1. 1.2 Evaluate and Simplify Algebraic Expressions

2. In this lesson you will:
Evaluate algebraic expressions,
Simplify algebraic expressions by combining like terms,
Solve real life problems using these skills.

3. Numerical expressions consist of:
These are numerical expressions:
Numbers
Operations
Grouping symbols
These are NOT:

4. Exponents are used to represent repeated factors in multiplication.
Base
Exponent
5 factors of 2

5. To evaluate powers (exponents), notice the ( ):
( ) protect the negative and carry it through the entire problem

6. Write the expression using exponents:

7. To avoid confusion, an order of operations is needed for expression like the one above
First, do operations that occur within grouping symbols (like parentheses).
Next, evaluate powers.
Then, do multiplications and divisions in order from left to right.
Finally, do additions and subtractions in order from left to right.

8. Add within parentheses
Evaluate power
Multiply
Add
To help you remember the order of operations:
PEMDAS (Please Excuse My Dear Aunt Sally: Parentheses, Exponents, Multiplication & Division, Addition & Subtraction.

9. Evaluate the expression:
P E M D A S
Evaluate the expression:

10. A Variable Is a letter used to represent one or more numbers.
Any number used to replace a variable is a value of the variable.
An expression involving variables is called an algebraic expression.

11. Evaluate
when x = -2.

12. Evaluate the expression:

13. Simplifying Algebraic Expressions

14. For an expression such as 2x + 3
The 2x and 3 are called terms.
When a term is the product of a number and a power of a variable such as or
The number is the coefficient of the power.
Are like terms because they have the same variable part.
and
The distributive property makes it possible to combine like terms into a single term.
Constant terms such as –4 and 2 are also like terms.

15. Writing and Evaluating a Real-Life Model

16. Suppose you have $50 and are buying some movies on DVD’s that cost $15 each. Write an expression that shows how much money you have left after buying n movies. Evaluate the expression when n = 2 and n = 3. -
Original
Amount
Price per
movie
Number of movies bought
Verbal
Model
Original amount = $50
Price per movie = $15
Number of movies bought = n
Labels
When you buy 2 movies, you have 50-15(2) = $20 left
When you buy 3 movies, you have 50 – 15(3) = $ 5 left.
50-15n
Algebraic Model