1. 1.7 Exponents and Order of Operations
Exponential Notation:
Shorthand for writing repeated multiplication of the same number.

2. 1.7 Exponents and 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

3. 1.7 Exponents and Order of Operations
PEMDAS

4. 1.7 Exponents and Order of Operations
PEMDAS

5. 1.7 Exponents and Order of Operations
PEMDAS

6. 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.

7. 1.8 Variables, Algebraic Expressions and Equations
Evaluate the following:

8. 1.8 Variables, Algebraic Expressions and Equations
Evaluate the following: OR

9. 1.8 Variables, Algebraic Expressions and Equations
Evaluate the following:

10. 1.8 Variables, Algebraic Expressions and Equations
Determine whether 8 is a solution of the equation
True statement,
8 is a solution.

11. 1.8 Variables, Algebraic Expressions and Equations
Determine which numbers in the set { 10, 6, 8} are solutions of the equation
False statement,
True statement,
False statement,
10 is not a solution.
6 is a solution.
8 is not a solution.

12. 1.8 Variables, Algebraic Expressions and Equations
Write an Algebraic Expression. Use x to represent “a number.”
Twice a number
8 increased by a number
10 minus a number
10 subtracted from a number
The quotient of a number and 6 or

13. 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.

14. 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!

15. 2.1 Introduction to Integers
Graphing Integers
Graph -4, -1, 2, and -2 on the number line.
Negative integers
Zero
Positive integers

16. 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.
2. The tamarack tree survives at the edge of the arctic tundra at 85 degrees below zero.
3. The bottom of Crater Lake is located at 4,229 feet above sea level.
4. The world’s deepest colony of bats is located in a New York zinc mine at a depth of 3805 feet.

17. 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”

18. 2.1 Introduction to Integers
Comparing Integers
Insert or between each pair of numbers to make a true statement.

19. 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: | |

20. 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
YES NO

21. 2.1 Introduction to Integers
Opposite Numbers
Find the opposite values of the following numbers:

22. 2.1 Introduction to Integers
Mixed Practice