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

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1.2 Symbols and Sets of Numbers

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives  Identify sets of numbers  Find absolute value of numbers  Translate sentences into mathematical statements

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Set of Numbers Natural Numbers: {1, 2, 3, 4, 5, 6...} Whole Numbers: {0, 1, 2, 3, 4...} Integers: {... –3, –2, –1, 0, 1, 2, 3...} Rational Numbers: the set of all numbers that can be expressed as a quotient of integers, with denominator  0. Irrational Numbers: nonrational numbers that correspond to points on a number line. Real Numbers: all numbers that correspond to points on a number line.

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Equality and Inequality Symbols SymbolMeaning a = b a  b a < b a > b a  b a  b a is equal to b. a is not equal to b. a is less than b. a is greater than b. a is less then or equal to b. a is greater than or equal to b.

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. The Number Line A number line is a line on which each point is associated with a number. 2– – 1– 3– 4– 5 Negative numbers Positive numbers –

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. For any two real numbers a and b, a is less than b if a is to the left of b on the number line. a < b means a is to the left of b on a number line. a > b means a is to the right of b on a number line. Order Property for Real Numbers ab a

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Determine whether each mathematical statement is true. a. 4 < 5 True b. 27 ≥ 27 True c. 0 > 5 False d. 16 ≤ 9 False

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Determine whether each mathematical statement is true. a. 4 < 5 True b. 27 ≥ 27 True c. 0 > 5 False d. 16 ≤ 9 False

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Determine whether each mathematical statement is true. a. 4 < 5 True b. 27 ≥ 27 True c. 0 > 5 False d. 16 ≤ 9 False

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Determine whether each mathematical statement is true. a. 4 < 5 True b. 27 ≥ 27 True c. 0 > 5 False d. 16 ≤ 9 False

13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Determine whether each mathematical statement is true. a. 4 < 5 True b. 27 ≥ 27 True c. 0 > 5 False d. 16 ≤ 9 False

14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Translate each sentence into a mathematical statement. a. Thirteen is less than or equal to nineteen. b. Five is greater than two. c.Seven is not equal to eight.

15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Translate each sentence into a mathematical statement. a. Thirteen is less than or equal to nineteen. 13 ≤ 19 b. Five is greater than two. c. Seven is not equal to eight.

16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Translate each sentence into a mathematical statement. a. Thirteen is less than or equal to nineteen. 13 ≤ 19 b. Five is greater than two. 5 > 2 c.Seven is not equal to eight.

17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Translate each sentence into a mathematical statement. a. Thirteen is less than or equal to nineteen. 13 ≤ 19 b. Five is greater than two. 5 > 2 c. Seven is not equal to eight. 7 ≠ 8

18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Graph the numbers on a number line.

19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Graph the numbers on a number line.

20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Graph the numbers on a number line.

21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Graph the numbers on a number line.

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Graph the numbers on a number line.

23 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 3 Graph the numbers on a number line.

24 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Insert, or = between the pairs of numbers to form true statements. a b c. – 4 – 7 d. <

25 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Insert, or = between the pairs of numbers to form true statements. a. 4.7 > b c. – 4 – 7 d. <

26 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Insert, or = between the pairs of numbers to form true statements. a. 4.7 > b = c. – 4 – 7 d. <

27 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Insert, or = between the pairs of numbers to form true statements. a. 4.7 > b = c. – 4 > – 7 d. <

28 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Insert, or = between the pairs of numbers to form true statements. a. 4.7 > b = c. – 4 > – 7 d. <

29 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Absolute Value The absolute value of a real number a, denoted by |a|, is the distance between a and 0 on the number line. 2– – 1– 3– 4– 5 | –4| = 4 Distance of 4 Symbol for absolute value |5| = 5 Distance of 5

30 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Find the absolute value of each number. a. b. c. d.

31 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Find the absolute value of each number. a. b. c. d.

32 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Find the absolute value of each number. a. b. c. d.

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Find the absolute value of each number. a. b. c. d.

34 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 5 Find the absolute value of each number. a. b. c. d.

35 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 Insert, or = between the pairs of numbers to form true statements. a. b. c.

36 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 Insert, or = between the pairs of numbers to form true statements. a. b. c.

37 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 Insert, or = between the pairs of numbers to form true statements. a. b. c.

38 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 Insert, or = between the pairs of numbers to form true statements. a. b. c.