3 and 4 can be represented as 24/8 and 32/8 respectively.

Therefore, six rational numbers between 3 and 4 are

25/8, 26/8, 27/8, 28/8, 29/8, 30/8.

3/5 = 3×6 / 5×6 = 18 / 30

4/5 = 4×6 / 5×6 = 24/30

Therefore, five rational numbers between 3/5 and 4/5 are

19/30, 20/30, 21/30, 22/30, 23/30.

State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

ANS: True, since the collection of whole numbers contains all natural numbers.

(ii) Every integer is a whole number.

ANS: False, as integers may be negative but whole numbers are always positive.

(iii) Every rational number is a whole number.

ANS: False, as rational numbers may be fractional but whole numbers may not be.

(i) Every irrational number is a real number.

ANS: True, since the collection of real numbers is made up of rational and irrational numbers.

(ii) Every point on the number line is of the form√*m*, where m is a natural number.

ANS: False, since positive number cannot be expressed as square roots.

(iii) Every real number is an irrational number.

ANS: False, as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number.