Question 1: Is zero a rational number? Can you write it in the form \(\frac{p}{q}\), where p and q are integers and q ≠ 0?

Solution:
Yes, zero is a rational number. We can express 0 as: \[ 0 = \frac{0}{1} = \frac{0}{2} = \frac{0}{-3} = \cdots \] Here, p = 0 and q can be any non-zero integer. This satisfies all conditions of rational numbers.

Question 2: Find six rational numbers between 3 and 4.

Solution:
Convert numbers to equivalent fractions: \[ 3 = \frac{21}{7},\quad 4 = \frac{28}{7} \] Six rational numbers between them: \[ \frac{22}{7},\ \frac{23}{7},\ \frac{24}{7},\ \frac{25}{7},\ \frac{26}{7},\ \frac{27}{7} \] Alternatively: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6

Question 3: Find five rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\).

Solution:
Multiply numerator and denominator by 10: \[ \frac{3}{5} = \frac{30}{50},\quad \frac{4}{5} = \frac{40}{50} \] Five rational numbers between them: \[ \frac{31}{50},\ \frac{32}{50},\ \frac{34}{50},\ \frac{37}{50},\ \frac{39}{50} \] Simplified forms: \(\frac{31}{50},\ \frac{16}{25},\ \frac{17}{25},\ \frac{37}{50},\ \frac{39}{50}\)

Question 4: State true/false with reasons:

(i) Every natural number is a whole number.
True: Natural numbers (1,2,3…) are subset of whole numbers (0,1,2,3…)

(ii) Every integer is a whole number.
False: Negative integers (-1, -2) are not whole numbers

(iii) Every rational number is a whole number.
False: Rational numbers like \(\frac{1}{2}\) or \(-\frac{3}{4}\) aren’t whole numbers