__CHAPTER 2__

__WHOLE NUMBERS__

**NATURAL NUMBERS**

All numbers starting from 1 are called natural numbers.

**PREDECESSOR AND SUCCESSOR**

Subtracting 1 from a number gives its predecessor.

Adding 1 to a number gives its successor.

Note that 1, as a natural number, does not have a predecessor.

**WHOLE NUMBERS**

All the numbers from 0, 1, 2… are called whole numbers.

**THE NUMBER LINE**

Arranging the numbers on a line such that they are in an increasing order from left to right, having equal distance between them, forms a number line.

The distance between 0 and 1 is called ‘unit’ distance.

**ADDITION USING NUMBER LINE**

Consider 4+2. Start from 4 and make 2 jumps to the right. You get 6. And 4=2=6.

Therefore, to add, you move to the right.

**SUBTRACTION USING NUMBER LINE**

Consider 4-2. Start from 4 and make 2 jumps to the left. You get 2. And 4-2=2

**MULTIPLAICATION USING NUMBER LINE**

Again, consider 4×2. Start from 0 and move 4 units at a time to the right. Make 2 such moves and you’ll reach 8. And 4×2=8

**PROPERTIES OF WHOLE NUMBERS**

- The sum and product of two whole numbers is a whole number. Therefore, the Closure Property is applicable under addition and multiplication of whole numbers. However, closure property is not applicable on subtraction and division.
- Addition and multiplication of whole numbers is commutative.

E.g. 5+7= 7+5= 12

5×7= 7×5= 35

- Addition and multiplication of whole numbers is associative.

E.g. (2+5) +4= 2+ (5+4)= 11

(2×5) x4= 2x (5×4)= 40

- Addition and multiplication of whole numbers follow the distributive property.

E.g. 4x(2+3)= (4×2)+(4×2)= 20

- Zero is the identity element for addition of whole numbers. Zero added to any number gives the number itself.

E.g. 1+0=1

- One is the identity element for multiplication of whole numbers. One multiplied with any number gives the number itself.

E.g. 10×1=10

NOTE: Division by zero is not defined.