variables and expressions order of operations real numbers and the number line objective: to solve...
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Variables and ExpressionsOrder 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
Writing Expressions with Multiplication and Division
Got it?
Got it?
nb
na
18)
6)
Got it?
nb
na
18)
6)
6
6
)
y
y
Noc
Writing an Expression with Two Operations
Got it?
Got it?
84) xa
Got it?
84) xa )8(2) xb
Got it?
84) xa )8(2) xbx
c12
5)
Writing a Rule to Describe a Pattern
Writing a Rule to Describe a Pattern
Got it?
Got it?
2n
Class Work
• Top of Page 7 (lesson check)• 1, 2, 7, 8
Homework
• Pages 7-8• 9-25 odd• 39, 41, 43
Exponents
Exponents
• An exponential is expressed in the following:
• 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….
35
25
4555
Simplifying Powers
Got it?
Got it?
813333
Got it?
813333 27
8
3
2
3
2
3
2
Got it?
813333 27
8
3
2
3
2
3
2 125.5.5.5.
Order of Operations
Order of Operations
• Please• Excuse• My• Dear• Aunt• Sally
Order of Operations
• 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.
49)7()43( 22
222 43)43(
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?
248
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!• Right!
188248
422248
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:
2475 2
52512
27
34 4
Got it?
• Solve the following:
27835216352475 2
52512
27
34 4
Got it?
• Solve the following:
27835216352475 2
751252512
27
34 4
Got it?
• Solve the following:
27835216352475 2
751252512
175
85
5
814
27
34 4
Evaluating Algebraic Expressions Using Substitution
Evaluating Algebraic Expressions Using Substitution
Got it?
• Solve the following if a = 3 and b = 4.
23 ab ab 72 2
Got it?
• Solve the following if a = 3 and b = 4.
3912
)3()4(3
32
2
ab ab 72 2
Got it?
• Solve the following if a = 3 and b = 4.
3912
)3()4(3
32
2
ab
112132
21)16(2
)3(7)4(2
722
2
ab
Class Work
• Top of page 13 (lesson check)• 1-7 all
Homework
• Page 13• 9-33 odd• 37, 39, 41• 45, 47, 49
Square Roots
Simplifying a Square Root
Perfect Squares
14412
12111
10010
819
648
497
366
255
164
93
42
2
2
2
2
2
2
2
2
2
2
2
Perfect Squares
14412
12111
10010
819
648
497
366
255
164
93
42
2
2
2
2
2
2
2
2
2
2
2
12144
11121
10100
981
864
749
636
525
416
39
24
Got it?
Got it?
648
864)2
a
255
525)2
b
Got it?
648
864)2
a
255
525)2
b
3612
61
61
361
)(
)
c
121812
119
119
12181
)(
)
d
Real Number System
Graphing and Ordering Real Numbers
Homework
• Page 20• 9-17 odd• 45, 47, 49