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Thinking
Mathematically
Algebra: Equations and Inequalities
6.1 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 Inequalities
6.1 Algebraic Expressions and Formulas