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 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

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

C=3 and d=7 6c+4-3d 4(d-c)+1 d²+5d-6

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

P=5 and q=12 4q Q+2(p=1) q² 4p-2