**Q1. Is 0 a rational number? Can you write it in the form \(\frac{P}{Q}\), where P and Q are integers and Q ≠ 0? **

**Solution:**

Yes, 0 is a rational number and it can be written in \(P\div Q\)

0 is an integer and it can be written various forms, for example

\(0\div 2 , 0\div 100 , 0\div 95\)

**Q2. Find five rational numbers between 1 and 2**

**Solution:**

Given that to find out 5 rational numbers between 1 and 2

- Rational number lying between 1 and 2

= \(\frac{1+2}{2}\)

= \(\frac{3}{2}\)

= \(1<\frac{3}{2}<2\)

- Rational number lying between 1 and \(\frac{3}{2}\)

= \(\frac{1+\frac{3}{2}}{2}\)

= \(\frac{5}{4}\)

= \(1< \frac{5}{4}<\frac{3}{2}\)

- Rational number lying between 1 and \(\frac{5}{4}\)

= \(\frac{1+\frac{5}{4}}{2}\)

= \(\frac{9}{8}\)

= \(1<\frac{9}{8}<\frac{5}{4}\)

- Rational number lying between \(\frac{3}{2}\)
and 2

= \(\frac{\frac{3}{2}+2}{2}\)

= \(\frac{7}{4}\)

= \(\frac{3}{2}<\frac{7}{4}<2\)

- Rational number lying between \(\frac{7}{4}\)
and 2

= \(\frac{\frac{7}{4}+2}{2}\)

= \(\frac{15}{8}\)

= \(\frac{7}{4}<\frac{15}{8}<2\)

Therefore, \(1<\frac{9}{8}<\frac{5}{4}<\frac{3}{2}<\frac{7}{4}<\frac{15}{8}<2\)

**Q3. Find out 6 rational numbers between 3 and 4**

**Solution: **

Given that to find out 6 rational numbers between 3 and 4

We have,

3 \(\times \frac{7}{7}\)

4 \(\times \frac{6}{6}\)

We know 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28

- \(\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}\)
- \(3<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<4\)

Therefore, 6 rational numbers between 3 and 4 are

\(\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}\)

Similarly to find 5 rational numbers between 3 and 4, multiply 3 and 4 respectively with \(\frac{6}{6}\)

**Q4. Find 5 rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\)**

**Solution :** Given to find out the 5 rational numbers between \(\frac{3}{5}\)

To find 5 rational numbers between \(\frac{3}{5}\)

We have,

\(\frac{3}{5}\)

\(\frac{4}{5}\)

We know 18 < 19 < 20 < 21 < 22 < 23 < 24

- \(\frac{18}{30}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{24}{30}\)
- \(\frac{3}{5}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{4}{5}\)

Therefore, 5 rational numbers between \(\frac{3}{5}\)

**Q5. Answer whether the following statements are true or false? Give reasons in support of your answer.**

** (i) Every whole number is a rational number**

**(ii) Every integer is a rational number**

**(iii) Every rational number is an integer**

**(iv) Every natural number is a whole number**

**(v) Every integer is a whole number**

**(vi) Every rational number is a whole number**

**Solution:**

(i) True. As whole numbers include and they can be represented

For example – \(\frac{0}{10},\frac{1}{1},\frac{2}{1},\frac{3}{1}\)

(ii) True. As we know 1, 2, 3, 4 and so on, are integers and they can be represented in the form of \(\frac{1}{1},\frac{2}{1},\frac{3}{1} \frac{4}{1}\)

(iii) False. Numbers such as \(\frac{3}{2},\frac{1}{2},\frac{3}{5},\frac{4}{5}\)

(iv) True. Whole numbers include all of the natural numbers.

(v) False. As we know whole numbers are a part of integers.

(vi) False. Integers include -1, -2, -3 and so on….. .which is not whole number