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
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.