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Properties of Addition and Multiplication

Key Takeaways:

  • Commutative Property: despite the order terms are multiplied or added in, the result is the same

  • Associative Property: grouping numbers when adding or multiplying will still give the same result

  • Distributive Property: distributing a term with an operation to other terms

  • These properties DO NOT work for subtraction or division 

Practice Questions

1. Emily rewrote the expression 5x+7 as 7+5x. Which property did she use?

a) The Associative Property of Addition
b) The Commutative property of Multiplication
c) The Distributive Property of Multiplication
d) The Commutative Property of Addition


2. What property is being used to simplify the expression below?

         (6 x 8) x 5  -->  6 x (8 x 5)  -->  6 x 40  -->  240

a) The Associative Property of Addition
b) The Commutative property of Multiplication
c) The Associative Property of Multiplication
d) The Commutative Property of Addition


3. The algebraic steps below show how to add the two expressions 4y+10 and 6y+21. Justify each step by writing the property used to make the statement.

Step 1:  (4y+10) + (6y+21) = 4y + (10+6y) + 21     a)

Step 2:  4y + (10+6y) + 21 = 4y + (6y+10) + 21     b)

Step 3:  4y + (6y+10) + 21 = (4y+6y) + (10+21)     c)
                                           = 10y + 31


4. Rewrite the following expression using the distributive property:

2z (5z + 3)  -->  ( ____ x ____ ) + ( ___ x ___ )  -->  ( __ ) + ( __ )  = ___

Answer Key

1. d) The Commutative Property of Addition

2. c) The Associative Property of Multiplication

3a. The Associative Property of Addition

3b. The Commutative Property of Addition

3c. The Associative Property of Addition

4. 2z (5z + 3)  -->  ( 2z x 5z ) + ( 2z x 3 )  -->  ( 10z^2 ) + ( 6z )  = 10z^2 + 6z
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