RD Sharma solution class 7 chapter 5 Operations On Rational numbers Exercise 5.5

Exercise 5.5

Page-5.16

Question 1:

Find six rational numbers between $\frac{-4}{8}$ and $\frac{3}{8}$.

Answer 1:

 $$\begin{gathered} \mathrm{Since} -4<-3<-2<1<0<1<2<3, \\ \mathrm{six} \mathrm{rational} \mathrm{numbers} \mathrm{between}\frac{-4}{8} \mathrm{and} \frac{3}{8} \mathrm{are} \\ \frac{-3}{8}, \frac{-2}{8}, \frac{-1}{8}, \frac{0}{8},\frac{1}{8},\frac{2}{8} \end{gathered}$$

Question 2:

Find 10 rational numbers between $\frac{7}{13}$ and $\frac{-4}{13}$.

Answer 2:

Since

$$\begin{gathered} -4<-3<-2<-1<0<1<2<3<4<5<6<7, \\ 10 \mathrm{rational} \mathrm{numbers} \mathrm{between} \frac{7}{13} \mathrm{and} \frac{-4}{13}\mathrm{are}, \\ \frac{-3}{13},\frac{-2}{13}, \frac{-1}{13}, \frac{0}{13},\frac{1}{13},\frac{2}{13},\frac{3}{13}\frac{4}{13},\frac{5}{13},\frac{6}{13} \end{gathered}$$

Question 3:

State true or false:
(i) Between any two distinect integers there is always an linteger.
(ii) Between any two distinct rational numbers there is always a rational number.
(iii) Between any two distinct rational numbers there is always a rational number.

Answer 3:

(i) False, because there is no integer between 2 and 3.
(ii) True
(iii) True