Question

1. Find :-

$\frac{1}{3} \: + \: \bigg( \frac{ - 4}{5} \bigg) \: + \: \bigg( \frac{- 3}{2} \bigg) \: + \: \frac{6}{7}$


2. Find :-

$\frac{5}{14} \: \times \: \frac{ - 2}{11} \: \times \: \frac{ - 7}{10} \: \times \: \frac{33}{16}$


3. Find :-

$\frac{2}{5} \: \times \: \frac{4}{7} \: - \: \frac{1}{3} \: + \: \frac{4}{7} \: \times \: \frac{8}{5}\ \textless \ br /\ \textgreater$


4. Find using distributivity :-

$\bigg( \frac{9}{16} \: \times \: \frac{4}{12} \bigg) \: + \: \bigg( \frac{9}{16} \: \times \: \frac{ - 3}{9} \bigg)$

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Answer 1

Question - 1

$\boxed{ \pink{ \sf\dfrac{1}{3} \: + \: \bigg( \dfrac{ - 4}{5} \bigg) \: + \: \bigg( \dfrac{- 3}{2} \bigg) \: + \: \dfrac{6}{7}}}$

$\sf \: First \: of \: all \: we \: have \: to \: make \: the \: denominator \: same.$

${\sf \dfrac{1 \times 70}{3 \times 70} + \dfrac{(-4) \times 42}{5 \times 42} + \dfrac{(-3) \times 105}{2 \times 105} + \dfrac{6 \times 30}{7 \times 30}}$

${\sf \dfrac{70}{210} + \dfrac{(-168)}{210} + \dfrac{(-315)}{210} + \dfrac{180}{210}}$

$\sf \: \underline{Taking \: denominator \: as \: common}$

${\sf \dfrac{70 + (-168) + (-315) + 180}{210}}$

$\sf \: \underline {Simplifying \: the \: Expression}$

${\sf \dfrac{70-168 - 315 + 180}{210}}$

$\longrightarrow \: \boxed{ \green{{\sf \:\dfrac{-233}{210}}}}$

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Question - 2

$\boxed{ \pink{\dfrac{5}{14} \: \times \: \dfrac{ - 2}{11} \: \times \: \dfrac{ - 7}{10} \: \times \: \dfrac{33}{16}}}$

$\sf\dfrac{5}{7} \: \times \: \dfrac{ - 1}{11} \: \times \: \dfrac{ - 7}{10} \: \times \: \dfrac{33}{16}$

$\sf \: \dfrac{5 \times - 1}{7 \times 11} \: \times \: \dfrac{ - 7}{10} \: \times \: \dfrac{33}{16}$

$\sf \sf \: \dfrac{ - 5 }{77} \: \times \: \dfrac{ - 7}{10} \: \times \: \dfrac{33}{16}$

$\sf \: \dfrac{ - 1 }{77} \: \times \: \dfrac{ - 7}{2} \: \times \: \dfrac{33}{16}$

$\sf \: \dfrac{ - 1 }{11} \: \times \: \dfrac{ -1}{2} \: \times \: \dfrac{33}{16}$

$\sf \: \: \dfrac{1}{22} \: \times \: \dfrac{33}{16}$

$\sf \: \: \dfrac{1}{2} \: \times \: \dfrac{3}{16}$

$\sf \: \longrightarrow \: \boxed{ \green{{\sf \:\dfrac{3}{32}}}}$

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Question - 3

$\boxed{ \pink{\sf \: \dfrac{2}{5} \: \times \: \dfrac{4}{7} \: - \: \dfrac{1}{3} \: + \: \dfrac{4}{7} \: \times \: \dfrac{8}{5}}}$

$\sf \: \dfrac{8}{35} \: - \: \dfrac{1}{3} \: + \: \dfrac{32}{35}$

$\sf \: \dfrac{40 }{35} \: + \: \dfrac{ - 1}{3}$

$\sf \: \dfrac{8}{7} \: - \: \dfrac{1}{3}$

$\sf \: \bigg(\dfrac{8}{7} \times \dfrac{3}{3} = \dfrac{24}{21} \bigg) \: - \: \bigg(\dfrac{1}{3} \times \dfrac{7}{7} = \dfrac{7}{21} \bigg)$

$\sf \: \dfrac{24 -7}{2}$

$\sf \: \longrightarrow \: \boxed{ \green{{\sf \:\dfrac{17}{21}}}}$

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Question - 4

$\boxed{ \pink{ \sf \: \bigg( \dfrac{9}{16} \: \times \: \dfrac{4}{12} \bigg) \: + \: \bigg( \dfrac{9}{16} \: \times \: \dfrac{ - 3}{9} \bigg)}}$

${\sf \: \dfrac{9}{16} \times \bigg( \dfrac{4}{12} + \dfrac{(-3)}{9} \bigg)}$

$\sf \: \dfrac{9}{16} \times \bigg( \dfrac{4 \times 9}{12 \times 9} + \dfrac{(-3) \times 12}{9 \times 12} \bigg)$

$\sf { \dfrac{9}{16} \times \bigg( \dfrac{36}{108} + \dfrac{(-36)}{108} \bigg)}$

$\sf { \dfrac{9}{16} \times \dfrac{36 - 36}{108} }$

$\sf { \dfrac{9}{16} \times \dfrac{0}{108} }$

$\sf { \dfrac{1}{16} \times \dfrac{0}{12} }$

$\sf { \dfrac{0}{16 - 12} }$

$\sf \: \longrightarrow \: \boxed{ \green{{\sf \large\:0 \: }}}$

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