Page 79 - Algebra 1

Example
1
Identifying Properties
Identify the property illustrated in each equation. a. 1·8=8
SOLUTION Since 8 is multiplied by 1, its value does not change. This is the Identity Property of Multiplication.
b. 13+5=5+13
SOLUTION The order of the terms is changed. This is the Commutative
Property of Addition.
c. (3·4)·7=3·(4·7)
SOLUTION The terms and the order are not changed; only the grouping of the factors is changed. This is the Associative Property of Multiplication.
d. (12+9)+5=(9+12)+5
SOLUTION The terms are the same and the same two terms are grouped. However, the order of the grouped terms has changed. This is the Commutative Property of Addition.
Using Properties to Justify Statements
Tell whether each statement is true or false. Justify your answer using the properties. Assume all variables represent real numbers.
a. gh=hg
SOLUTION The statement is true. It illustrates the Commutative Property of
Multiplication.
Check Substituteavalueforeachvariabletodeterminewhetherthe statement is true.
Let g = 6 and h = 7. 6·7 7·6
42=42 ✓ b. b+1=b
SOLUTION The statement is false. To illustrate the Identity Property of Addition, the equation should be b + 0 = b.
Check Substituteavalueforthevariabletodeterminewhetherthestatement is true.
Let b = 13. 13+1≠13 ✗
Hint
Compare the left side
of the equation to the right side. Determine what changes have been made.
Math Reasoning
Analyze Why does the Commutative Property not apply to subtraction?
Example
2
Write
Explain why it is necessary to substitute only one value for the variable to show that the statement is false.
64 Saxon Algebra 1