question_answer 28)

Find: (i) \[\frac{2}{5}\div \frac{1}{2}\]                (ii) \[\frac{4}{9}\div \frac{2}{3}\]                               (iii) \[\frac{3}{7}\div \frac{8}{7}\]                       (iv) \[2\frac{1}{3}\div \frac{3}{5}\] (v) \[3\frac{1}{2}\div \frac{8}{3}\]                             (vi) \[\frac{2}{5}\div 1\frac{1}{2}\]                            (vii) \[3\frac{1}{5}\div 1\frac{2}{3}\]                 (viii) \[2\frac{1}{5}\div 1\frac{1}{5}\].

Answer:

                (i) \[\frac{2}{5}\div \frac{1}{2}=\frac{2}{5}\times \frac{2}{1}=\frac{2\times 2}{5\times 1}=\frac{4}{5}\] (ii) \[\frac{4}{9}\div \frac{2}{3}=\frac{4}{9}\times \frac{3}{2}=\frac{4\times 3}{9\times 2}=\frac{12}{18}=\frac{12\div 6}{18\div 6}=\frac{2}{3}\] (iii) \[\frac{3}{7}\div \frac{8}{7}=\frac{3}{7}\times \frac{7}{8}=\frac{3\times 7}{7\times 8}=\frac{21}{56}=\frac{21\div 7}{56\div 7}=\frac{3}{8}\] (iv)  \[2\frac{1}{3}\div \frac{3}{5}=\frac{7}{3}\div \frac{3}{5}=\frac{7}{3}\times \frac{5}{3}=\frac{7\times 5}{3\times 3}=\frac{35}{9}=3\frac{8}{9}\] (v) \[3\frac{1}{2}\div \frac{8}{3}=\frac{7}{2}\div \frac{8}{3}=\frac{7}{2}\times \frac{3}{8}=\frac{7\times 3}{2\times 8}=\frac{21}{16}=1\frac{5}{16}\] (vi) \[\frac{2}{5}\div 1\frac{1}{2}=\frac{2}{5}\div \frac{3}{2}=\frac{2}{5}\times \frac{2}{3}=\frac{2\times 2}{5\times 3}=\frac{4}{15}\] (vii) \[3\frac{1}{5}\div 1\frac{2}{3}=\frac{16}{5}\div \frac{5}{3}=\frac{16}{5}\times \frac{3}{5}=\frac{16\times 3}{5\times 5}\]\[=\frac{48}{25}=1\frac{23}{25}\]                 (viii) \[2\frac{1}{5}\div 1\frac{1}{5}=\frac{11}{5}\div \frac{6}{5}=\frac{11}{5}\times \frac{5}{6}=\frac{11\times 5}{5\times 6}=\frac{55}{30}\]\[=\frac{55\div 5}{30\div 5}=\frac{11}{6}=1\frac{5}{6}\]