# Q.1 Solve (a)$$\frac{2}{3} + \frac{1}{7}$$ (b)$$\frac{3}{10} + \frac{7}{15}$$ (c) $$\frac{4}{9} + \frac{2}{7}$$ (d) $$\frac{5}{7} + \frac{1}{3}$$ (e) $$\frac{2}{5} + \frac{1}{6}$$ (f) $$\frac{4}{5} + \frac{2}{3}$$ (g) $$\frac{3}{4} - \frac{1}{3}$$ (h) $$\frac{5}{6} - \frac{1}{3}$$ (i) $$\frac{2}{3} + \frac{3}{4} + \frac{1}{2}$$ (j) $$\frac{1}{2} + \frac{1}{3} + \frac{1}{6}$$ (k) $$1\frac{1}{3} + 3\frac{2}{3}$$ (l) $$4\frac{2}{3} + 3\frac{1}{4}$$ (m) $$\frac{16}{5} - \frac{7}{5}$$ (n) $$\frac{4}{3} - \frac{1}{2}$$

(a)$$\frac{2}{3} + \frac{1}{7}$$
LCM of 7 and 3 = 21
$$\frac{2×7}{3×7} + \frac{1×3}{7×3}$$
= $$\frac{14}{21} + \frac{3}{21}$$
= $$\frac{17}{21}$$
(b)$$\frac{3}{10} + \frac{7}{15}$$
LCM of 10 and 15 = 30
$$\frac{3×3}{10×3} + \frac{7×2}{15×2}$$
= $$\frac{9}{30} + \frac{14}{30}$$
= $$\frac{23}{30}$$
(c) $$\frac{4}{9} + \frac{2}{7}$$
LCM of 9 and 7 = 63
$$\frac{4×7}{9×7} + \frac{2×9}{7×9}$$
= $$\frac{28}{63} + \frac{18}{63}$$
= $$\frac{46}{63}$$
(d) $$\frac{5}{7} + \frac{1}{3}$$
LCM of 7 and 3 = 21
$$\frac{5×3}{7×3} + \frac{1×7}{3×7}$$
= $$\frac{15}{21} + \frac{7}{21}$$
= $$\frac{22}{21}$$
(e) $$\frac{2}{5} + \frac{1}{6}$$
LCM of 5 and 6 = 30
$$\frac{2×6}{5×6} + \frac{1×5}{6×5}$$
= $$\frac{12}{30} + \frac{5}{30}$$
= $$\frac{17}{30}$$
(f) $$\frac{4}{5} + \frac{2}{3}$$
LCM of 5 and 3 = 15
$$\frac{4×3}{5×3} + \frac{2×5}{3×5}$$
= $$\frac{12}{15} + \frac{10}{15}$$
= $$\frac{22}{15}$$
(g) $$\frac{3}{4} - \frac{1}{3}$$
LCM of 4 and 3 = 12
$$\frac{3×3}{4×3} - \frac{1×4}{3×4}$$
= $$\frac{9}{12} - \frac{4}{12}$$
= $$\frac{5}{12}$$
(h) $$\frac{5}{6} - \frac{1}{3}$$
LCM of 6 and 3 = 6
$$\frac{5}{6} - \frac{1×2}{3×2}$$
= $$\frac{5}{6} - \frac{2}{6}$$
= $$\frac{3}{6}$$ = $$\frac{1}{2}$$
(i) $$\frac{2}{3} + \frac{3}{4} + \frac{1}{2}$$
LCM of 3, 4 and 2 = 12
$$\frac{2×4}{3×4} + \frac{3×3}{4×3} + \frac{1×6}{2×6}$$
$$\frac{8}{12} + \frac{9}{12} + \frac{6}{12}$$
$$\frac{23}{12}$$
(j) $$\frac{1}{2} + \frac{1}{3} + \frac{1}{6}$$
LCM of 2, 3 and 6 = 6
$$\frac{1×3}{2×3} + \frac{1×2}{3×2} + \frac{1}{6}$$
$$\frac{3}{6} + \frac{2}{6} + \frac{1}{6}$$
$$\frac{6}{6}$$ = 1
(k) $$1\frac{1}{3} + 3\frac{2}{3}$$
= $$\frac{4}{3} + \frac{11}{3}$$
= $$\frac{15}{3}$$ = 5
(l) $$4\frac{2}{3} + 3\frac{1}{4}$$
= $$\frac{14}{3} + \frac{13}{4}$$
LCM of 3 and 4 = 12
$$\frac{14×4}{3×4} + \frac{13×3}{4×3}$$
= $$\frac{56}{12} + \frac{39}{12}$$
= $$\frac{95}{12}$$ \)
(m) $$\frac{16}{5} - \frac{7}{5}$$
$$\frac{9}{5}$$ = $$1\frac{4}{5}$$
(n) $$\frac{4}{3} - \frac{1}{2}$$
LCM of 3 and 2 = 6
$$\frac{4×2}{3×2} - \frac{1×3}{2×3}$$
= $$\frac{8}{6} - \frac{3}{6}$$
= $$\frac{5}{6}$$ \)