Chapter 1 Algebra, Mathematical Models, and Problem Solving

1.1 Algebraic Expressions and Real Numbers

Variables in Algebra 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, 6e – Slide #3 Section 1.1

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, 6e – Slide #4 Section 1.1 Algebraic Expressions

Blitzer, Algebra for College Students, 6e – Slide #5 Section 1.1 English PhraseMathematical Operation sum plus increased by more than Addition difference minus decreased by less than Subtraction product times of (used with fractions) twice Multiplication quotient divide per ratio Division Translating Phrases into Expressions

Blitzer, Algebra for College Students, 6e – Slide #6 Section 1.1 Translating Phrases into ExpressionsEXAMPLE Write the English phrase as an algebraic expression. Let x represent Four more than five times a number SOLUTION the number.

Blitzer, Algebra for College Students, 6e – Slide #7 Section 1.1 Evaluating an Algebraic ExpressionEXAMPLE 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, 6e – Slide #8 Section 1.1 Evaluating an Algebraic Expression Multiply Therefore CONTINUED Subtract.

Blitzer, Algebra for College Students, 6e – Slide #9 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.

In evaluating expressions, what comes first? #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. Remember by “PEMDAS” - Please Excuse My Dear Aunt Sally parentheses, exponents, multiplication, division, addition, subtraction Blitzer, Algebra for College Students, 6e – Slide #10 Section 1.1

Blitzer, Algebra for College Students, 6e – Slide #11 Section 1.1 Order of Operations - PEMDAS Evaluate for. EXAMPLE Replace R with 3 Evaluate inside parentheses first Evaluate – first exponent SOLUTION

Blitzer, Algebra for College Students, 6e – Slide #12 Section 1.1 Order of Operations - PEMDAS -135Subtract Multiply CONTINUED (81) Evaluate – second exponent

Blitzer, Algebra for College Students, 6e – Slide #13 Section 1.1 Order of Operations - PEMDAS Evaluate for. EXAMPLE #2 Replace x with 6 Evaluate inside parentheses first Evaluate exponent SOLUTION Multiply Subtract

1.1 Assignment p. 10 (4-24 even)