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1.3 Properties of Real Numbers
February 07, 2011
MATH 1010 ~ Intermediate Algebra
Chapter 1 Fundamentals of Algebra
Section 1.3: Properties of Real Numbers
Objectives:
✵ Identify and use the properties of real numbers.
✵ Develop additional properties of real numbers.
Which properties are used?
a(b+c) = ab + ac = ba + ca = ca + ba = (c+b)a
PROPERTIES OF REAL NUMBERS
Commutative Property:
Associative Property:
Distributive Property of _________________ over _____________________:
Additive Identity Property:
Multiplicative Identity Property:
Additive Inverse Property:
Multiplicative Inverse Property:
1.3 Properties of Real Numbers
February 07, 2011
PROPERTIES OF EQUALITY
Addition Property of Equality:
Multiplication Property of Equality:
Cancellation Property of Addition:
Cancellation Property of Multiplication:
PROPERTIES OF ZERO
Multiplication Property of Zero:
Division Property of Zero:
Division by Zero is Undefined:
1.3 Properties of Real Numbers
February 07, 2011
PROPERTIES OF NEGATION
Multiplication by -1:
Placement of Negative Signs:
Product of Two Opposites:
① EXAMPLE: Simplify and state the properties used.
a) 10(2x) =
b) 17 - 17 =
c) (-3/4)(-4/3) =
d) 6(x+3) =
e) The additive inverse of -16 is_________, the multiplicative inverse is___________.
f) The additive inverse of -2/3 is__________, the multiplicative inverse is___________.
g) 12($19.95) =
h) BEWARE (a+b)2 =
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