RD Sharma Solutions Class 7 Operations On Rational Numbers Exercise 5.5

RD Sharma Solutions Class 7 Chapter 5 Exercise 5.5

Exercise 5.5

Q1. Find six rational numbers between $\frac{-4}{8}$ and $\frac{3}{8}$

We know that

-4,-3,-2,-1,0,1,2,3

Therefore $\frac{-4}{8}$$\frac{-3}{8}$$\frac{-2}{8}$$\frac{-1}{8}$$\frac{0}{8}$$\frac{1}{8}$$\frac{2}{8}$$\frac{3}{8}$

Hence 6 rational numbers between $\frac{-4}{8}$ and $\frac{3}{8}$ are $\frac{-3}{8}$, $\frac{-2}{8}$, $\frac{-1}{8}$, $\frac{0}{8}$, $\frac{1}{8}$, $\frac{2}{8}$

Q2. Find 10 rational numbers between $\frac{7}{13}$ and $\frac{-4}{13}$

We know that

76543210-1-2-3-4

Therefore $\frac{7}{13}$ $\frac{6}{13}$ $\frac{5}{13}$ $\frac{4}{13}$ $\frac{3}{13}$ $\frac{2}{13}$ $\frac{1}{13}$ $\frac{0}{13}$ $\frac{-1}{13}$ $\frac{-2}{13}$ $\frac{-3}{13}$ $\frac{-4}{13}$

Hence the 10 rational numbers between $\frac{7}{13}$ and $\frac{-4}{13}$ are

$\frac{-3}{13}$, $\frac{-2}{13}$,$\frac{-1}{13}$,$\frac{0}{13}$,$\frac{1}{13}$,$\frac{2}{13}$,$\frac{3}{13}$,$\frac{4}{13}$,$\frac{5}{13}$,$\frac{6}{13}$, $\frac{7}{13}$,,

Q3. State true or false:

(i) Between any two distinct integers there is always an integer.

FALSE

(ii) Between any two distinct rational numbers there is always a rational number.

TRUE

(iii) Between any two distinct rational numbers there are infinitely many rational numbers.

TRUE