1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Real Numbers and Introduction to Algebra

2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.2 Exponents, Order of Operations, and Variable Expression

3. Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation We may use exponential notation to write products in a more compact form. The 2 is called the base; it is the repeated factor. The 5 is called the exponent and is the number of times the base is used as a factor. can be written as

4. Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

5. Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Using the Order of Operations Order of Operations 1. Perform all operations within grouping symbols first, starting with the innermost set. 2. Evaluate exponential expressions. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right.

6. Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify. Write 3 2 as 9. Divide 9 by 3. Add 3 to 6. Divide 9 by 9.

7. Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Evaluating Algebraic Expressions Variable: A letter to represent all the numbers fitting a pattern. Algebraic Expression: A collection of numbers, variables, operation symbols, and grouping symbols. Evaluating the Expression: Replacing a variable in an expression by a number and then finding the value of the expression

8. Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Evaluate when z = ‒ 3.

9. Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solutions of Equations Solving: In an equation containing a variable, finding which values of the variable make the equation a true statement. Solution: In an equation, a value for the variable that makes the equation a true statement.

10. Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example – 7 is not a solution. Determine whether ‒ 7 is a solution of x + 23 = ‒ 16.

11. Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Translating Phrases Addition ( + ) Subtraction ( - ) Multiplication ( ∙ ) Division ( ÷ ) Equal Sign sum differenceproductquotientequals plus minus timesdividegives added to subtracted from multiplyinto is/was/ should be more than less thantwiceratioyields increased by decreased byofdivided byamounts to total less represents is the same as

12. Martin-Gay, Developmental Mathematics, 2e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Write as an algebraic expression. Use x to represent “a number.” a. 5 decreased by a number 5 – x b. The quotient of a number and 12