Lesson 8: algebra - properties
I Can...
...produce equivalent expressions using the distributive, commutative, and associative properties.
...simplify expressions using the order of operations.
...simplify expressions using the order of operations.
Words to Know
Equivalent Expressions: Two expressions having the same value.
Distributive Property:
Commutative Property of Addition: changing the order of addition does not change solution. Example: 1 + 2 + 3 = 1 + 3 + 2.
Commutative Property of Multiplication: changing the order of multiplication does not change solution. Example: 1 x 2 x 3 = 1 x 3 x 2.
Associative Property Addition: changing the grouping of addition does not change the solution. Example: (1 + 2) + 3 = 1 + (2 + 3)
Associative Property Multiplication: changing the grouping of multiplication does not change the solution. Example: (1 x 2) x 3 = 1 x (2 x 3)
Identity Property of Addition: identifying the value of a number. Example: 8 + 0 = 8
Identity Property of Multiplication: identifying the value of a number. Example: 8 x 1 = 8
Distributive Property:
Commutative Property of Addition: changing the order of addition does not change solution. Example: 1 + 2 + 3 = 1 + 3 + 2.
Commutative Property of Multiplication: changing the order of multiplication does not change solution. Example: 1 x 2 x 3 = 1 x 3 x 2.
Associative Property Addition: changing the grouping of addition does not change the solution. Example: (1 + 2) + 3 = 1 + (2 + 3)
Associative Property Multiplication: changing the grouping of multiplication does not change the solution. Example: (1 x 2) x 3 = 1 x (2 x 3)
Identity Property of Addition: identifying the value of a number. Example: 8 + 0 = 8
Identity Property of Multiplication: identifying the value of a number. Example: 8 x 1 = 8
Examples
2. Use Properties to Evaluate Expressions
Video
Video
Tips
Look for numbers that you can group together with the associative and commutative properties to allow you to use mental math and easy calculations!
Extra Examples
- Click here for additional examples and self check quizzes.
Problems of the DAY
Answers must be submitted by 9am the following school day!
Find the expression, justify each step:
1. 91 + (15 + 9)
2. Use the Distributive Property to rewrite the expression, then evaluate: 2(6 + 7).
Find the expression, justify each step:
1. 91 + (15 + 9)
2. Use the Distributive Property to rewrite the expression, then evaluate: 2(6 + 7).