Transcript 1.8 Properties of Real Numbers • For every real number a, b, and c, – Commutative Property of Addition • a+b=b+a Ex.

1.8 Properties of Real Numbers
• For every real number a, b, and c,
– Commutative Property of Addition
• a+b=b+a
Ex. 3 + 7 = 7 + 3
– Commutative Property of Multiplication
• a•b=b•a
Ex. 3 • 7 = 7 • 3
– Associative Property of Addition
• (a + b) + c = a + (b + c) Ex. (6 + 4) + 5 = 6 + (4 + 5)
– Associative Property of Multiplication
• (a • b) • c = a • (b • c)
Ex. (6 • 4) • 5 = 6 • (4 • 5)
Properties of Real Numbers
• For every real number a, b, and c,
– Identity Property of Addition
•a+0=a
Ex. 9 + 0 = 9
– Identity Property of Multiplication
•a•1=a
Ex. 6 • 1 = 6
– Inverse Property of Addition
• For every a, there is an additive inverse –a such
that a + (-a) = 0
Ex. 5 + (-5) = 0
– Inverse Property of Multiplication
• For every a (a ≠ 0), there is a multiplicative
1

1
1

inverse
such that a    1. Ex. 5    1
a
a
 5
Properties of Real Numbers
• For every real number a, b, and c,
– Distributive Property
• a (b + c) = ab + ac
• a (b – c) = ab – ac
Examples
5(4 + 2) = 5(4) + 5(2)
5(4 – 2) = 5(4) – 5(2)
– Multiplication Property of Zero
• For every real number n, n • 0 = 0.
-35 (0) = 0
– Multiplication Property of -1
• For every real number n, -1 • n = -n
-1 (-5) = 5
•
a.
b.
c.
d.
Identifying Properties
Name the property that each equation
illustrates.
9+7=7+9
Commutative Property of Addition
(d • 4) • 3 = d • (4 • 3)
Associative Property of Multiplication
t+0=t
Identity Property of Addition
-q = -1q
Multiplication Property of -1
Deductive Reasoning
9/27/10
• Deductive Reasoning – the process of
reasoning logically from given facts to a
conclusion.
Justifying Steps
Simplify each expression. Justify each step.
a. -4b + 9 + b
-4b + 9 + b = -4b + 9 + 1b
= -4b + 1b + 9
= (-4 + 1)b + 9
= -3b + 9
Identity Property of Mult.
Commutative Property
Distributive Property
Addition
Justifying Steps
Simplify each expression. Justify each step.
a. 7z – 5(3 + z)
7z – 5(3 + z) = 7z – 15 – 5z
= 7z + (-15) + (-5z)
= 7z + (-5z) + (-15)
= [7 + (-5)]z + (-15)
= 2z + (-15)
= 2z - 15
Distributive Property
Definition of Subtraction
Commutative Property
Distributive Property
Addition
Definition of subtraction
More Practice!!!!!
• Textbook p. 56 # 1 – 15 all