question_answer

  Find five rational numbers between \[\frac{-5}{7}\] and\[\frac{-3}{8}\]?

Answer:

We have, \[\frac{-5}{7}=\frac{-5\times 8}{7\times 8}=\frac{-40}{56}\] and, \[\frac{-3}{8}=\frac{-3\times 7}{8\times 7}=\frac{-21}{56}\] We know that \[\frac{-40}{56}<\frac{-39}{56}<\frac{-38}{56}<\frac{-37}{56}<.....<\frac{-22}{56}<\frac{-21}{56}\]     Hence, five rational numbers between \[\frac{-5}{7}\] and \[\frac{-3}{8}\] may be taken as \[\frac{-39}{56},\frac{-38}{56},\frac{-37}{56},\frac{36}{56}\] and\[\frac{-35}{56}\].