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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) \(\frac{4}{3} - \frac{1}{2} \)

Answer :

(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
\(\frac{4×2}{3×2} - \frac{1×3}{2×3} \)
= \(\frac{8}{6} - \frac{3}{6} \)
= \(\frac{5}{6} \) \)