Chapter 1 Algebra Mathematical Models and Problem Solving

Chapter 1 Algebra, Mathematical Models, and Problem Solving

1. 1 Algebraic Expressions and Real Numbers

Variables in Algebra uses letters such as x and y to represent numbers. If a letter is used to represent various numbers, it is called a variable. For example, the variable x might represent the number of minutes you can lie in the sun without burning when you are not wearing sunscreen. Blitzer, Algebra for College Students, 6 e – Slide #3 Section 1. 1

Algebraic Expressions A combination of variables and numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots, is called an algebraic expression. Blitzer, Algebra for College Students, 6 e – Slide #4 Section 1. 1

Translating Phrases into Expressions English Phrase sum plus increased by more than difference minus decreased by less than product times of (used with fractions) twice quotient divide per ratio Mathematical Operation Addition Subtraction Multiplication Division Blitzer, Algebra for College Students, 6 e – Slide #5 Section 1. 1

Translating Phrases into Expressions EXAMPLE Write the English phrase as an algebraic expression. Let x represent the number. Four more than five times a number SOLUTION Blitzer, Algebra for College Students, 6 e – Slide #6 Section 1. 1

Evaluating an Algebraic Expression EXAMPLE The formula expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. Use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. SOLUTION Replace F with 50 Blitzer, Algebra for College Students, 6 e – Slide #7 Section 1. 1

Evaluating an Algebraic Expression CONTINUED Subtract Multiply Therefore . Blitzer, Algebra for College Students, 6 e – Slide #8 Section 1. 1

Order of Operations - PEMDAS 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 occur, working from left to right. Blitzer, Algebra for College Students, 6 e – Slide #9 Section 1. 1

In evaluating expressions, what comes first? Remember by “PEMDAS” - Please Excuse My Dear Aunt Sally parentheses, exponents, multiplication, division, addition, subtraction • #1 Start with the parentheses. Parentheses say “Me First!” • #2 Then evaluate the exponential expressions. • #3 Multiplication and division are equal in the order of operations – Perform them next. • #4 Addition and subtraction are also equal to each other in order – and they come last. Blitzer, Algebra for College Students, 6 e – Slide #10 Section 1. 1

Order of Operations - PEMDAS EXAMPLE Evaluate for . SOLUTION Replace R with 3 Evaluate inside parentheses first Evaluate Blitzer, Algebra for College Students, 6 e – Slide #11 Section 1. 1 – first exponent

Order of Operations - PEMDAS CONTINUED Evaluate 27 -2(81) 27 -162 Multiply -135 Subtract – second exponent Blitzer, Algebra for College Students, 6 e – Slide #12 Section 1. 1

Order of Operations - PEMDAS EXAMPLE #2 Evaluate for . SOLUTION Replace x with 6 Evaluate inside parentheses first Evaluate exponent Multiply Subtract Blitzer, Algebra for College Students, 6 e – Slide #13 Section 1. 1

1. 1 Assignment p. 10 (4 -24 even)