Thinking Mathematically

Algebra: Equations and Inequalities6.1 Algebraic Expressions and Formulas

Order of Operations

1. First, perform all operations within grouping symbols.

2. Next, evaluate all exponential expressions.3. Next, do all multiplications and divisions in the

order in which they occur, working from left to right.

4. Finally, do all additions and subtractions in the order in which they ocuur, working from left to right.

“Algebraic Expressions”

An “algebraic expression” uses addition, subtraction, multiplication, division, powers, roots, etc. to combine numbers and letters that represent numbers. Letters that stand for numbers are called “variables.” In an algebraic expression the ordinary rules of arithmetic, including the order of operations, apply.

When a number is multiplied times a variable they are written next to each other. For example 2x means “two” times “x.”

Exercise Set 6.1 #7

Evaluate x2 – 6; for x = -2

Vocabulary of Alegraic Expressions

• Terms – parts separated by addition or subtraction

• Coefficient – the numeric multiplier of a term

• Constant term – term which does not contain a variable.

• Like terms – terms which share a common variable.

Properties of Real Numbers

Commutative Property of addition: a+b=b+a

Commutative Property of Multiplication: ab=ba

Associative Property of addition: (a+b)+c=a+(b+c)

Associative Property of multiplication: (ab)c=a(bc)

Distributive Property

a(b + c) = ab + ac

a(b - c) = ab - ac

“Simplifying”Algebraic Expressions

Simplied expression – parenthesis have been removed and like terms have been combined.

The rules of arithmetic can be used to “simplify” an algebraic expression.

Exercise Set 6.1 #45, 49, 53

Simplify

3(x + 5) = ?

5(3x + 4) -4 = ?

7(3y – 5) + 2(4y + 3) = ?

Thinking Mathematically

Algebra: Equations and Inequalities6.1 Algebraic Expressions and Formulas