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

Answer: –  Yes, zero is a rational number it can be written in the form pq. 0 = 0/1 = 0/2 = 0/3 etc. denominator q can also be taken as negative integer.

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

Answer : –

To find six rational numbers between 3 and 4 let’s follow the steps given below,

3 = 3 × (7/7) and 4 = 4 × (7/7)

3 = 21 / 7 and 4 = 28 / 7

Thus, we can choose 6 rational numbers as follows 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7 lying between 3 and 4.

Question 3  Find any five rational numbers between $\frac{\mathrm{3/}}{5}$ and $\frac{\mathrm{4/}}{5}$ .

Let us see how to find rational numbers between 3/5 and 4/5 using the following steps.

• Step 1: We need to find 5 rational numbers between 3/5 and 4/5. Let us use 6 as a multiplier. We will multiply and divide the numerator and denominator of 3/5 and 4/5 by 6. 3/5 = (3 × 6) ÷ (5 × 6) = 18/30. Similarly, 4/5 = (4 × 6) ÷ (5 × 6) = 24/30
• Step 2: Here, 18/30 and 24/30 are equivalent fractions for 3/5 and 4/5 respectively.
• Step 3: Finding a rational number between 3/5 and 4/5 is easy now because we will list down the numbers between the new numerators 18 and 24. In this way, we get, 19/30, 20/30, 21/30, 22/30 and 23/30
• Step 4: Thus, 5 rational numbers between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22/30 and 23/30.

Question 4  Statement whether the following statement are true or false. Give reasons for your answers :
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

Answer  (i) Every natural number is a whole number.

This statement is true because the set of natural numbers is represented as N = {1, 2, 3…} and the set of whole numbers is W = {0, 1, 2, 3…}. We see that every natural number is present in the set of whole numbers. For example, 5 is a natural number as well as a whole number.

ii) Every integer is a whole number.

This statement is false because the set of integers is represented as Z = { -2, -1, 0, 1, 2…} and the set of whole numbers is W = {0, 1, 2, 3…}. We see that the negative integers are not the elements of the whole numbers set. Thus, negative integers are not a subset of whole numbers. For example, -2 is an integer but not a whole number.

iii) Every rational number is a whole number.

This statement is false as every number represented in the form of p/q where q ≠ 0 does not get simplified to a whole number. For example, 1/2 is a rational number, but not a whole number.