1.7 Exponents and Order of Operations Exponential Notation:

Shorthand for writing repeated multiplication of the same number.

8  8  8  8  8 4 3  3  3  3 3 10  10  10  10  10  10 5 5  5  4  4  4  4  4  4  5 2  4 6 4 2  4  4 2 3  10 2  6 5  7 5  7  7  7  7  7 2  2  2  10  10  6  6  6  6  6

1.7 Exponents and Order of Operations Order of Operations:

The order in which mathematical operations must be performed.

P E M D A S PEMDAS → → → → → → Parenthesis Exponents Multiplication Division Addition Subtraction

1.7 Exponents and Order of Operations Order of Operations:

9  27 3   8 8   4 4 48 48   3 3   2 4 2

PEMDAS

 10   4   7 2  4   3 2 2  3 2 27 25  2 16  4 64 81  2  9 81  18 99

1.7 Exponents and Order of Operations

6

Order of Operations:

36  6  3  5 36

PEMDAS

 20 

 

  18 3   5 5 36   8   4 2 36    20 12  4 2  6 23 36  12  16  6   4 2 6 3 19  16  6  6  6 13

1.7 Exponents and Order of Operations Order of Operations:

25  2 8



3   2 2 



3 2  25

PEMDAS

 8  2   25



25



25



41     8 8   2 2   9 16



  2 9 3 2 3 2   9







 2   2  2



3  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 7  2 5

if x is

7

y

 6

x

18  6 6

if



x

 6

and y

 18 24 6  4

y

4 4

 

x

8

 

  3



3



20

if x

 8

and y

 4

1.8 Variables, Algebraic Expressions and Equations Evaluate the following:

25 

z

3 

x if z

 2

and x

 1 25  2 3  1

if z

 2

and x

 1

OR

if z

 2

and x

 1 25  25  8  1 17  1 18

1.8 Variables, Algebraic Expressions and Equations Evaluate the following:

5



F

 5



41 9  32 32

 

if F

 41 5

 

9 9 45 9  5

1.8 Variables, Algebraic Expressions and Equations Determine whether 8 is a solution of the equation

3



y

3



8   6



6



  6 6 3

 

 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

5

solutions of the equation

5

n



 

 4  34 5

 

 4 4   34 34 5

 

 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.” Twice a number

2

x

8 increased by a number 10 minus a number 10 subtracted from a number

8 

x

10 

x 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 – numbers and zero.

Positive numbers, negative

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



make a true statement.

0   5  3  3  7   12 521  784  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  586  586 0  0 37  37

YES 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

 

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

62  62

Mixed Practice



 43



  43 

 

 8   7   7  4  4

Evaluate

: 

x if x

  10   10   10