Download 1-4 Identity and Equality Properties

1-4 Identity and Equality
Properties
The properties need to be memorized and understood.
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
Identity Property
Additive Identity: The sum of a number and 0 is the
number. Thus, 0 is called the additive identity.
16 + 0 = 16
n+0=n
Multiplicative Identity: The product of any number
and 1 is the number. Thus, 1 is called the multiplicative
identity.
16 • 1 = 16
n•1=n
Inverse Property
Additive Inverses: Two numbers with a sum of zero
are called additive inverses.
45   45  0
n   n   0
45   45  0
n  n  0
Multiplicative Inverses: Two numbers whose product
is 1 are called multiplicative inverses or reciprocals.
1
1
5  1
n  1
5
n
1
1When two
n 1
5  1
nsigns are
5
needed use
parentheses or
a superscript!
Zero
Zero has no reciprocal because any number times 0 is 0.
Multiplicative Property of Zero:
number and 0 is equal to zero.
8 0  0
The product of any
n0  0
Equality Properties
Reflexive: Any quantity is equal to itself.
3=3
5+2=5+2
n=n
Symmetric: If one quantity equals a second quantity,
then the second quantity is equal to the first.
If 16 + 4 = 20, then 20 = 16 + 4.
If a = b, then b = a.
Equality Properties
Transitive: If one quantity equals a second quantity
and the second quantity equals a third quantity, then
the first quantity equals the third quantity.
If 5 + 4 = 6 + 3 and 6 + 3 = 9, then 5 + 4 = 9.
If a = b and b = c, then a = c.
Substitution: A quantity may be substituted for its
equal in any expression.
If n = 4, then 5n = 5(4).
If a = b, then 3a = 3b.
Find the value of n in each equation. Then name the
property that is used.
42n  42
n 1
9n  1
1
n
9
Given
Multiplicative Identity
because 42 • 1 = 42
Given
Multiplicative Inverse (Reciprocal)
because 9 
1
9
1
Find the value of n in each equation. Then name the
property that is used.
Example 1 7 = 7 + n
n=0
Given
Additive Identity
Example 2 9 - n = 0
n=9
Given
Additive Inverse
because 7 + 0 = 7
because 9 - 9 = 0
The properties of identity and equality can be used to
justify each step when evaluating expressions.
Evaluate. Name the property used in each step.
1
Given
23  2  5  3 
3
1
Substitution
26  5  3 
3
1
Substitution
21  3 
3
1
Multiplicative Identity
2  3
3
Multiplicative Inverse
21
3
Substitution
Copy in your
spiral
notebook!
Evaluate. Name the property used in each step.
Example 3
1
12  8  315  5  2
4
Example 4
1



4 15  2 4  

4
Example 3 Evaluate. Name the property used in each step.
1
12  8  315  5  2
4
1
4  315  5  2
4
1
4  33  2
4
1
4  31
4
Given
Substitution
Substitution
Substitution
1  31
Multiplicative Inverse
13
Multiplicative Identity
4
Substitution
Example 4 Evaluate. Name the property used in each step.
1
415   2 4  
 4
415   21
60  21
60  2
62
Given
Multiplicative Inverse
Substitution
Multiplicative Identity
Substitution
1-A6 Pages 23-25 #8-23,26-28,40-41,46.