Whole Numbers and Natural Numbers

Natural numbers are set of numbers starting from 1 counting up to infinity. The set of natural numbers is denoted as ′N′.Whole numbers are set of numbers starting from 0 and going up to infinity. So basically they are natural numbers with the zero added to the set. The set of whole numbers is denoted as ′W′Closure Property Closure property is applicable for whole numbers in the case of addition and multiplication while it isn’t in the case for subtraction and division. This applies to natural numbers as well. Commutative Property Commutative property applies for whole numbers and natural numbers in the case of addition and multiplication but not in the case of subtraction and division. Associative Property Associative property applies for whole numbers and natural numbers in the case of addition and multiplication but not in the case of subtraction and division.

Integers

In simple terms Integers are natural numbers and their negatives. The set of Integers is denoted as ′Z′ or ′I′Closure Property Closure property applies to integers in the case of addition, subtraction and multiplication but not division. Commutative Property Commutative property applies to integers in the case of of addition and multiplication but not subtraction and division. Associative Property Associative property applies to integers in the case of addition and multiplication but not subtraction and division.

Associative Property of Rational Numbers

For any three rational numbers a,b and c, (a∗b)∗c=a∗(b∗c). i.e., Associative property is one where the result of an equation must remain the same despite a change in the order of operators. Given three rational numbers a,b and c, it can be said that : (a+b)+c = a+(b+c). Therefore addition is associative. (a−b)−c≠a−(b−c). Because (a-b)-c = a-b-c whereas a-(b-c) = a-b+c. Therefore we can say that subtraction is not associative. (a×b)×c=a×(b×c). Therefore multiplication is associative.(a÷b)÷c≠(a÷b)÷c. Therefore division is not associative.

Distributive Property of Rational Numbers

Given three rational numbers a,b and c, the distributivity of multiplication over addition and subtraction is respectively given as : a(b+c)=ab+ac    , a(b−c)=ab−ac