Transcript Order of Operations

Variables and Expressions
Order of Operations
Real Numbers and the Number
Line
Objective: To solve problems by
using the order of operations.
Variables
Variables
Problem 1
Got it?
• What is an algebraic expression for 18 more than a
number n?
Got it?
• What is an algebraic expression for 18 more than a
number n?
n + 18
Got it?
• What is an algebraic expression for 22 less than a
number n?
Got it?
• What is an algebraic expression for 22 less than a
number n?
n – 22
Got it?
• What is an algebraic expression for 22 less than a
number n?
n – 22
• What is an algebraic expression for 30 less a number
n?
Got it?
• What is an algebraic expression for 22 less than a
number n?
n – 22
• What is an algebraic expression for 30 less a number
n?
30 – n
Writing Expressions with
Multiplication and Division
Got it?
Got it?
a )6 n
18
b)
n
18  n
Got it?
a )6 n
18
b)
n
18  n
c) No
6 y
y6
Writing an Expression with Two
Operations
Got it?
Got it?
a)4 x  8
Got it?
a)4 x  8
b) 2( x  8)
Got it?
a)4 x  8
b) 2( x  8)
5
c)
12  x
Writing a Rule to Describe a
Pattern
Writing a Rule to Describe a
Pattern
Got it?
Got it?
n2
Class Work
• Top of Page 7 (lesson check)
• 1, 2, 7, 8
Homework
• Pages 7-8
• 9-45 odd
Exponents
Exponents
• An exponential is expressed in the following:
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2
is read 5 to the second power or 5 squared.
is read 5 to the third power or 5 cubed.
is read 5 to the fourth power.
is read 5 to the fifth power.
Etc….
5
53
4
5
55
Simplifying Powers
Got it?
Got it?
3  3  3  3  81
Got it?
3  3  3  3  81
2 2 2 8
  
3 3 3 27
Got it?
3  3  3  3  81
2 2 2 8
  
3 3 3 27
.5  .5  .5  .125
Order of Operations
Order of Operations
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Please
Excuse
My
Dear
Aunt
Sally
Order of Operations
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Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Order of Operations
• Parenthesis- Always simplify everything inside of any
grouping symbol before doing anything else.
Order of Operations
• Parenthesis- Always simplify everything inside of any
grouping symbol before doing anything else.
• Exponents- After simplifying everything in the
grouping symbol, you then apply the exponent.
Order of Operations
• Parenthesis- Always simplify everything inside of any
grouping symbol before doing anything else.
• Exponents- After simplifying everything in the
grouping symbol, you then apply the exponent.
(3  4) 2  (7) 2  49
(3  4) 2  32  42
Order of Operations
• Multiplication
• Division.
• These operations are equal. You do not always
multiply before you divide. These operations are
done from left to right.
Order of Operations
• Multiplication
• Division.
• These operations are equal. You do not always
multiply before you divide. These operations are
done from left to right.
• Let’s look at the following. What do you think the
answer is?
8  4 2
Order of Operations
• Multiplication
• Division.
• These operations are equal. You do not always
multiply before you divide. These operations are
done from left to right.
• Let’s look at the following. What do you think the
answer is?
• Wrong!
8  4 2  8 8 1
• Right!
8  4 2  2 2  4
Order of Operations
• Addition.
• Subtraction.
• These operations are equal. You do not always add
before you subtract. These operations are done from
left to right.
Order of Operations
Got it?
• Solve the following:
5  7  42  2
12  25  5
4  34
72
Got it?
• Solve the following:
5  7  4 2  2  35  16  2  35  8  27
12  25  5
4  34
72
Got it?
• Solve the following:
5  7  4 2  2  35  16  2  35  8  27
12  25  5  12  5  7
4  34
72
Got it?
• Solve the following:
5  7  4 2  2  35  16  2  35  8  27
12  25  5  12  5  7
4  34 4  81 85


 17
72
5
5
Evaluating Algebraic Expressions
Using Substitution
Evaluating Algebraic Expressions
Using Substitution
Got it?
• Solve the following if a = 3 and b = 4.
3b  a
2
2b 2  7 a
Got it?
• Solve the following if a = 3 and b = 4.
3b  a
2
3(4)  (3) 2
12  9  3
2b 2  7 a
Got it?
• Solve the following if a = 3 and b = 4.
3b  a
2b 2  7 a
2
3(4)  (3)
12  9  3
2
2(4)  7(3)
2(16)  21
2
32  21  11
Class Work
• Top of page 13 (lesson check)
• 1-8 all
Homework
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Page 13
9-33 odd
37, 39, 41
45, 47, 49
Square Roots
Simplifying a Square Root
22  4
32  9
4 2  16
5 2  25
6 2  36
7 2  49
8 2  64
9 2  81
10 2  100
11  121
2
12 2  144
Perfect Squares
22  4
32  9
Perfect Squares
4 2
9 3
4 2  16
16  4
5 2  25
25  5
6 2  36
36  6
7 2  49
49  7
8 2  64
64  8
9 2  81
81  9
10 2  100
100  10
11  121
121  11
12 2  144
144  12
2
Got it?
Got it?
a ) 64  8
b) 25  5
82  64
52  25
Got it?
a ) 64  8
b) 25  5
c)
82  64
52  25
( 16 ) 2  361
1
36

1
6
d)
81
121
 119
81
( )  121
9 2
11
Cube Roots
• When looking at square roots, we ask what number
times itself gives the desired value. A cube root asks
what number times itself 3 times gives the desired
value. For example:
3
82
3
27  3
3
64  4
3
125  5
Real Number System
Example 3
• Classify each number.
a) 15
b) -1.4583
c) 57
Example 3
• Classify each number.
a) 15
b) -1.4583
c) 57
Natural, Whole, Integer, Rational
Example 3
• Classify each number.
a) 15
b) -1.4583
c) 57
Natural, Whole, Integer, Rational
Rational
Example 3
• Classify each number.
a) 15
b) -1.4583
c) 57
Natural, Whole, Integer, Rational
Rational
Irrational
Graphing and Ordering Real
Numbers
Homework
• Page 20
• 9-35 odd
• 45, 47, 49