Using appropriate properties find |
(a) \[-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}\] |
(b) \[\frac{2}{5}\times \left( -\frac{3}{7} \right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}\] |
Answer:
(a) \[-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}=-\frac{2}{3}\times \frac{3}{5}-\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}\] (by commutanvity) \[=\frac{3}{5}\left( -\frac{2}{3}-\frac{1}{6} \right)+\frac{5}{2}\] (by distributivity) \[=\frac{3}{5}\left( \frac{-4-1}{6} \right)+\frac{5}{2}\] \[=\frac{3}{5}\times \frac{-5}{6}+\frac{5}{2}\] \[=\frac{-1}{2}+\frac{5}{2}=2\] (b) \[\frac{2}{5}\times \left( \frac{-3}{7} \right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}=\frac{2}{5}\times \left( \frac{-3}{7} \right)+\frac{1}{14}\times \frac{2}{5}-\frac{1}{6}\times \frac{3}{2}\] (by associativity) \[=\frac{2}{5}\times \left( \frac{-3}{7}+\frac{1}{14} \right)-\frac{1}{4}\] (by distributivity) \[=\frac{2}{5}\left( \frac{-6+1}{14} \right)-\frac{1}{4}\] \[=\frac{2}{5}\times \frac{-5}{14}-\frac{1}{4}\] \[=-\frac{1}{7}-\frac{1}{4}=\frac{-4-7}{28}=\frac{-11}{28}\]
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