Table of Contents
What is Commutative Property?
The commutative property is a mathematical property that states that the order of the factors in a multiplication does not affect the product. For example, 2×3=6 and 3×2=6. The commutative property can also be applied to addition, as in the example 4+3=7 and 3+4=7.
Commutative Property Definition
The commutative property states that the order of the operands in an algebraic expression does not affect the value of the expression. In other words, the order of addition or multiplication does not matter. For example, the expressions 2 + 3 and 3 + 2 are both equal to 5.
1.Commutative Property of Addition
The commutative property of addition states that the order of addition does not affect the sum of two numbers. In other words, the sum of two numbers is the same regardless of the order in which the numbers are added. For example, 3 + 5 = 5 + 3 and 2 + 4 = 4 + 2.
2. Commutative Property of Subtraction
For all real numbers a, b, and c:
a − b = b − a
3. Commutative Property of Multiplication
For all real numbers a and b, a × b = b × a.
4. Commutative Property of Division
The commutative property of division states that the order of division does not affect the result. That is, for any two numbers a and b, a/b = b/a.
Commutative Property Example Problems
1. Add 4 + 5.
2. Add 5 + 4.
3. Add -6 + 7.
4. Add 7 + -6.
Comparison Between The Commutative Property And The Associative Property
The commutative property states that the order of the terms in a mathematical equation does not affect the equation’s result. The associative property states that the order of grouping terms in an equation does not affect the equation’s result.
Comparison Between The Commutative Property And The Distributive Property
The commutative property states that the order of the numbers does not affect the product. The distributive property states that the product of a number and a sum is equal to the sum of the products of the numbers and the sums.
Commutative Property- Common Uses
The commutative property states that the order of the operands in an operation does not affect the result of the operation. This property is often used in algebra when simplifying equations.
