Download Section 1.1: Basic Properties of Real Numbers Goal: Use a number

Section 1.1: Basic Properties of Real Numbers
Goal: Use a number line to graph and order real numbers and
identify properties of and use operations with real number.
Subsets of Real Numbers ( \ )
Definition/Description
Natural (Counting) Numbers:
Examples
Whole Numbers:
Integers:
Rational Numbers: Any number that
can be expressed as the __________ of
two _________________.
Decimal numbers that _____________ or
__________________.
Irrational Numbers: Any number that
is _____________________.
Properties of Real Numbers
Property
Addition
Multiplication
Closure
a + b is a _____ number
a·b is a ____ number
Commutative
a+b=b+a
a·b = _____
(Order)
Associative
a + (b + c) = ____________
a(bc) = ______
(Grouping)
Identity
a + ___ = a
a· ___ = a
a ⋅ ____ =1
Inverse
a + ____ = 0
Distributive
a(b + c) = __________
Examples:
1. Graph each number on the numbers line. Then, write the
number in increasing order.
-1.25,
12
1
, 5, 2.5, - 3
5
3
x
-5
-4
-2
0
2
4
5
2. Identify each property illustrated.
a. (6·4)·5 = 6·(4·5)
b. 5 + 3 = 3 + 5
c. 4·1 = 4
d. 10 + (-10) = 0
Section 1.2: Algebraic Expressions and Models
Goal: Evaluate algebraic expressions and simplify algebraic
expressions by combining like terms.
Evaluating Algebraic Expressions
1. Substitute
2. Simplify using Order of Operations (PEMDAS)
Examples: Evaluate each expression
2. 3x 3 + 4 when x = - 2
1. x 2 (4- x ) when x = 2
3. 4x + 3y + 2 when x = 4
and y = -3
4. 9(m – n)2 when m = 1
and n = 4
Simplifying and Combining Like Terms
Like terms must have the same ______________ and same ______________.
Examples: Simplify each expression.
1. 7x – (9x + 5)
2. 2(n2 + n) – 5(n2 – 4n)
3. 7x - 2y + 3 – 9y + 4 - 5x