question_answer

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)

\[=\frac{9}{16}\left\{ \frac{4}{12}-\frac{3}{9} \right\}=\frac{9}{16}\left\{ \frac{12-12}{36} \right\}\]

\[=\frac{9}{16}\times 0=0\]