1. Order of Operations
PEMDAS

2. Expression
Any combination of numbers and operations (parentheses, exponents, multiply/divide, and addition/subtraction)
Examples: 2+2
3x6-8+4
(2+4)x8

3. Evaluating an Expression
To evaluate an expression- find the numerical value of an expression using order of operations
1. Parentheses
2. Exponents
3. Multiply/Divide
4. Add/Subtract

4. PEMDAS
Parentheses- Do all problems in parentheses before like problems not in parentheses. If there are more than one set of parentheses do the inner most expression in parentheses and work your way out.
Example: 45-2x(15-3) Work the parentheses 1st,
15-3 is 12
=45-2x12 Now follow order of operations
from left to right
= Subtract
=21 The answer is 21!!

5. PEMDAS
Exponents- After working the parentheses you will work the exponents in a problem
Example: 4+(8-6)+22 Work Parentheses 1st
= Now work
Exponents
= Follow PEMDAS
=10 The answer is 10!

6. PEMDAS
Multiply/Divide- perform the multiplication and division from left to right, whatever comes first.
Example: 42/7(4-3) Parentheses 1st
=42/7(1) Order of Operations from left
to right: Division Next
=6(1) Multiply
=6 The Answer is 6!

7. PEMDAS
Addition/Subtraction- perform the addition and subtraction of the expression from left to right, whatever comes first
Example: 7(5+(13-4)/3)) Parentheses 1st
=7(5+(9)/3)) Division in the
parentheses next
=7(5+3) Parentheses next
=7(8) Multiply
=56 The Answer is 56!

8. PEMDAS Proof
This is how you are expected to solve your problems. On the left side of the line you work your problem and on the right side of the line you put your justification.
Example:
Problem: 2+10(8-6)/22
Proof:
=2+10(2)/22
Parenthesis (Subtraction)
=2+10(2)/4
Exponents
=2+20/4
Multiplication
=2+5
Division =7
Addition

9. Examples 7+2x3 8+4x2 15/3+12/4 (56-8)+36/3 [5(8+2)-46]x10 5{7+4-2(7)}
(72+12)/(35+7)