Properties Of Addition & Substraction

Properties Of Addition & Substraction

Properties of Addition
    (i)    Closure Property : If ‘a’ and ‘b’ are two whole numbers and their sum is c, i.e., a + b = c, 
then c  will always be a whole number. This property of a addition is called the closure property of addition.
        For ex. :  2 + 8 = 10 i.e., whole number + whole number = whole number

    (ii)    Commutative Property : If a and b are two whole numbers a + b = b + a. This property of addition, where the order of addition does not alter the sum, is called the commutative property of addition
        For ex.     3 + 4 = 7
        Also,     4 + 3 = 7
        i.e.,    3 + 4 = 4 + 3

    (iii)    Associative Property : If a, b and c are three whole numbers, then a + (b + c) = (a + b) + c. In other words, in the addition of whole numbers, the sum does not change even if the grouping is changed. This property is called the associative property of addition.
        For ex.    2 + (3 + 4) = (2 + 3) + 4 
            2 + 7 = 5 + 4
            9 = 9 

    (iv)    Additive Identity : If a is a whole number ,then  a + 0 = 0 + a = a. 
        Hence, zero is called the additive identity of the whole numbers because it maintains (or does not change) the identity (value) of the numbers during the operation of addition.
        For ex.     7 + 0 = 7 = 0 + 7

Properties of subtraction
    (i)    Closure Property : If a and b are two whole numbers, then a – b will be a whole number only if a is greater than b or a is equal to b. If a is smaller than b, then the answer will not be a whole number. Hence, subtraction is not closed under whole numbers.
        For ex.     7 – 2 = 5 is whole number 
            but 3 – 8 is not a whole number

(ii)    Commutative Property : If a and b are two distinct whole numbers, then a – b is not equal to b – a. Hence, the commutative property is not true for subtraction of whole numbers.
        For ex.     a – b ≠ b – a 
            7 – 2 ≠ 2 – 7 

    (iii)    Associative Property : If a, b and c are whole numbers, then (a – b) – c is not equal to a – (b – c). So, the associative property also does not hold true for subtraction of whole numbers
        For ex.     (12 – 4) – 3 = 8 – 3 = 5
            12 – (4 – 3) = 12 –1 = 11 
       Therefore    (12 – 4) – 3 ¹12 – (4 – 3)