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3.7 Natural Numbers

{1,2,3,..........} is called the set of Natural Numbers and is denoted by 'N'.

Properties of Natural Numbers in Addition

Closure Property: For any two natural numbers "a" and "b" their sum (a+b) is also a natural number. This is called the closure property of addition for natural numbers.
Example: 3, 5 are natural numbers, then 3 + 5 is also a natural number.
That is 3 + 5 = 8 is also a natural number.

Commutative Property: For any two natural numbers "a" and "b" a+b = b+a. This property is called commutative property of addition for natural numbers.
Example: 3, 5 are natural numbers, Then 3 + 5 = 5 + 3 is True
3 + 5 = 8
5 + 3 = 8

Associative Property: For any three natural numbers a, b, and c, a+(b+c) = (a+b)+c. This property is called the associative property of addition for natural number. Example: 3, 5 and 7 are three natural numbers, Then 3 + (5 + 7) = (3 + 5) + 7 3 + (5 + 7) = 3 + 12 = 15
(3 + 5) + 7 =8 + 7 = 15

Properties of Natural Numbers in Multiplication

Closure Property: For any two natural numbers a and b their product a*b is also a natural number. This property is called the closure property of multiplication for natural number. Example: 3, 5 are natural numbers, Then 3 x 5 is also a natural number
3 x 5 = 15

Commutative Property: For any two natural numbers a and b a*b =b*a. This is called the commutative property of multiplication in natural numbers. Example: 3, 5 are natural numbers, Then 3 x 5 = 5 x 3
3 x 5 = 15
5 x 3 = 15

Associative Property: For any three natural numbers a, b, and c a*(b*c) = (a*b)*c. This is called the associative property of multiplication in natural numbers. Example: 2, 3 and 4 are natural numbers, Then 2 x (3 x 4) = (2 x 3) x 4
2 x (3 x 4) = 2 x 12 = 24
(2 x 3) x 4 = 6 x4 = 24

Multiplicative Identity: For any natural number a, a*1 = 1*a = a. Here 1 is called the multiplicative identity in the set of all natural numbers.
Example: 5 * 1 = 1 * 5 = 5


Directions: Answer the following questions. Write these properties and prove that they do not hold true for for subtraction and division. Also, write at least five examples of each property.
Q 1: Set of natural numbers is denoted by _______.
M
P
I
N

Q 2: For any three numbers a, b, and c, a*(b*c) = (a*b)*c; name the property.
Commutative Property
Associative Property
Distributive Property
Identity Property

Q 3: What is the multiplicative identity in natural numbers?
Zero
One
Square
Two

Q 4: For any two natural numbers a and b, a+b = b+a; name the property.
Identity Property
Distributive Property
Commutative Property
Associative Property

Q 5: {1, 2, 3, 4, .......} is called a set of ______.
Prime Numbers
Fractions
Natural Numbers
Decimals

Q 6: For any three natural numbers a, b, and c, a+(b+c) = (a+b)+c; name the property.
Identity Property
Associative Property
Commutative Property
None of these

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Question 8: This question is available to subscribers only!


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