Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 Real Numbers and Introduction to Algebra

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4 Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE = 3 Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE TRUE = 3 Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE TRUE = 3 ¾ > 4+-6 Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE TRUE = 3 ¾ > 4+-6 ¾ > -2 Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE TRUE = 3 ¾ > 4+-6 ¾ > -2 Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4FALSE TRUE = 3 ¾ > 4+-6 ¾ > -2 8 ≠ |-8| Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The absolute value of negative two is less than negative four. 1. The sum of five and negative two is a whole number. 3. The quotient of three and four is greater than the sum of four and negative six. 3. Eight is not equal to the the absolute value of negative eight. |-2| < -4 FALSE TRUE = 3 ¾ > 4+-6 ¾ > -2 8 ≠ |-8| Translate the following into mathematical sentences. Then, determine if the sentence is true or false.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1.3 Exponents, Order of Operations, and Variable Expression

14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives:  Define and use exponents and order of operations  Evaluate algebraic expressions  Determine whether a number is a solution to an equation  Translate phrases into expressions and sentences into equations

15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation We may use exponential notation to write products in a more compact form. can be written as

16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation We may use exponential notation to write products in a more compact form. can be written as 2525

17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation We may use exponential notation to write products in a more compact form. can be written as 2525 base – repeated factor (number being multiplied) can be written as

18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Exponential Notation We may use exponential notation to write products in a more compact form. can be written as 2525 exponent - number of times the base is a factor (repeatedly multiplied) base – repeated factor (number being multiplied) can be written as

19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

23 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

24 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

25 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

26 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

27 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Evaluate. a. 2 6 = 2 · 2 · 2 · 2 · 2 · 2 = 64 b. 5 4 = 5 · 5 · 5 · 5 = 625 c. 9 1 = 9 d.

28 Copyright © 2012 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.

29 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Simplify.

30 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Simplify.

31 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Simplify.

32 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Simplify.

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Simplify.

34 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Simplify.

35 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Simplify.

36 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Simplify.

37 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Simplify.

38 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Simplify.

39 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify.

40 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9.

41 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9.

42 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9. Divide 9 by 3.

43 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9. Divide 9 by 3.

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9. Divide 9 by 3. Add 3 to 6.

45 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9. Divide 9 by 3. Add 3 to 6.

46 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9. Divide 9 by 3. Add 3 to 6. Divide 9 by 9.

47 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify. Write 3 2 as 9. Divide 9 by 3. Add 3 to 6. Divide 9 by 9.

48 Copyright © 2012 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

49 Copyright © 2012 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 Plug it in!

50 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3.

51 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in!

52 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in!

53 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in!

54 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in! Simplify.

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in! Simplify.

56 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in! Simplify.

57 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Evaluate when z = ‒ 3. Plug it in! Simplify.

58 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solutions of Equations **Recall: An equation is when two algebraic expressions or mathematical statements are connected by an equal sign. 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.

59 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 7 is a solution of x + 23 = ‒ 16. Example 6

60 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 7 is a solution of x + 23 = ‒ 16. Example 6 Plug it in!

61 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 7 is a solution of x + 23 = ‒ 16. Example 6 Plug it in! Simplify.

62 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 7 is a solution of x + 23 = ‒ 16. Example 6 Plug it in! Simplify.

63 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. – 7 is not a solution. Determine whether ‒ 7 is a solution of x + 23 = ‒ 16. Example 6 Plug it in! Simplify.

64 Copyright © 2012 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

65 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 7 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

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 7 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

67 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 7 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