Class 7 Operations on Rational Numbers Exercise 5.5

\begin{array}{l} \text {Q1. Find six rational numbers between } \frac{-4}{8} \text { and } \frac{3}{8} \end{array}\begin{array}{l} \text {Sol. } \\ \text {We know that -3,-2,-1,0,1,2 lies between -4 and 3} \\ \therefore \text {Six rational numbers between } \frac{-4}{8} \text { and } \frac{3}{8} \text { are } \\ \\\frac{-3}{8},\frac{-2}{8},\frac{-1}{8},0,\frac{1}{8},\frac{2}{8},\frac{3}{8} \\ \end{array}\begin{array}{l} \text {Q2. Find 10 rational numbers between } \frac{7}{13} \text { and } \frac{-4}{13} \end{array}\begin{array}{l} \text {Sol. } \\ \text {We know that -3,-2,-1,0,1,2,3,4,5,6 lies between -4 and 7 } \\ \therefore \text {10 rational numbers between } \frac{7}{13} \text { and } \frac{-4}{13} \text { are } \\ \\\frac{-3}{13},\frac{-3}{13},\frac{-3}{13},\frac{0}{13},\frac{1}{13},\frac{2}{13},\frac{3}{13},\frac{4}{13},\frac{5}{13},\frac{6}{13} \end{array}\begin{array}{l} \text {Q3. State true or false: } \\ \text {(i) Between any two distinct integers there is always an integer.} \\ \text {(ii) Between any two distinct rational numbers there is always a rational number. } \\ \text {(iii) Between any two distinct rational numbers there are infinitely many rational numbers.} \end{array}\begin{array}{l} \text {Sol. } \\ \text {(i) False.} \\ \text {(ii) True. According to the properties of rational numbers between any two distinct rational numbers there is always a rational number.} \\ \text {(iii) True. According to the properties of rational numbers between any two distinct rational numbers there are infinitely many rational numbers.} \end{array}