﻿ Associative, Distributive and Commutative Properties -Practice using these properties

# Associative, Distributive and Commutative Properties

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### Properties and Operations

Let's look at how (and if) these properties work with addition, multiplication, subtraction and division

Distributive Property
Associative
Commutative
Summary: All 3 of these properties apply to addition

#### Multiplication

Property Example with Multiplication
Distributive Property The distributive property is an application of multiplication (so there is nothing to show here)
Associative
Commutative
Summary: All 3 of these properties apply to multiplication

#### Subtraction

Property Example with Subtraction
Distributive Property
Associative
Commutative
Summary: The distributive property is the only one that applies to subtraction.

#### Division

Property Example with Subtraction
Distributive Property
Associative
Commutative
Summary: The distributive property does not apply to any of these 4 properties.

### Practice Problems

Which of the following statements illustrate the distributive, associate and the commutative property?

Directions: Click on each question mark to see what property goes with the statement on the left.
Statement Property
7 + 2 = 2 + 7
6 + (2 + 11) = (6 + 2 ) + 11
5 (2 + 4) = 5 • 2 + 5 •4
(12 • 44) • 13 • 5= 12 • 44 • (13 • 5)
5 • 3 • 11 = 11 • 5 • 3
6 (3 +11+4) =6 • 3 + 6 •11+ 6 •4

All three of these properties can also be applied to Algebraic Expressions

Which of the following statements illustrate the distributive, associate and the commutative property?

Directions: Click on each question mark to see what property goes with the statement on the left.
Statement Property
a + c = c + a
a (x + y + z) =a • x + a •y + a •z
(a • y) • x • z= a • y • (x • z )

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