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Page 1 of 4 Comparing and Ordering Integers BEFORE Now WHY? You compared and ordered whole numbers and fractions. You’ll compare and order integers. So you can order historic dates, as in Ex. 41. In the Real World Word Watch integer, p. 251 negative integer, p. 251 positive integer, p. 251 opposite, p. 251 Football In three plays of a football game, there is a gain of 7 yards, a loss of 10 yards, and a gain of 9 yards. What numbers can you use to represent each gain or loss? The following numbers are integers : . . . , 4, 3, 2, 1, 0, 1, 2, 3, 4, . . . Negative integers are integers that are less than zero. Positive integers are integers that are greater than 0. Zero is neither positive nor negative. Integers and Their Opposites Zero Negative integers Positive integers with Reading The integer 4 is read “negative four.” A number other than 0 that has no sign is considered to be positive, so the integer 4 is read “positive four” or “four.” 4 3 2 1 0 1 2 3 4 Two numbers are opposites if they are the same distance from 0 on a number line but are on opposite sides of 0. For example, 3 is the opposite of 3. The opposite of 0 is 0. EXAMPLE 1 Writing Integers You can use integers to represent the gains and losses described above. 7 yard gain: 7 Your turn now 1. 15 10 yard loss: 10 9 yard gain: 9 Write the opposite of the integer. 2. 8 Lesson 6.1 3. 35 4. 100 Comparing and Ordering Integers 251 Page 2 of 4 Comparing Integers You can use a number line to compare and order integers. Remember that numbers decrease as you move to the left on a number line and increase as you move to the right. EXAMPLE tch Out! Wa 2 Comparing Integers Using a Number Line a. Compare 2 and 5. 5 Don’t confuse a negative sign with a subtraction sign. A negative sign indicates a direction on a number line, not an operation. 2 2 is to the right of 5. 6 5 4 3 2 1 1 0 2 ANSWER 2 > 5 or 5 < 2. b. Compare 6 and 1. 6 1 6 5 4 3 2 1 0 1 6 is to the left of 1. 2 ANSWER 6 < 1 or 1 > 6. Your turn now Copy and complete the statement using < or >. 5. 0 _?_ 7 EXAMPLE 3 6. 9 _?_ 4 7. 5 _?_ 4 8. 3 _?_ 13 Ordering Integers Using a Number Line Weather The table shows the average temperatures, in degrees Celsius, for six months in the Gobi Desert of Mongolia. Which of these months has the least average temperature? Month Average Temperature Nov. Dec. Jan. Feb. Mar. Apr. 6C 14C 15C 12C 3C 6C Solution You can graph each integer on a number line to order the temperatures. Jan. Dec. Feb. 16 14 12 10 8 Nov. 6 Mar. 4 2 Apr. 0 2 4 6 8 The temperatures from least to greatest are: 15, 14, 12, 6, 3, 6. ANSWER At 15C, January has the least average temperature. 252 Chapter 6 Integers Page 3 of 4 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 710 Getting Ready to Practice 1. Vocabulary Which of the following numbers are integers? 3 4 2675, 0, 56, , 75, 0.65 Write the integer that represents the situation. Then write the opposite of that integer. 2. 1333 feet above sea level 3. Sixteen degrees below zero 4. A nine million dollar loss 5. A $15 account withdrawal Copy and complete the statement using < or >. 6. 2 _?_ 5 7. 8 _?_ 12 8. 36 _?_ 25 9. 1 _?_ 5 Order the temperatures from least to greatest. 10. 7C, 2C, 4C, 8C with Homework Example Exercises 1 12–17, 41 2 18–23, 33–40 3 24, 29–32, 41 Online Resources CLASSZONE.COM • More Examples • eTutorial Plus 11. 5F, 9F, 2F, 3F, 1F Practice and Problem Solving Draw a number line and graph the integer. Then give a real-world situation that the integer could represent. 12. 5 13. 0 14. The opposite of 7 15. 9 16. 4 17. The opposite of 3 Copy and complete the statement using < or >. 18. 34 _?_ 43 19. 17 _?_ 13 20. 42 _?_ 37 21. 18 _?_ 3 22. 7 _?_ 4 23. 26 _?_ 26 24. Miniature Golf In miniature golf, par is the expected number of strokes to finish a hole. Your score for the game is the sum of your number of strokes above or below par for each hole. The player with the least score wins. Order the scores given in the table from least to greatest to determine the order of finish. Player Andrew Mandy Mitchell Pedro Score 5 3 0 4 Algebra Name two integer values of the variable that make the statement true. 25. 0 < d 26. c < 23 27. 10 > k Lesson 6.1 Comparing and Ordering Integers 253 Page 4 of 4 5 28. Writing Is the fraction an integer? Explain your reasoning. 6 History Order the integers from least to greatest. 29. 28, 18, 7, 17, 0, 12 30. 99, 42, 13, 2, 11, 49 31. 150, 235, 435, 345, 75 32. 66, 21, 9, 10, 22, 44 Tell whether the statement is true or false. Explain your reasoning. 33. 3 < 2 34. 6 > 8 35. 6 > 1 36. 0 > 10 37. 7 > 5 38. 50 < 55 39. 100 > 0 40. 67 < 68 41. Roman Battles The location and date of five Roman battles are listed in the table. Use a number line to order the battles from earliest in time to most recent. Let positive integers represent the years A.D. and negative integers represent the years B.C. (for example, 89 B.C. 89). ■ Roman Battles Around 160 B.C., the armor worn by a soldier in the Roman army often included a body shield called a scutum. A scutum weighed about 10 kg. About how many pounds did a scutum weigh? Use the fact that 1 kg ≈ 2.2 lb. Location Alexandria Byzantium Carthage Jerusalem Syracuse Date 47 B.C. 196 A.D. 147 B.C. 70 A.D. 211 B.C. 42. Challenge If the missing integer in the list of numbers below is the median of the numbers, what could the missing integer be? 44, 23, 11, 12, 27, _?_, 4, 0, 1 Mixed Review Find the sum or difference. (Lesson 2.2) 43. 12.7 87.35 44. 98.6 5.01 45. 300 11.3 46. 254.65 9.202 Find the sum or difference. (Lesson 5.6) 47. 4 gal 3 qt 5 gal 1 qt 48. 8 yd 10 in. 49. 5 ft 9 in. 1 yd 11 in. 4 ft 10 in. 50. 13 ft 5 in. 2 ft 7 in. Basic Skills Find the sum or difference. 51. 63 49 52. 109 57 53. 46 27 54. 513 24 Test-Taking Practice 55. Multiple Choice Which statement is true? INTERNET State Test Practice A. 56 < 58 CLASSZONE.COM B. 1 < 112 C. 7 > 5 D. 9 > 11 56. Short Response The integers 17, 10, 32, 29, and 0 are temperature readings in degrees Fahrenheit. Graph the integers on a number line and find the median temperature. 254 Chapter 6 Integers