Commutative Property and Associative Property

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Mathematics, Operations (+, -, x, /, etc.)

Grade 5- 8

Objective

Students learn about properties of multiplication.

Directions

Introduce students to Commutative and Associative properties with the following information.
The Commutative Property of Multiplication states that when the order of the factors is changed, the product stays the same. Multiplication is a commutative operation. For example, in the equation 5 x 9, the order of the factors does not affect the answer because 5 x 9 = 45 and 9 x 5 = 45. The Commutative Property works for any number of factors. Show students the following examples:
Example A
30 x 80 = 80 x 30
30 x 80 = 2, 400
80 x 30 = 2, 400
Example B
10 x 9 x 8 = 8 x 9 x 10
10 x 9 x 8 = 720
8 x 9 x 10 = 720
The Associative Property of Multiplication states that when the grouping of the factors is changed, the product stays the same. The way the factors are grouped within parentheses does not affect the answer. Multiplication is associative. Show students the following examples:
Example C
5 x (8 x 9) = (5 x 8) x 9
5 x (8 x 9) = 360
(5 x 8) x 9 = 360
Example D
30 x (50 x 90) = (30 x 50) x 90
30 x (50 x 90) = 135, 000
(30 x 50) x 90 = 135, 000
Distribute copies of the activity sheets to students and have them apply these properties to solve the problems on the pages.

Resources

Multiplying by Using the Commutative Property activity sheet (one per student)
Multiplying by Using the Associative Property activity sheet (one per student)
pencils

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