exponents, order of operations, and inequalities · 2014. 8. 22. · order of operations please...
TRANSCRIPT
Exponents, Order of Operations, and Inequalities
Objectives
• An expression like is called a power
• and is read x to the nth power.
base
exponent
The exponent indicates the number of times
the base is used as a factor
OBJECTIVE 1 Use exponents.
Power
3 to the first power 3
3 to the second power or 3 squared 3x3
3 to third power or 3 cubed 3x3x3
By definition, for any nonzero number x,
Evaluate each expression.
a.
b.
Answer: 625
Answer: 32
• 1) Evaluate expressions inside grouping symbols
• 2) Evaluate all powers.
• 3) Do all multiplications and/or divisions from left to right.
• 4) Do all additions and/or subtractions from left to right
Please Excuse My Dear Aunt Sally
OBJECTIVE 2 Use the rules for order of operations.
Order of Operations
Please Excuse My Dear Aunt Sally
1) Parentheses, brackets, braces, fraction bars
2) Exponents
3) Multiplication and Division (left to right)
4) Addition and Subtraction (left to right)
Example:
2 ∙ (3 + 4)
2 ∙ 7
14
Order of Operations
Please Excuse My Dear Aunt Sally
1) Parentheses, brackets, braces, fraction bars
2) Exponents
3) Multiplication and Division (left to right)
4) Addition and Subtraction (left to right)
Example: 2 ∙ 4 + 10 ÷ 5
8 ∙ + 10 ÷ 5
8 + 2
10
Order of Operations
Please Excuse My Dear Aunt Sally
1) Parentheses, brackets, braces, fraction bars
2) Exponents
3) Multiplication and Division (left to right)
4) Addition and Subtraction (left to right)
Example: 22 ∙ (4 - 2) + 3
22 ∙ 2 + 3
4 ∙ 2 + 3
8 + 3
11
Order of Operations
[32 ∙ (6 - 3)] + 6
[32 ∙ 3] + 6
[9 ∙ 3] + 6
27 + 6
33
Please Excuse My Dear Aunt Sally
1) Parentheses, brackets, braces, fraction bars
2) Exponents
3) Multiplication and Division (left to right)
4) Addition and Subtraction (left to right)
Please Excuse My Dear Aunt Sally
1) Parentheses, brackets, braces, fraction bars
2) Exponents
3) Multiplication and Division (left to right)
4) Addition and Subtraction (left to right)
Example
OBJECTIVE 3 Use more than one grouping symbol.
Example 2-2a
Evaluate .
Evaluate inside
grouping symbols.
Multiply.
Answer: Multiply.
Evaluate numerical expressions Grouping symbols
Evaluate the numerator
Evaluate the denominator
Evaluate numerical expressions Fraction Bar
Example 2-3c
Evaluate
Answer: 1
> is greater than or equal to
> is greater than
< is less than or equal to
< less than
= equal to
Read left to right:
5 < 7 5 is less than 7
5 < 7 5 is less than or equal to 7
6 > 3 6 is greater than 3
6 > 4 6 is greater than or equal to 4
5 = 5 5 is equal to 5
OBJECTIVE 5. Translating from words to symbols.
Example Write each word statement in symbols.
a.) Twelve equals ten plus two.
b.) Nine is less than ten
c.) Fifteen is not equal to eighteen.
d.) Seven is greater than four.
e.) Thirteen is less than or equal to forty.
f.) Eleven is greater than or equal to eleven.
1111 f.
40 13 e.
47 d.
18 15 c.
109 b.
21012 a.
Write statements that change the direction of inequality
610 106 83 38