1.2 Variables, Expressions, and Properties

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.

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

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

Identify PropertiesName the property

1) 2*(5*n)=(2*5)*n

2) 42+x+8=42+8+x

3) 3x+0=3x

4) 3(2+5)=3(2)+3(5)

5) 6(5*2)=(6*5)2

Evaluate Algebraic Expressions• A= 5 and B= 4

4a-3b+1

• G=5g²-2g-4

• C=3 and d=76c+4-3d

4(d-c)+1

d²+5d-6

Evaluate Algebraic Fractions• M=9 and n=5

4+6m2n-8

• P=5 and q=123p-68-p

• P=5 and q=124q

Q+2(p=1)

q²4p-2