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The sum of two rational numbers is \(\frac{-1}{2}\). If one of the numbers is \(\frac{5}{6}\), find the other.

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Sum of two rational numbers = \(\frac{-1}{2}\)

One number = \(\frac{5}{6}\)

Let the other rational number = x


According to question,

\(\frac{5}{6}+\) x \(=\frac{-1}{2}\) 

\(\Rightarrow\) x \(=\frac{-1}{2}-\frac{5}{6}\)

\(\Rightarrow\) x \(= \frac{-3-5}{6}\)

\(\Rightarrow\) x \(=\frac{-8}{6}\)

In lowest terms,

\(= \frac{-8÷2}{6÷2}= \frac{-4}{3}\)

Therefore, the other rational number is \(\frac{-4}{3}\)

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