question_answer 15)

                Find ten rational numbers between \[\frac{-2}{5}\] and \[\frac{1}{2}\].

Answer:

                \[\frac{-2}{5}\,=\frac{-2\times 2}{5\times 2}\,=\frac{-4}{10}\]                    | Converting them into rational numbers with the same denominators \[\frac{1}{2}=\frac{1\times 5}{2\times 5}\,=\frac{5}{10}\]                  Now,    \[\frac{-4}{10}=\frac{-4\times 2}{10\times 2}\,=\frac{-8}{20}\]    | Multiplying the numerator and denominator both by 2                 \[\frac{5}{10}\,=\frac{5\times 2}{10\times 2}\,=\frac{10}{20}\]                   | Multiplying the numerator and denominator both by 2                 Thus, ten rational numbers between \[\frac{-2}{5}\] and \[\frac{1}{2}\] may be taken as:                \[\frac{-7}{20},\,\frac{-6}{20},\,\frac{-5}{20},\,\frac{-4}{20},\,\frac{-3}{20},\,\frac{-2}{20},\] \[\frac{-1}{20},\,0,\,\frac{1}{20},\,\frac{2}{20}\].