The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.
Let us see if the commutative property holds true for all the four arithmetic operations, i.e. addition, subtraction, multiplication and division.
The commutative property of addition states that changing the order of the addends does not change the value of the sum. If 'x' and 'y' are two numbers, then
x + y = y + x , for example 2 + 3 = 3 + 2 = 5
The commutative property of multiplication state that the order in which we multiply two numbers does not change the final product. If 'a' and 'b' are two numbers, then
a × b = b × a , for example 2 × 3 = 3 × 2 = 6
The commutative property does not hold true for Subtraction and Division. Let's verify using few examples:
3 − 2 = 1 but 2 − 3 ≠ 1, therefore 3 − 2 ≠ 2 − 3
The change in the order of two numbers in division affects the result, hence the commutative property is not true in the case of division.
4 ÷ 2 ≠ 2 ÷ 4
Example 1: Find the missing number 84 × _____ = 39 × 84
Solution: 39; by commutative property of multiplication
Example 2: Riya bought 3 packets of 4 pens each. John bought 4 packets of 3 pens each. Who bought more pens?
Solution: Even if both have different numbers of packets with each having a different number of pens in them, they both bought an equal number of pens, because 3 × 4 = 4 × 3.
Example 3: Choose the set of numbers to make the statement true. 7 + _____ = 3 + _____
Solution: 7 + 3 = 3 + 7
