Question

$- \frac{2}{5} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6} \ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater \ [tex]\frac{2}{5} \times ( - \frac{3}{7} ) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5}$

Help me pleass @shirley and my followings​

Answer 1

Step by step Explanation -

(i)

$\dashrightarrow \sf \: \bigg\{\dfrac{7}{5} \times \bigg( \dfrac{ - 3}{12} \bigg) \bigg\} + \bigg\{ \dfrac{7}{5} \times \dfrac{5}{12} \bigg\} \\ \\ \\\dashrightarrow\sf \: \dfrac{7}{5} \times \bigg\{ \dfrac{ - 3}{12} + \dfrac{5}{12} \bigg\} \\ \\ \\ \dashrightarrow \sf \dfrac{7}{5} \times \bigg\{ \dfrac{ - 3 + 5}{12} \bigg\} \\ \\ \\ \dashrightarrow\sf \dfrac{7}{5} \times \dfrac{2}{12} \\ \\ \\ \dashrightarrow \underline{\boxed{\sf{ \red{ \dfrac{7}{30} }}}}$

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(ii)

$\dashrightarrow \sf\: \bigg\{\dfrac{9}{16} \times \dfrac{ 4}{12} \bigg\} + \bigg\{ \dfrac{9}{16} \times \dfrac{ - 3}{9} \bigg\} \\\\\\\dashrightarrow\sf \:\dfrac{9}{16} \times \bigg\{ \dfrac{ 4}{12} + \dfrac{ - 3}{9} \bigg\} \\\\\\ \dashrightarrow \sf \dfrac{9}{16} \times \bigg\{ \dfrac{ 12 + -( 12)}{36}\bigg\} \\\\\\\dashrightarrow\sf \dfrac{9}{12} \times \dfrac{0}{36} \\\\\\\dashrightarrow \underline{\boxed{\sf{ \red{ {0} }}}}$

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Part 2:-

(i)

$\dashrightarrow\sf- \dfrac{2}{5} \times \dfrac{3}{5} + \dfrac{5}{2} - \dfrac{3}{5} \times \dfrac{1}{6} \\\\\\ \dashrightarrow \sf \dfrac{ - 2}{3} \times \dfrac{3}{5} - \dfrac{3}{5} \times \dfrac{1}{6} + \dfrac{5}{2} \\ \\\\ \dashrightarrow\sf \dfrac{ - 3}{5} \bigg( \dfrac{2}{3} + \dfrac{1}{6} \bigg) + \dfrac{5}{2}\\ \\ \\ \dashrightarrow \sf \dfrac{ - 3}{5}\bigg( \dfrac{4 + 1}{6} \bigg) + \dfrac{5}{2} \\ \\\\ \dashrightarrow \sf \frac{ - 3}{5} \times \dfrac{5}{6} + \dfrac{5}{2} \\ \\\\ \dashrightarrow \sf \dfrac{ - 1}{2} + \dfrac{5}{2} \\ \\ \\ \dashrightarrow \sf \dfrac{ - 1 + 5}{2} \\ \\ \\\dashrightarrow \sf \dfrac{4}{2} \\ \\\\ \dashrightarrow \underline{\boxed{\sf{ \red{2}}}}$

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(ii)

$\dashrightarrow\sf \: \: \dfrac{2}{5} \times ( - \dfrac{3}{7} ) - \dfrac{1}{6} \times \dfrac{3}{2} + \dfrac{1}{14} \times \dfrac{2}{5} \\ \\ \\ \dashrightarrow \sf \dfrac{2}{5} \times \dfrac{ - 3}{7} + \dfrac{1}{14} \times \dfrac{2}{5} - \dfrac{1}{6} \times \dfrac{3}{2} \\ \\\\ \dashrightarrow \sf \dfrac{2}{5} \bigg( \dfrac{ - 3}{7} + \frac{1}{14} \bigg) - \dfrac{1}{6} \times \dfrac{3}{2} \\ \\ \\ \dashrightarrow \sf \dfrac{2}{5} \bigg( \dfrac{ - 6 + 1}{14} \bigg) - \dfrac{1}{6} \times \dfrac{3}{2} \\ \\ \\ \dashrightarrow \sf \dfrac{2}{5} \times \dfrac{ - 5}{14} - \dfrac{1}{6} \times \dfrac{3}{2} \\ \\ \\ \dashrightarrow \sf \: { \dfrac{ - 1}{7} - \dfrac{1}{4} } \\ \\ \\ \dashrightarrow \sf \frac{ - 4 - 7}{28} \\ \\ \\ \dashrightarrow \underline{ \boxed{\sf { \red{\dfrac{ - 11}{28}} }}}$

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★ In part 2, we have solve both questions through commutative property then using distributive property..

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