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NATURAL NUMBER
The counting numbers from 1 onwards are called NATURAL NUMBERS.
Ex: 1, 2, 3, 4, 5, 6, 7, …………………
PROPERTIES OF NATURAL NUMBER
The first and the smallest natural number is 1.
Every natural number except 1 can be obtained by adding 1 to the previous natural number.
There are infinitely many natural numbers. So, there is no greatest natural number.
WHOLE NUMBER
The calculating numbers from 0 onwards are called WHOLE NUMBERS. (All natural numbers
along with the number 0.)
Ex: 0, 1, 2, 3, 4, 5, …………………………
So, a whole number is either 0 or a natural number.
PROPERTIES OF WHOLE NUMBER
The first and smallest whole number is 0.
All natural numbers are whole number. But, all whole numbers are not natural numbers.
Every whole number except 0 can be obtained by adding 1 to the previous whole number.
There are infinitely many whole numbers. So, there is no greatest whole number.
WHOLE NUMBER OPERATIONS
We know the four fundamental operations of addition, subtraction, multiplication and division.
Let us now find the properties of these operations on whole numbers.
FOR ADDITION
PROPERTY
Closure Property
Commutative Property
Associative Property
Existence of Identity Property
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IF
x and y are whole numbers
x and y are whole numbers
x, y and z are whole numbers
x is whole number
THEN
x + y is also whole number
x+y=y+x
(x + y) + z = x + (y + z)
x + 0 = x (0 is additive identity)
Page 1
FOR SUBTRACTION
PROPERTY
Closure Property
Commutative Property
Associative Property
Existence of Identity Property
IF
x and y are whole numbers
such that x > y or x = y
x and y are whole numbers
x, y and z are whole numbers
x is whole number other than 0
THEN
x - y is also whole number
x-y≠y-x
(x - y) - z ≠ x - (y - z)
x-0=x
(0 – any whole number is not
defined.)
FOR MULTIPLICATION
PROPERTY
Closure Property
Commutative Property
Associative Property
Existence of Identity Property
IF
a and b are whole numbers
a and b are whole numbers
a, b and c are whole numbers
a is whole number
Distributive Property
(Over addition)
a, b and c are whole numbers
THEN
a x b is also whole number
axb=bxa
(a x b) x c = a x (b x c)
ax1=a
(1 is multiplicative identity)
a x (b + c) = (a x b) +( a x c)
OR
(b + c) x a = (b x a) + (c x a)
FOR DIVISION
PROPERTY
Closure Property
Commutative Property
Associative Property
Existence of Identity Property
Distributive Property
(Over addition)
Operation with 0
Inverse of multiplication
Division Algorithm
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IF
a and b are whole numbers
and b ≠ 0
a and b are whole numbers
a, b and c are whole numbers
a is whole number
THEN
a ÷ b or a/b is not necessarily
a whole number
a÷b≠b÷a
(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)
a ÷ 1 = a or a ÷ a = 1
a, b and c are whole numbers
a ÷ (b + c) ≠ (a ÷ b) +( a ÷ c)
a is whole number such that
a≠0
a, b, c are whole numbers
such that b ≠ 0, c ≠ 0 and
a ÷ b = c or a ÷ c = b
a ÷ b where a and b are whole
number such that b ≠ 0 and
0÷a=0
But, a ÷ 0 = Not defined
bxc=a
a = bm + n, where m and n are
whole numbers such that
n = 0 or, n < b
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