NCERT Solutions for Class 6 Maths Chapter 2 Exercise 2.1

Class VI Mathematics NCERT book Ex. 2.1 of chapter 2 Whole Numbers in Hindi and English Medium updated for new session 2024-25 free to download. Student can use NCERT class 6 Maths Ex. 2.1 solution online or download in PDF file format free. Videos related to exercise 2.1 is also given to explain better.

Since our childhood we are familiar with counting numbers 1, 2, 3, …. These are known as natural numbers.

All natural numbers along with the number zero form the collection of. That is numbers 0, 1, 2, 3, 4, … are called whole numbers. Clearly, every natural number is a whole number but 0 is a whole number which is not a natural number.

There is no last or greatest whole number.
There are infinitely many whole numbers.

The successor of a whole number is the number obtained by adding 1 to it. Clearly, the successor of 0 is 1; the successor of 1 is 2; the successor of 2 is 3. Every whole number has its successor.

The predecessor of a whole number is 1 less than the given number. Clearly, the predecessor of 1 is 0; the predecessor of 2 is 1; the predecessor of 3 is 2. Every whole number (except zero) has its predecessor.

We can represent whole numbers by points on a line. In order to represent whole numbers on a number line, we draw a straight line and mark a point O on it. Starting from O, mark points A, B, C, D, E, F etc., on the line at equal distances to the right of O.

Label the point O as 0. Let, OA = 1 unit.
Then AB = BC = CD = DE = EF = 1 unit.
Now, OB = OA + AB = 1 + 1 = 2 units
OC = OB + BC = 2 + 1 = 3 units
OD = OC + CD = 3 + 1 = 4 units and so on.

1. The number line is endless and every whole number can be represented on it.
2. There is no whole number to the left of 0. Every whole number on the right of 0 is greater than 0.
3. Thus, 0 is the smallest whole number.
4. Every whole number on the number line is greater than every other whole number on its left.
   Example: 4 > 3, 25 > 24, 1 > 0. Thus, there is no longer whole number.
5. Every whole number on the number line is less than every other whole number on its right.
   Examples: 0 < 1, 2 < 3, 19 < 20, 85 < 90.
6. Between any two consecutive whole numbers, there is no whole number. However, between two non-consecutive whole numbers, there always exists a whole number.
   Example: 6 lies between 3 and 8. Here, 3 < 6 and 6 < 8. We can express this as 3 < 6 < 7. Also 4, 5, 6, 7 lie between 3 and 8.

We are already familiar with the four basic operations of addition, subtraction, multiplication and division on whole numbers. In this chapter, we shall study the properties of these operations on whole numbers.

What do we conclude? We conclude that the sum of any two whole numbers is a whole number.
Thus, we have the following property, known as the closure property of addition.

Property 1:
If a and b are any two whole numbers, then a + b is also a whole number.

Let us take a pair of whole numbers. Now, add them in two different orders and see whether the sum remains the same. Repeat it with more pairs.

What do we conclude? We conclude that in whatever order we add two whole numbers; the sum remains the same.
Thus, we have the following property, called the commutative law of addition.

Property 2:
If a and b are any two whole numbers then a + b = b + a.

Take any whole numbers and add them to zero as under:
Example:

• (a) 5 + 0 = 0 + 5 = 5,
• (b) 12 + 0 = 0 + 12 = 12,
• (c) 19 + 0 = 0 + 19 = 19.

What do we observe? We conclude that the sum of any whole number and 0 is the number itself.
This property is called the additive property of zero.

Property 3:
If a is any whole number then a + 0 = 0 + a = a

To find the sum of three whole numbers, we add two of them and add the third number to the sum.
Let us take three whole numbers, say 4, 7, 8.
(4 + 7) + 8 = 11 + 8 = 19; and 4 + (7 + 8) = 4 + 15 = 19.
Thus, (4 + 7) + 8 = 4 + (7 + 8).
Again, take three more numbers, say 5, 9, 13.
(5 + 9) + 13 = 14 + 13 = 27; and 5 + (9 + 13) = 5 + 22 = 27.
Thus, (5 + 9) + 13 = 5 + (9 + 13).

We thus find that in the addition of whole numbers, the manner of associating the numbers does not affect the sum.
So, we have the following property, called the associative law of addition.

Property 4:
If a, b, c are any three whole numbers then (a + b) + c = a + (b + c).

While adding three or more numbers, we group them in such a way that the calculation becomes easier. We need not add them in the given order.