Find using distributivity. |
(a) \[\left\{ \frac{7}{5}\times \left( \frac{-3}{12} \right) \right\}+\left\{ \frac{7}{5}\times \frac{5}{12} \right\}\] |
(b) \[\left\{ \frac{9}{16}\times \frac{4}{12} \right\}+\left\{ \frac{9}{16}\times \frac{-3}{9} \right\}\] |
Answer:
(a) \[\left\{ \frac{7}{5}\times \left( \frac{-3}{12} \right) \right\}+\left\{ \frac{7}{5}\times \frac{5}{12} \right\}=\frac{7}{5}\times \frac{-3}{12}+\frac{7}{5}\times \frac{5}{12}\] \[=\frac{7}{5}\left\{ \frac{-3}{12}+\frac{5}{12} \right\}\] (by distributivity) \[=\frac{7}{5}\left\{ \frac{-3+5}{12} \right\}\] \[=\frac{7}{5}\times \frac{2}{12}=\frac{14}{60}=\frac{7}{30}\] (b) \[\left\{ \frac{9}{16}\times \frac{4}{12} \right\}+\left\{ \frac{9}{16}\times \frac{-3}{9} \right\}=\frac{9}{16}\times \frac{4}{12}+\frac{9}{16}\times \frac{-3}{9}\] \[=\frac{9}{16}\left\{ \frac{4}{12}+\left( \frac{-3}{9} \right) \right\}\] (by distributivity) \[=\frac{9}{16}\left\{ \frac{4}{12}-\frac{3}{9} \right\}=\frac{9}{16}\left\{ \frac{12-12}{36} \right\}\] \[=\frac{9}{16}\times 0=0\]
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