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Lesson 4-1
Using
Properties
Lesson 4-1: Using Properties
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Commutative & Associative Property
Commutative Property ...order does not matter.
Addition:
Examples
4+5=5+4
a+b=b+a
2•3=3•2
Multiplication: a • b = b • a
Associative Property ...grouping does not matter
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 commutative and associative property does not work for
subtraction or division.
Lesson 4-1: Using Properties
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Properties for Addition & Multiplication
Additive Identity: “0”is the identity element for addition
a+0 =a
Additive Inverse:
a and (-a) are called opposites
a + (-a) = 0
Multiplicative Identity “1”is the identity element for multiplication
a• 1 =a
Multiplicative Inverse a and
1
a
are called reciprocals
1
a•
=1
a
Lesson 4-1: Using Properties
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Multiplicative & Distributive Property
Multiplicative Property of Zero
0
a • 0 = ___
Multiplicative Property of -1
a • -1 = ___
-a
The Distributive Property
The process of distributing the number on the outside of the
parentheses to each term on the inside.
a(b + c) = a b + ac
a(b - c) = ab - ac
and
(b + c) a = b a + ca
(b - c) a = ba - ca
Lesson 4-1: Using Properties
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Examples………….
Name the property :
1) 5a + (6 + 2a) = 5a + (2a + 6) Commutative (switch order)
2) 5a + (2a + 6) = (5a + 2a) + 6 Associative (switch groups)
3) 2(3 + a) = 6 + 2a
Distributive
Lesson 4-1: Using Properties
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Properties of Equality
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
x0
Lesson 4-1: Using Properties
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Properties of Equality & Congruence
Reflexive: a = a
5=5
Symmetric: If a = b then b = a
If 4 = 2 + 2 then 2 + 2 = 4
Transitive: If a=b and b=c, then a=c
If 4 = 2 + 2 and 2 + 2 = 3 + 1, then 4 = 3 + 1
Reflexive: a  a
A  A
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
Lesson 4-1: Using Properties
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