(9) Rational number between \(\frac{-1}{3}\) and \(\frac{1}{2}\)
\(=\frac{1}{2}(\frac{-1}{3}+\frac{1}{2})\)
\(=\frac{1}{2}(\frac{-1\times2+1\times3}{6})\)
\(=\frac{1}{2}(\frac{-2+3}{6})\)
= \(\frac{1}{2}\times\frac{1}{6}\)
= \(\frac{1}{12}\)
Now,
\(=\frac{1}{2}(\frac{1}{12}+\frac{1}{2})\)
\(=\frac{1}{2}(\frac{1+6}{12})\)
\(=\frac{1}{2}\times\frac{7}{12}\)
\(=\frac{7}{24}\)
(13) The correct option is (a) \(\frac{5}{6}\).
Let the other number be x
Then,
\(\frac{-3}{10}\times\text{x}=\frac{-1}{4}\)
\(\Rightarrow\) \(\text{x}=\frac{-1}{4}\div\frac{-3}{10}\)
\(\Rightarrow\) \(\text{x}=\frac{-1}{4}\times\frac{10}{-3}\)
\(\Rightarrow\) \(\text{x}=\frac{-1\times10}{4\times-3}\)
\(\Rightarrow\) \(\text{x}=\frac{-10}{-12}=\frac{-10\times-1}{-12\times-1}=\frac{10}{12}\)
\(\Rightarrow\) \(\text{x}=\frac{10}{12}=\frac{10\div2}{12\div2}=\frac{5}{6}\)
(15) \(\frac{4}{3} \div ? = \frac{-5}{2}\)
\(\frac{-4}{3} ÷ x = \frac{-5}{2}\)
\(\frac{-4}{3} × \frac{1}{x} = \frac{-5}{2}\)
\(\frac{1}{x} = \frac{-5}{2} × \frac{-3}{4}\)
\(\frac{1}{x} = \frac{15}{8}\)
\({x} = \frac{8}{15}\)
