1.8 Intro to Variables, Algebraic Expressions, and Equations
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1 1.8 Intro to Variables, Algebraic Expressions, and Equations Professor Tim Busken M.S. Applied Mathematics with a Concentration in Dynamical Systems San Diego State University 2011 Southwestern College Math Faculty February 18, 2012
2 Talk Outline 1 Objective A: Evaluate Algebraic Expressions.
3 Talk Outline 1 Objective A: Evaluate Algebraic Expressions. 2 Objective B: Identify Solutions of Equations.
4 Talk Outline 1 Objective A: Evaluate Algebraic Expressions. 2 Objective B: Identify Solutions of Equations. 3 Objective C: Translate Phrases into Variable Expressions.
5 Section 1 Objective A: Evaluate Algebraic Expressions.
6 Definition +,,, and are called the arithmetic operations
7 Definition +,,, and are called the arithmetic operations Definition A variable is a symbol or letter used to represent a number, or set of numbers.
8 Definition +,,, and are called the arithmetic operations Definition A variable is a symbol or letter used to represent a number, or set of numbers. Definition A combination of arithmetic operations on variables and numbers is called an algebraic expression or expression.
9 If two variables or a number and a variable are next to each other, with no operations sign between them, the operation is multiplication. For example, 2x means 2 x and xy or x(y) means x y
10 Also, the meaning of an exponent remains the same when the base is a variable.
11 Also, the meaning of an exponent remains the same when the base is a variable. For example, x 2 = x }{{} x and y 5 = y y y y y }{{} 2 factors of x 5 factors of y
12 Also, the meaning of an exponent remains the same when the base is a variable. For example, x 2 = x }{{} x and y 5 = y y y y y }{{} 2 factors of x 5 factors of y Algebraic expressions such as 4x have different values depending on replacement values for x.
13 Also, the meaning of an exponent remains the same when the base is a variable. For example, x 2 = x }{{} x and y 5 = y y y y y }{{} 2 factors of x 5 factors of y Algebraic expressions such as 4x have different values depending on replacement values for x. For instance, if x = 3, then 4x becomes 4x = 4 3 = 12.
14 If x = 5, then 4x becomes 4x = 4 5 = 20.
15 If x = 5, then 4x becomes 4x = 4 5 = 20. Definition Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression for the variable.
16 If x = 5, then 4x becomes 4x = 4 5 = 20. Definition Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression for the variable. When finding the value of an expression, remember to follow the Order of Operations.
17 The Order of the Arithmetic Operations When evaluating or simplifying an algebraic or arithmetic expression, we always use the ORDER OF OPERATIONS. In other words we evaluate the expression in the following order: P Parenthesis E Exponents M Multiplication D Division A Addition S Subtraction The operations +,,, must be performed from left to right! The acronym PEMDAS helps us to recall the ORDER OF OPERATIONS.
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