1. 1.2 Variables, Expressions, and Properties

2. Vocabulary
Variable: A symbol, usually a letter, used to represent a number.
Algebra: Branch of mathematics that involves expressions with variables.
Algebraic Expression: It contains a variable, a number, and at least one operation. Example, 4n
Evaluate: Find the value of an algebraic expression, first replace the variable or variables with the known values
Numerical Expression: One with only numbers and operations
Counterexample: Opposite
Property: A feature of an object or a rule that is always true.

3. Order of Operations (PEMDAS)
Parenthesis first. Start with the innermost grouping.
Exponents. (5²)
Multiply
Divide from left to right
Add
Subtract from left to right

4. Properties
Commutative: Applies ONLY to addition and multiplication. Examples, 2+1=3 as 1+2=3; 2*8=16 and 8*2=16
Associative: Applies ONLY to addition and multiplication. Examples 2+(3+8)=(2+3)+8; as 3*(4*5)=(3*4)*5
Distributive: The word says it all DISTRIBUTE. Example, 4(6+2)=4*6+4*2
Identity: Something that does not affect the original number. Example,9+0=9, 5*1=5

5. Identify Properties Name the property 2*(5*n)=(2*5)*n 42+x+8=42+8+x
3(2+5)=3(2)+3(5)
6(5*2)=(6*5)2

6. Evaluate Algebraic Expressions
A= 5 and B= 4
4a-3b+1
G=5
g²-2g-4

7. C=3 and d=7
6c+4-3d
4(d-c)+1
d²+5d-6

8. Evaluate Algebraic Fractions
M=9 and n=5
4+6m
2n-8
P=5 and q=12
3p-6
8-p

9. P=5 and q=12 4q
Q+2(p=1) q²
4p-2