Display Title
DefinitionMath PropertiesCommutative Property of Multiplication
Display Title
DefinitionMath PropertiesCommutative Property of Multiplication
This is part of a collection of definitions of math properties. These downloadable images can easily be incorporated into a lesson plan.
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The next section provides background information on math properties. Refer to this section as you review the math properties definitions.
Math Properties
As you work with numbers, it's important to know properties of operations and equations. Learn these and you'll have an easier time combining certain expressions.
Let's start by looking at the properties relating to addition.
Addition Properties
Commutative Property. When adding two numbers, it doesn't matter in what order you add them. The Commutative Property of Addition means that for any two numbers a and b,
a + b = b + a
Why is this an important property to use? Take a look at this expression:
7 + 25 + 3
Use the Commutative Property to rewrite the expression this way
7 + 3 + 25
Do you see how the 7 and 3 easily combine to form a 10, making the sum much easier to find:
7 + 3 + 25 = 10 + 25 = 35
Look for opportunities to use the Commutative Property to simplify addition.
Associative Property. When adding three or more numbers, you can choose any pair of numbers to add first. The Associative Property of Addition means that you can add any pair of numbers first.
(a + b) + c = a + (b + c)
Here's how to use the Associative Property to simplify addition:
(25 + 3) + 7 = 25 + (3 + 7) = 25 + 10 = 35
In this case using the Associative Property simplifies the addition.
Multiplication Properties
Commutative Property. When multiplying two numbers, it doesn't matter in what order you multiply them. The Commutative Property of Multiplication means that for any two numbers a and b,
a • b = b • a
Why is this an important property to use? Take a look at this expression:
25 • 27 • 4
Use the Commutative Property to rewrite the expression this way
27 • 25 • 4
Do you see how the product of 25 and 4 is 100, making the product much easier to find:
27 • 25 • 4 = 27 • 100 = 2700
Look for opportunities to use the Commutative Property to simplify multiplication.
Associative Property. When multiplying three or more numbers, you can choose any pair of numbers to multiply first. The Associative Property of Multiplication means that you can multiply any pair of numbers first.
(a • b) • c = a • (b • c)
Here's how to use the Associative Property to simplify addition:
(37 • 20) • 5 = 37 • (20 • 5) = 37 • 100 = 3700
In this case using the Associative Property simplifies the multiplication.
Equation Properties
As you solve an equation, use the properties shown above in the solution process. Also, take advantage of the following equation properties
Addition Property of Equality. When solving an equation, you may have to remove a number from one side of the equation in order to isolate the variable. Use the Addition Property of Equality, which states that whatever you add to one side of an equation, you also have to add to the other side of the equation.
Here is an example of using the Addition Property of Equality to solve an equation:
Notice how 2 is added to both sides in order to get x by itself to solve the equation.
Subtraction Property of Equality. When solving an equation, you may have to remove a number from one side of the equation in order to isolate the variable. Use the Subtraction Property of Equality, which states that whatever you subtract from one side of an equation, you also have to subtract from the other side of the equation.
Here is an example of using the Subtraction Property of Equality to solve an equation:
Notice how 2 is subtracted from both sides in order to get x by itself to solve the equation.
Multiplication Property of Equality. When solving an equation, you may have to remove a number from one side of the equation in order to isolate the variable. Use the Multiplication Property of Equality, which states that whatever you multiply by on one side of an equation, you also have to multiply by on the other side of the equation.
Here is an example of using the Multiplication Property of Equality to solve an equation:
Division Property of Equality. When solving an equation, you may have to remove a number from one side of the equation in order to isolate the variable. Use the Division Property of Equality, which states that whatever you divide by on one side of an equation, you also have to divide by on the other side of the equation. Note: You cannot divide by zero.
Here is an example of using the Division Property of Equality to solve an equation:
Notice how both sides of the equation are divided by 2 in order to get x by itself to solve the equation.
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Common Core Standards  CCSS.MATH.CONTENT.3.OA.B.5, CCSS.MATH.CONTENT.7.NS.A.2.C 

Grade Range  3  7 
Curriculum Nodes 
Algebra • The Language of Math • Numerical Expressions 
Copyright Year  2014 
Keywords  definition, Commutative Property of Multiplication 