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 :-

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

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

To Find:-

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

⇒  $\dfrac{1}{3} - \dfrac{4}{5} - \dfrac{3}{2} + \dfrac{6}{7}$

⇒  $\dfrac{70 - 168 - 315 + 180}{210}$                   [ Taking L.C.M ]

⇒  $\dfrac{-233}{210}$   ← $\ ans$

$(2).\ \ \dfrac{5}{14} \times \dfrac{-2}{11} \times \dfrac{-7}{10} \times \dfrac{33}{16}$

⇒  $\dfrac{1}{1} \times \dfrac{-1}{1} \times \dfrac{-1}{2} \times \dfrac{3}{16}$

⇒  $\dfrac{3}{32}$  ← $\ ans$

$(3). \ \ \dfrac{2}{5} \ \times\ \dfrac{4}{7} \ - \ \dfrac{1}{3} \ +\ \dfrac{4}{7} \ \times \ \dfrac{8}{5}$

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

⇒  $\dfrac{24 - 35 + 96}{105}$                         [ Taking L.C.M ]

⇒  $\dfrac{85}{105}$

⇒  $\dfrac{17}{21}$  ← $\ ans$

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

⇒  $\dfrac{9}{16}\bigg(\dfrac{4}{12} - \dfrac{3}{9}\bigg)$                   [ Taking common ]

∵ Distributive property = $x ( a + b ) = ( x \times a ) + ( x \times b )$

⇒  $\dfrac{9}{16} \times \dfrac{0}{36}$

⇒  $\dfrac{9}{16} \times 0$

⇒  0  ← $\ ans$

Answer 2

1. Find

$\frac{1}{3} \: + \: \bigg( \frac{ - 4}{5} \bigg) \: + \: \bigg( \frac{- 3}{2} \bigg) \: + \: \frac{6}{7} \\ \\ \implies \bigg[ \frac{1}{3} \: + \: \bigg( \frac{ - 4}{5} \bigg) \bigg] \: + \bigg[ \bigg( \frac{- 3}{2} \bigg) \: + \: \frac{6}{7} \bigg] \\ \\ \sf{\to \: \red{take \: L.CM}} \\ \\ \implies \bigg[\frac{5 + ( - 12)}{15} \bigg] + \bigg[ \frac{( - 21) + 12}{14} \bigg] \\ \\ \implies\bigg[ \frac{ - 7}{15} \bigg] + \bigg[ \frac{ - 9}{14} \bigg] \\ \\ \sf{\to \: \red{take \: L.CM}} \\ \\ \implies \frac{ - 98 + ( - 135)}{210} \\ \\ \implies \green{\frac{ - 233}{210} }$

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2. Find

$\frac{5}{14} \: \times \: \frac{ - 2}{11} \: \times \: \frac{ - 7}{10} \: \times \: \frac{33}{16} \\ \\ \implies\bigg[ \frac{5}{14} \: \times \: \frac{ - 2}{11} \bigg] \times \: \frac{ - 7}{10} \: \times \: \frac{33}{16} \\ \\ \implies \bigg[ \frac{ - 5}{77} \bigg] \times \frac{ - 7}{10} \: \times \: \frac{33}{16} \\ \\ \implies \red{ \frac{3}{32}}$

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3. Find

$\frac{2}{5} \: \times \: \frac{4}{7} \: - \: \frac{1}{3} \: + \: \frac{4}{7} \: \times \: \frac{8}{5} \\ \\ \implies \frac{8}{35} - \frac{1}{3} +\frac{28}{35}\\ \\ \implies \frac{36}{35} - \frac{1}{3}\\ \\ \implies \frac{108 - 35}{105} \\ \\ \implies \blue{ \frac{73}{105} }$

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4. Find using distributivity :-

$\bigg( \frac{9}{16} \: \times \: \frac{4}{12} \bigg) \: + \: \bigg( \frac{9}{16} \: \times \: \frac{ - 3}{9} \bigg) \\ \\ \implies\frac{9}{16} \times \bigg[ \frac{4}{12}+\frac{ - 3}{9} \bigg] \\ \\ \implies\frac{9}{16} \times \bigg[ \frac{1}{3} + \frac{ - 1}{3}\bigg] \\ \\ \implies\frac{9}{16} \times 0 \\ \\ \implies \pink{0}$

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