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Transcript
1.7 Exponents and Order of Operations
Exponential Notation:
Shorthand for writing repeated multiplication
of the same number.
3
4
3 3 3  3
8888  8
10 10 10 10 10  10
5
2
6
5

4

5 5 4 4 4 4 4 4
75  7  7  7  7  7
23  102  65  2  2  2 10 10  6  6  6  6  6
42
 4 4
1.7 Exponents and Order of Operations
Order of Operations:
The order in which mathematical operations
must be performed.
PEMDAS
P
→
Parenthesis
E
→
Exponents
M →
Multiplication
D
→
Division
A
→
Addition
S
→
Subtraction
1.7 Exponents and Order of Operations
Order of Operations: PEMDAS
93  8  4
27  8  4
27  2
25
48  3  2
48  3  4
16  4
64
2
10  7   2  32
4
3  2  32
4
81  2  9
81 18
99
1.7 Exponents and Order of Operations
Order of Operations: PEMDAS
36  6  3  5
63  5
18  5
23
36  20  4  2  4 2  6
36  20  8  4 2  6
36  12  4 2  6
36  12  16  6
3  16  6
19  6
13
1.7 Exponents and Order of Operations
Order of Operations: PEMDAS
25  8  2  32
23  2 
25  8  2  3  23  2
25  8  2  3  21
2
2
25  8  2  9  2
25  16  9  2
41  9  2
32  2
16
1.8 Variables, Algebraic Expressions and Equations
Definitions:
Variable - A letter that represents a number or a
set of numbers.
Algebraic Expression - A combination of operations
on variables and numbers.
Equation- Two algebraic expressions that are equal.
Solution- The value or values for the variable that
make an equation true.
Evaluate- Substituting a value for the variable of an
expression or equation and calculating the result.
1.8 Variables, Algebraic Expressions and Equations
Evaluate the following:
x  2 if x is 7
72
5
y  x  3 if x  8 and y  4
48  3
45
20
y6
if x  6 and y  18
x
18  6
24

 4
6
6
1.8 Variables, Algebraic Expressions and Equations
Evaluate the following:
25  z 3  x if z  2 and x  1
25  2  1 if z  2 and x  1
3
OR
25  2  1 if z  2 and x  1
3
25  8  1
17  1
18
1.8 Variables, Algebraic Expressions and Equations
Evaluate the following:
5F  32 
if F  41
9
541  32 
9
59 
9
45
 5
9
1.8 Variables, Algebraic Expressions and Equations
Determine whether 8 is a solution of the equation
3 y  6   6
38  6   6
32   6
66
True statement,
8 is a solution.
1.8 Variables, Algebraic Expressions and Equations
Determine which numbers in the set { 10, 6, 8} are
solutions of the equation
5n  4  34
510   4  34
56   4  34
58  4  34
50  4  34
30  4  34
40  4  34
54  34
34  34
44  34
False statement,
True statement,
False statement,
10 is not a solution.
6 is a solution.
8 is not a solution.
1.8 Variables, Algebraic Expressions and Equations
Write an Algebraic Expression. Use x to represent “a
number.”
2x
Twice a number
8 x
8 increased by a number
10 minus a number
10  x
10 subtracted from a number
x  10
The quotient of a number and 6
x
6
or
x 6
2.1 Introduction to Integers
Definitions:
Positive numbers – All numbers greater than zero.
The positive sign states that the number is to the
right of zero on a number line.
Negative numbers – All numbers less than zero. The
negative sign states that the number is to the left of
zero on a number line.
Signed numbers – Positive numbers, negative
numbers and zero.
2.1 Introduction to Integers
Definitions:
Integers – All positive numbers, negative numbers
and zero, but no fractions or decimals.
Negative integers
Zero
Positive integers
NOTE: Zero is neither positive or negative!
2.1 Introduction to Integers
Graphing Integers
Graph -4, -1, 2, and -2 on the number line.
Negative integers


Zero

Positive integers

2.1 Introduction to Integers
Representing Position with Integers
Use an integer to represent each of the following
positions.
1. The wreck of the Titanic was located at 12,460 feet
below sea level.  12,460 feet
2. The tamarack tree survives at the edge of the arctic
tundra at 85 degrees below zero.  85
3. The bottom of Crater Lake is located at 4,229 feet above
sea level. 4229 feet
4. The world’s deepest colony of bats is located in a New
York zinc mine at a depth of 3805 feet.
 3805 feet
2.1 Introduction to Integers
Comparing Integers
For any two numbers graphed on a number line,
the number to the right is the greater number
and the number to the left is the smaller number.
Inequality Symbols

“is greater than”

“is less than”

“is greater than or equal to”

“is less than or equal to”
2.1 Introduction to Integers
Comparing Integers
Insert  or  between each pair of numbers to
make a true statement.
0  5
521  784
3  3
 7   12
 126   79
2.1 Introduction to Integers
Absolute Value of a Number
The distance a number is from 0 on the number
line.
The distance a number is from 0 is always 0 or a
positive distance – NEVER a negative value.
The symbol or operator for the Absolute Value is:
| |
22  22
15  15
0
0
 586  586
37  37
2.1 Introduction to Integers
Opposite Numbers
Two numbers that are the same distance from zero
but are on opposite sides of zero.
Which of the following represent opposites?

YES
NO


YES



2.1 Introduction to Integers
Opposite Numbers
Find the opposite values of the following numbers:
14   14
9  9
58   58
2.1 Introduction to Integers
Mixed Practice
62  62
 43   43
  8  8
4  4
 7  7
Evaluate :  x if x  10
  10 
 10