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By what rational number should \(\frac{-8}{39}\) be multiplied to obtain \(\frac{1}{26}?\)

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Let x be multiplied by \(\frac{-8}{39}\) to get \(\frac{1}{26}\)

It can be written as,

\(\frac{-8}{39}\times\) \(\text{x}=\frac{1}{26}\)

\(\Rightarrow\) \(\text{x}=\frac{1}{26}\div\frac{1}{26}\) 

\(\Rightarrow\) \(\text{x}=\frac{1}{26}\times\frac{39}{-8}\)

\(\Rightarrow\) \(\text{x}= \frac{1\times39}{26\times-8}\)

\(\Rightarrow\) \(\text{x}=\frac{39}{-208}=\frac{39\times-1}{-208\times-1}=\frac{-39}{208}\)

\(\Rightarrow\) \(\text{x}=\frac{-39}{208}=\frac{-39\div13}{208\div13}=\frac{-3}{16}\)

Hence, 

it should be multiplied by is \(\frac{-3}{16}\)

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