Lesson 1-4

Example 1	Identify Properties
Name the property shown by each statement.
a.	5  7  2 = 7  5  2

The order of the numbers changes.  This is the Commutative Property of Multiplication.

b.        (1 + 8) + 4 = 1 + (8 + 4)

The grouping of the numbers changes.  This is the Associative Property of Addition.

Example 2	Mental Math
Find 13 + 25 + 87 mentally.
	
Group 13 and 87 together because 13 + 87 = 100.  It is easy to add to 100 mentally.

13 + 25 + 87 = (13 + 87) + 25		Commutative and Associative Properties of Addition  
	         = 100 + 25		Add 13 and 87 mentally.
	         = 125			Add 100 and 25 mentally.

Example 3	Find a Counterexample
State whether the following conjecture is true or false.  If false, provide a counterexample.
		Subtraction of whole numbers is commutative.

Write two subtraction expressions using the Commutative Property, and then check to see whether they are equal.
 18 – 7	 7 – 18	State the conjecture.
       11	 –11		Subtract.

We found a counterexample.  That is, 18 – 7  7 – 18.
So, subtraction is not commutative.  The conjecture is false.

Example 4	Simplify Algebraic Expressions 
Simplify each expression.
a.	(m + 6) + 2
	(m + 6) + 2 = m + (6 + 2)	Associative Property of Addition
		       = m + 8		Substitution Property of Equality; 6 + 2 = 8 

b.	(c  4)  7
	(c  4)  7 = c  (4  7)		Associative Property of Multiplication
    		   = c  28		Substitution Property of Equality; 4  7 = 28
		   = 28c		Commutative Property of Multiplication