1. Order of Operations
Chapter 1
Section 1.1

2. Objective
Students will simplify numerical expressions and evaluate algebraic expressions. Students will also simplify expressions with grouping symbols.

3. Vocabulary
Expression Variable Variable expression Numerical expression Substitution Grouping symbols Order of operations

4. Concept
An expression contains numbers, variables, and operations (no equal sign)

5. Concept
A variable is a symbol used to represent one or more numbers. example: a, x, y, n, … , any letter of alphabet

6. Concept
A variable expression is an expression that contains a variable example: 15 X n

7. Concept
Important to Remember: 19 X n can be written as 19n a X b can be written as ab ½ X x can be written as 1/2x

8. Concept
A numerical expression is an expression that names a particular number example: 4.5 X 5

9. Concept
Substitution Principle: An expression may be replaced by another expression that has the same value.

10. Concept
Evaluating the expression = replacing each variable in a variable expression by a given value and simplifying the result

11. Example
Evaluate each expression if a = 5 1. a a 35

12. Concept
When solving expressions is it important to remember that you must always follow the order of operations Parenthesis Exponents Multiply/Divide Add/Subtract

13. Example
Simplify each expression 1. (42 ÷ 6) ÷ (8 – 2) 9

14. Example
Evaluate the expression when x = 12 and y = 9 (5x) – (3 + y) 48

15. Example
Simplify 1. 6(5 – 3) (5) – 3 27

16. Concept
Some expressions contain grouping symbols other than parenthesis (brackets or fraction bar). Always begin by simplifying the expression in the innermost grouping symbol then work toward the outermost grouping symbol. If the expression contains a fraction bar, simplify top, simplify bottom, simplify top with bottom.

17. Example
Simplify – – [52 ÷ (7 + 6)] 14

18. Example
Simplify X – X 2 ÷ 8 15

19. Example
Evaluate if x = 3 and y = 8 4x + 5y 3x – y 52

20. Questions

21. Assignment
Worksheet