WarmUp

1
Warm-Up
5 minutes
Evaluate each expression.
2)
3)
1)
5)
6)
4)
2
2.1 Operations with Numbers

• Objectives
• Identify and use Properties of Real Numbers
• Evaluate expressions by using the order of
  operations

3
Number Sets
Natural numbers
1,2,3,
Whole numbers
0,1,2,3,
Integers
,-3,-2,-1,0,1,2,3,
Rational numbers
Irrational numbers
numbers whose decimal part does not terminate or
repeat
Real numbers
all rational and irrational numbers
4
Example 1
Classify each number in as many ways as possible.
a) 0.12122122212222
b) 56
c)
5
Properties of Real Numbers
For all real numbers a,b, and c
Addition
Multiplication
Closure
a b is a real number
ab is a real number
Commutative
a b b a
ab ba
Associative
(a b) c a (b c)
(ab)c a(bc)
Identity
There is a number 0 such that a 0 a and 0 a
a.
Inverse
For every real number a, there is a real number
a such that a (-a) 0.
6
The Distributive Property
For all real numbers a,b, and c
a(b c) ab ac and (b c)a ba ca
7
Example 2
Write and justify each step in the simplification
of (x y)(5 z).
x(5 z) y(5 z)
Distributive Prop
Distributive Prop
5x xz 5y yz
Commutative Prop
8
Order of Operations

• 1. innermost grouping symbols
• 2. exponents (powers)
• 3. multiplication and division in order from left
  to right
• 4. addition and subtraction in order from left to
  right

9
Example 3
Evaluate .
10
Practice
Evaluate.
1)
2)
11
Homework
p.90 17-55 odds,59,63,69,75