1. Properties The properties need to be memorized and understood.
Algebra Glencoe McGraw-Hill Malinda Young

2. Identity Property
Additive Identity: The sum of a number and 0 is the number. Thus, 0 is called the additive identity.
= 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

3. When two signs are needed use parentheses or a superscript!
Inverse Property
Additive Inverses: Two numbers with a sum of zero are called additive inverses.
Multiplicative Inverses: Two numbers whose product is 1 are called multiplicative inverses or reciprocals.
When two signs are needed use parentheses or a superscript!

4. Zero Zero has no reciprocal because any number times 0 is 0.
Multiplicative Property of Zero: The product of any number and 0 is equal to zero.

5. 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 equals the first.
If = 20
, then 20 =
If a = b, then b = a.

6. 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 = 6 + 3
and = 9
, then = 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.

7. Multiplicative Identity
Find the value of n in each equation. Then name the property that is used.
Write the problem.
Multiplicative Identity
because 42 • 1 = 42
Write the problem.
Multiplicative Inverse (Reciprocal)

8. Find the value of n in each equation
Find the value of n in each equation. Then name the property that is used.
Example 1 7 = 7 + n
Write the problem.
n = 0
Additive Identity
because = 7
Example n = 0
Write the problem.
n = 9
Additive Inverse
because = 0

9. Copy in your spiral notebook!
The properties of identity and equality can be used to justify each step when evaluating expressions.
Evaluate. Name the property used in each step.
Write the problem.
Substitution
Substitution
Multiplicative Identity
Multiplicative Inverse
Substitution
Copy in your spiral notebook!

10. Commutative Property
You can change the order when adding or multiplying without affecting the sum or product. =
abc=cba

11. Associative Property
You can change the grouping while adding or multiplying without affecting the sum or product.
(2 + 3) + 4 = 2 + (3 + 4)
(ab)c = a(bc)

12. Property of Negative One
Any quantity times negative 1 (-1) will result in it’s opposite
m(-1) = -m n(-1) = n

13. Closure Property
For example: The sum of any two whole numbers is a whole number. So, the set of whole numbers is said to be closed under addition.

14. 1-A3 Handout on Properties
Homework
1-A3 Handout on Properties