Transcript Section 1-2: Exponents and Order of Operations

Section 1-2: Exponents and
Order of Operations
Objectives: (1) To Simplify and evaluate formulas and
expressions
(2) To add, subtract, multiply and divide expression with
exponents
(3) To simplify and evaluate expressions with grouping
symbols
Definitions
• To simplify a numerical expression, you replace it
with its simplest name.
• An exponent tells how many times a number, the
base, is used as a factor.
• A power has two parts, a base and an exponent
• You evaluate an algebraic expression by
substituting a given number for each variable.
Then Simplify the numerical expression using the
order of operations.
Order of Operations
Please, excuse my dear Aunt Sally.
• Please
– Parenthesis ( ), or other grouping symbols like braces { } and brackets [ ]
• Excuse
– Exponents
• My
– Multiplication
• Dear
– Division
• Aunt
– Addition
• Sally
– Subtraction
Order of Operations
• This is the order in which you must begin
evaluating expressions.
• Multiplication and division are inverse
operations (they undo each other) and
therefore are done by the order in which they
appear in the expression
• Addition and subtraction are inverse
operations and are done by the order in which
they appear in the expression
Simplifying a Numerical Expression
Simplify 25 – 8 • 2 + 32
25 – 8 • 2 + 9
25 – 16 + 9
9+9
18
• Which operation appears
1st?
• Exponents! Find 32
• Now, multiplication
• Subtraction comes first
because add/subt is done
by whichever comes first
in the expression
• And Add
• 18 is the simplified
answer
Evaluating an Algebraic Expression
Evaluate 3a – 23 ÷ b
a=7
b=4
3(7) – 23 ÷ (4)
3(7) – 8 ÷ 4
21 – 2
19
• First replace all
variables with their
numerical counterparts
with parenthesis
• Exponents first
• Multiplication AND
Division
• Subtraction
• All Done
Real World Examples (Word Problems)
Your favorite pair of
sneakers are on sale for
$59.00. There is a 6%
sales tax in your state
with any purchase. Find
the total cost of the
sneakers.
Use the following formula:
C = p + r• p
C is the cost
P is the price
R is the sales tax rate
Real World Examples (Word Problems)
C = 59 + (0.06)(59)
C = 59 + 3.54
C = 62.54
You’re done!
• Replace with actually
values.
• Order of operations
tells us multiply first.
• Now add
• Easy, right?
Simplifying an Expression with
Parenthesis
Simplify
15(13 – 7) ÷ (8 – 5)
15(6) ÷ (3)
90 ÷ 3
30
All done!
• Simplify the stuff inside
the parenthesis first.
• Remember that no
symbol between a
number outside a
parenthesis and the
parenthesis means
multiply
• Now divide
Evaluating Expressions with Exponents
Evaluate each expression
for c = 15 and d = 12
a. (cd)2
[(15)(12)]2
(180)2
32,400
• Substitute 15 for c and
12 for d
• Simplify the parenthesis
first
• Now raise it to the
exponent
Evaluating Expressions with Exponents
Evaluate each expression
for c = 15 and d = 12
b. cd2
(15)(12)2
(15)(144)
2,160
• Substitute 15 for c and
12 for d
• Raise 12 to the 2nd
power first
• Now multiply
Simplifying an Expression
Simplify 2[(13 – 7)2 ÷ 3]
2[(6)2 ÷ 3]
2[36 ÷ 3]
2 [ 12 ]
24
And you are done!
• 1st simplify the
parenthesis
• 2nd Simplify the power
• Simplify the brackets
• Multiply
Real World Problem Solving:
Urban Planning
A neighborhood
association turned a
vacant lot into a park.
The park is shaped like
the trapezoid to the
right. Use the formula
b b 
A  h
to find the area
2


of the lot.
1
2
b1 = 100 ft
b2 = 200 ft
Real World Problem Solving:
Urban Planning
We know:
 b  b2 
A  h 1

 2 
 100  200 
A  130 

2


 300 
A  130 

2


A  130 (150 )
A  19 ,500
The area of the park is
19,500 ft2
• Substitute 130 for h, 100
for b1 and 200 for b2
• Simplify the numerator
• Simplify the fraction
• Multiply