1. Lesson 4-1 Using Properties Designed by Skip Tyler, Varina High School
and modified for review in Geometry

2. Commutative Property ...order does not matter. Addition: a + b = b + a
Examples
Addition: a + b = b + a
4 + 5 = 5 + 4
Multiplication: a • b = b • a
2 • 3 = 3 • 2
The commutative property does not work for subtraction or division.

3. Associative Property ...grouping does not matter
Examples
Addition: (a + b) + c = a + (b + c)
(1 + 2) + 3 = 1 + (2 + 3)
Multiplication: (ab) c = a (bc)
(2•3)•4 = 2•(3•4)
The associative property does not work for subtraction or division.

4. Properties for ADDITION
Additive Identity
a = a
“0”is the identity element for addition
(-a)
a = 0
Additive Inverse
a and (-a) are called opposites

5. Properties for MULTIPLICATION
Multiplicative Identity
a • = a 1
“1”is the identity element for
multiplication
Multiplicative Inverse
a • = 1
a and are called reciprocals

6. Properties for MULTIPLICATION
Multiplicative Property of Zero
a • 0 = ___
Multiplicative Property of -1 -a
a • -1 = ___

7. The Distributive Property
The process of distributing the number on the outside of the parentheses to each term on the inside.
a(b + c) = ab + ac
a(b - c) = ab - ac
and
(b + c) a = ba + ca
(b - c) a = ba - ca
5(x + 7)
Example
5 • x + 5 • 7
5x + 35

8. Name the property 1) 5a + (6 + 2a) = 5a + (2a + 6)
commutative (switching order)
2) 5a + (2a + 6) = (5a + 2a) + 6
associative (switching groups)
3) 2(3 + a) = 6 + 2a
distributive

9. Properties of Equality
x  0
If a = b, then
Addition
a + c = b + c
Subtraction
a - c = b - c
Multiplication
a • c = b • c
Division
a / c = b / c
Substitution:
If a = b, then a can be replaced by b
Example: (5 + 2)x = 7x

10. Properties of Equality
Reflexive: a = a
5 = 5
Symmetric: If a = b then b = a
If 4 = then = 4
Transitive: If a=b and b=c, then a=c
If 4 = and = 3 + 1, then 4 = 3 + 1

11. Properties of Congruence
Reflexive: a  a
A  B
Symmetric: If a  b then b  a
If C  D, then D  C
Transitive: If ab and bc, then ac
If XY and YZ, then XZ