question_answer 18)

Multiply and reduce to lowest form (if possible): (i) \[\frac{2}{3}\times 2\frac{2}{3}\]                       (ii) \[\frac{2}{7}\times \frac{7}{9}\]                          (iii) \[\frac{3}{8}\times \frac{6}{4}\]                              (iv) \[\frac{9}{5}\times \frac{3}{5}\] (v) \[\frac{1}{3}\times \frac{15}{8}\]                     (vi) \[\frac{11}{2}\times \frac{3}{10}\]                    (vii) \[\frac{4}{5}\times \frac{12}{7}\]

Answer:

                (i) \[\frac{2}{3}\times 2\frac{2}{3}=\frac{2}{3}\times \frac{8}{3}=\frac{16}{9}\]                 (ii) \[\frac{2}{7}\times \frac{7}{9}=\frac{2\times 7}{7\times 9}=\frac{14}{63}=\frac{14\div 7}{63\div 7}=\frac{2}{9}\]                 (iii) \[\frac{3}{8}\times \frac{6}{4}=\frac{3\times 6}{8\times 4}=\frac{18}{32}=\frac{18\div 2}{32\div 2}=\frac{9}{16}\]                 (iv) \[\frac{9}{5}\times \frac{3}{5}=\frac{9\times 3}{5\times 5}=\frac{27}{25}\] (v) \[\frac{1}{3}\times \frac{15}{8}=\frac{1\times 15}{3\times 8}=\frac{15}{24}=\frac{15\div 3}{24\div 3}=\frac{5}{8}\] (vi) \[\frac{11}{2}\times \frac{3}{10}=\frac{11\times 3}{2\times 10}=\frac{33}{20}\] (vii) \[\frac{4}{5}\times \frac{12}{7}=\frac{4\times 12}{5\times 7}=\frac{48}{35}\]