In continuation of Post 1 (Properties of Whole Numbers)
Commutative Properties:
Under Addition
For any two whole numbers “a” and “b”, a+b=b+a is commutative property of whole number under addition.
For example: 0 and 4 are two whole numbers then 0+4=4+0 is called commutative under addition. Similarly for 3 and 8 two whole numbers, 3+8=8+3 is called commutative under addition.
Under Subtraction
For any two whole numbers “a” and “b”, a-b ≠ b-a, Hence whole numbers are not commutative under subtraction.
For example: For 0 and 4 two whole numbers 0-4 ≠ 4-0 and is not commutative under subtraction. Similarly for 3 and 8 two whole numbers, 3-8≠8-3 is not commutative under subtraction.
Under Multiplication
For any two whole numbers “a” and “b”, a×b=b×a is commutative property of whole number under multiplication.
For example: For 0 and 4 two whole numbers 0×4=4×0 is called commutative under multiplication. Similarly for 3 and 8 two whole numbers, 3×8=8×3 is called commutative under multiplication.
Under Division
For any two whole numbers a and b, a÷b ≠ b÷a, Hence whole numbers are not commutative under division.
For example: For 0 and 4 two whole numbers 0÷4 ≠ 4÷0 and is not commutative under division. Similarly for 3 and 8 two whole numbers, 3÷8≠8÷3 is not commutative under division.
Associativity Properties:
Under Addition
For any three whole numbers a, b and c if (a+b)+c=a+(b+c) then these whole numbers are called Associative under addition.
Example: for 3, 5 and 8 whole numbers (3+5)+8=3+(5+8) is called associativity property under addition.
Under Subtraction
For any three whole numbers a, b and c , (a-b)-c≠a-(b-c) hence whole numbers are not Associative under subtraction.
Example: for 3, 5 and 8 whole numbers (3-5)-8≠3-(5-8) and hence not associative under subtraction.
Under Multiplication
For any three whole numbers a , b and c if (a×b)×c=a×(b×c) is called associative under multiplication.
Example: for 3, 5 and 8 whole numbers (3×5)×8=3×(5×8) is called associativity property under multiplication.
Distributive properties of multiplication:
Over Addition
For any three whole numbers a, b and c if a×(b+c)=a×b+a×c , then this operation is called law of distributive over addition.
Example: for 3, 5 and 8 whole numbers 3×(5+8)=3×5+3×8 is called distributive properties of multiplication over addition.
Over Subtraction
For any three whole numbers a, b and c if a×(b-c)=a×b-a×c , then this operation is called law of distributive over subtraction.
Example: for 3, 5 and 4 whole numbers 3×(5-4)=3×5-3×4 is called distributive properties of multiplication over subtraction.