Question

find the reciprocal of​

Answer 1

(v) |-5|

Reciprocal of |-5| = $\sf \dfrac{1}{5}$

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(vi) -1 3/8

Converting mixed fraction into simple fraction

$\sf \longmapsto \large| - 1 \dfrac{3}{8} \large| \\ \\ \sf\longmapsto \: \large| \dfrac{ - ( 8 \times 1+ 3}{8}) \large| \\ \\ \sf\longmapsto \large| \dfrac{ - 11 }{8}\large| \\ \\ \sf \longmapsto \dfrac{ 11}{8}$

Reciprocal of 11/8 = $\sf \dfrac{8}{11}$

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(vii)

$\longmapsto \large| - \{ \sf 2 \dfrac{3}{4} \} \large| \\ \\ \sf\longmapsto \large| - \{ \dfrac{11}{4} \} \large| \\ \\ \sf\longmapsto \dfrac{11}{4}$

Reciprocal of 11/4 = $\sf \dfrac{4}{11}$

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(viii)

$\sf\longmapsto \large| \dfrac{1}{6} - \dfrac{1}{4} \large| \\ \\ \sf\longmapsto \large| \dfrac{4 - 6}{24} \large| \\ \\ \sf\longmapsto \large| \dfrac{ - 2}{24 } \large| \\ \\ \sf\longmapsto \dfrac{1}{12}$

Reciprocal of 1/12 = 12/1

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(ix)

$\sf\longmapsto \: \large| - 1 \dfrac{3}{4} \times 2 \dfrac{5}{8} \large| \\ \\ \sf\longmapsto \: \large| \dfrac{ - 7}{4} \times \dfrac{21}{8} \large| \\ \\ \sf\longmapsto \: \large| \dfrac{ -147}{32} \large| \\ \\ \sf\longmapsto \dfrac{147}{32}$

Reciprocal of 147/32 = $\sf\dfrac{32}{147}$

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(x)

$\sf\longmapsto \large| \dfrac{ - 17}{81} \times \dfrac{ - 5}{34} \times | \dfrac{ - 9}{5} \large| \\ \\ \sf\longmapsto \large| \: \dfrac{ - 1 \times - 1 \times - 1}{9 \times 2 \times 1} \: \large| \\ \\ \sf\longmapsto \: \large| \: \dfrac{ - 1}{8} \large| \: \\ \\ \sf \longmapsto \dfrac{1}{8} \:$

Reciprocal of 1/8 = 8/1

Answer 2

${\large{\bold{\sf{\underline{Questions}}}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 5}}}$

${\bold{\bf{|- 5 |}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 6}}}$

${\bold{\bf{| - 1 \dfrac{3}{8} |}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 7}}}$

${\bold{\bf{ - |2 \dfrac{3}{4} |}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 8}}}$

${\bold{\bf{ | \dfrac{1}{6} - \dfrac{1}{4} |}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 9}}}$

${\bold{\bf{ - |1 \dfrac{3}{4} \times 2 \dfrac{5}{8} |}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 10}}}$

${\bold{\bf{ | - \dfrac{17}{81} \times \dfrac{ - 5}{34} \times \dfrac{ -9}{5} |}}}$

${\large{\bold{\sf{\underline{Answers}}}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Answer \: 5}}}$

${:\implies}$ ${\bold{\bf{|- 5 |}}}$

${:\implies}$ ${\bold{\bf{| \dfrac{-1}{5} |}}}$

${:\implies}$ ${\bold{\bf{\dfrac{1}{5}}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Answer \: 6}}}$

${:\implies}$ ${\bold{\bf{| - 1 \dfrac{3}{8} |}}}$

${:\implies}$ ${\bold{\bf{| \dfrac{-11}{8} |}}}$

${:\implies}$ ${\bold{\bf{| \dfrac{-8}{11} |}}}$

${:\implies}$ ${\bold{\bf{\dfrac{8}{11}}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Answer \: 7}}}$

${:\implies}$ ${\bold{\bf{ - |2 \dfrac{3}{4} |}}}$

${:\implies}$ ${\bold{\bf{- | \dfrac{11}{4} |}}}$

${:\implies}$ ${\bold{\bf{- | \dfrac{4}{11} |}}}$

${:\implies}$ ${\bold{\bf{\dfrac{-4}{11}}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Answer \: 8}}}$

${:\implies}$ ${\bold{\bf{ | \dfrac{1}{6} - \dfrac{1}{4} |}}}$

• Taking LCM

${:\implies}$ ${\bold{\bf{ | \dfrac{4-6}{24} |}}}$

${:\implies}$ ${\bold{\bf{ | \dfrac{-2}{24} |}}}$

${:\implies}$ ${\bold{\bf{ | \dfrac{-1}{24} |}}}$

${:\implies}$ ${\bold{\bf{ | -12 |}}}$

${:\implies}$ ${\bold{\bf{12}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Answer \: 9}}}$

${:\implies}$ ${\bold{\bf{-1 \dfrac{3}{4} \times 2 \dfrac{5}{8}}}}$

${:\implies}$ ${\bold{\bf{\dfrac{-7}{4} \times \dfrac{21}{8}}}}$

${:\implies}$ ${\bold{\bf{\dfrac{-147}{32}}}}$

${:\implies}$ ${\bold{\bf{\dfrac{-32}{147}}}}$

$\; \; \; \; \; \; \;{\bold{\sf{\longrightarrow Question \: 10}}}$

${:\implies}$ ${\bold{\bf{ | - \dfrac{17}{81} \times \dfrac{ - 5}{34} \times \dfrac{ -9}{5} |}}}$

• Cancelling the digits

${:\implies}$ ${\bold{\bf{ | - \dfrac{1}{9} \times \dfrac{ -1}{2} \times \dfrac{ -1}{1} |}}}$

${:\implies}$ ${\bold{\bf{|\dfrac{-1}{8}| }}}$

${:\implies}$ ${\bold{\bf{8}}}$

$\rule{150}{2}$

Remember : Inside | | the negative numbers are be positive by themselves. Means no number still negative inside it , they be positive when open.