}$$ =$$\frac{17}{30}$$
(iv) $$\frac{-3}{-11}$$ + $$\frac{5}{9}$$ = $$\frac{3×9}{11×9}$$ + $$\frac{5×11}{9×11}$$ =$$\frac{27}{99}$$ + $$\frac{55}{99}$$ = $$\frac{27+55}{99}$$ =$$\frac{82}{99}$$
(v) $$\frac{-8}{-19}$$ + $$\frac{(-2)}{57}$$ =$$\frac{8}{19}$$ - $$\frac{2}{57}$$ = $$\frac{8×3}{19×3}$$ - $$\frac{2}{57}$$=$$\frac{24-2}{57}$$ =$$\frac{22}{57}$$
(vi) $$\frac{-2}{3}$$ + 0 = $$\frac{-2}{3}$$
(vii) $$-2\frac{1}{3}$$ + $$4\frac{3}{5}$$= $$\frac{-7}{3}$$ + $$\frac{23}{5}$$
= $$\frac{-7×5}{3×5}$$ + $$\frac{23×3}{5×3}$$ = $$\frac{-35}{15}$$ + $$\frac{69}{15}$$
= $$\frac{-35+69}{15}$$=$$\frac{34}{15}$$=$$2\frac{4}{15}$$