2. Welcome to Interactive Chalkboard Mathematics: Applications and Concepts, Course 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Contents Lesson 5-1Greatest Common Factor Lesson 5-2Simplifying Fractions Lesson 5-3Mixed Numbers and Improper Fractions Lesson 5-4Least Common Multiple Lesson 5-5Comparing and Ordering Fractions Lesson 5-6Writing Decimals as Fractions Lesson 5-7Writing Fractions as Decimals

5. Lesson 1 Contents Example 1Find the GCF by Listing Factors Example 2Find the GCF by Using Prime Factors Example 3Use the GCF to Solve a Problem Example 4Use the GCF to Solve a Problem

6. Example 1-1a Find the GCF of 36 and 48 by making a list. Factors of 48 1, 48 2, 24 3, 16 4, 12 6, 8 Factors of 36 1, 36 2, 18 3, 12 4, 9 6, 6 The common factors are 1, 2, 3, 4, 6, and 12. The greatest common factor, or GCF, of 36 and 48 is 12.

7. Example 1-1b Use a Venn diagram to show the factors. Notice that the factors 1, 2, 3, 4, 6, and 12 are the common factors of 36 and 48 and the GCF is 12. Answer: 12

8. Example 1-1c Find the GCF of 45 and 75 by making a list. Answer: 15

9. Example 1-2a Find the GCF of 52 and 78 by using prime factors. Method 1 Write the prime factorization. 52 78

10. Example 1-2b Method 2 Divide by prime numbers. Divide both 52 and 78 by 2. Then divide the quotients by 13. Using either method, the common prime factors are 2 and 13. Answer: So, the GCF of 52 and 78 is

11. Example 1-2c Find the GCF of 64 and 80 by using prime factors. Answer: 16

12. Example 1-3a SALES Annessa sold bags of cookies at a bake sale. She sold small, medium, and large bags, with a different number of cookies in each size bag. By the end of the sale, she used 18 cookies to fill the small bags, 27 cookies to fill the medium bags, and 45 cookies to fill the large bags. She sold the same number of bags for the three sizes. What is the greatest number of bags that she could have sold?

13. Example 1-3b factors of 18: 1, 2, 3, 6, 9, 18 List all the factors of each number. Then find the greatest common factor. The GCF of 18, 27, and 45 is 9. Answer: So, the greatest number of bags she could have sold is 9 of each size, or factors of 27: 1, 3, 9, 27 factors of 45: 1, 3, 5, 9, 15, 45

14. Example 1-3c CANDY Sarah is making bags of candy for a school fund-raiser. She is making three different sizes of bags. By the time Sarah had finished making the bags, she had used 24 lollipops to fill the small bags, 40 lollipops to fill the medium bags, and 64 lollipops to fill the large bags. She completed the same number of bags for the three sizes. What is the greatest number of bags she could have made? Answer: 24 bags

15. Example 1-4a SALES Annessa sold bags of cookies at a bake sale. She sold small, medium, and large bags, with a different number of cookies in each size bag. By the end of the sale, she used 18 cookies to fill the small bags, 27 cookies to fill the medium bags, and 45 cookies to fill the large bags. If Annessa sold nine bags of each size, how many cookies were in each size bag? large bags: small bags: medium bags: Answer: 2 in the small bags, 3 in the medium bags, and 5 in the large bags

16. Example 1-4b CANDY Sarah is making bags of candy for a school fund-raiser. She is making three different sizes of bags. By the time Sarah had finished making the bags, she had used 24 lollipops to fill the small bags, 40 lollipops to fill the medium bags, and 64 lollipops to fill the large bags. If Sarah sold eight bags of each size, how many lollipops were in each size bag? Answer: 3 in the small bags, 5 in the medium bags, and 8 in the large bags

17. End of Lesson 1

18. Lesson 2 Contents Example 1Write Equivalent Fractions Example 2Write Equivalent Fractions Example 3Write Fractions in Simplest Form Example 4Express Fractions in Simplest Form

19. Example 2-1a Replace the  with a number in so the fractions are equivalent. multiply the numerator and denominator by 4. Answer:

20. Example 2-1b Answer: Replace the  with a number in so the fractions are equivalent.

21. Example 2-2a divide the numerator and denominator by 8. Answer: Replace the  with a number in so the fractions are equivalent.

22. Example 2-2b Answer: Replace the  with a number in so the fractions are equivalent.

23. Example 2-3a Method 1 Divide by common factors. Write in simplest form. 2 is a common factor of 14 and 42. 7 is a common factor of 7 and 21. Answer: Since 1 and 3 have no common factor greater than 1, the fraction is in simplest form.

24. Example 2-3b Method 2 Divide by the GCF. factors of 14: 1, 2, 7, 14 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The GCF of 14 and 42 is 14. Divide the numerator and denominator by the GCF, 14. Answer: Since the GCF of 1 and 3 is 1, the fraction is in simplest form.

25. Example 2-3c Write in simplest form. Answer:

26. Example 2-4a GYMNASTICS Lin practices gymnastics 16 hours each week. There are 168 hours in a week. Express the fraction in simplest form. Answer: In simplest form, the fraction is written So, Lin practices gymnastics for of the week. Divide the numerator and denominator by the GCF, 8.

27. Example 2-4b TRANSPORTATION There are 244 students at Longfellow Elementary School. Of those students, 168 ride a school bus to get to school. Express the fraction in simplest form. Answer:

28. End of Lesson 2

29. Lesson 3 Contents Example 1Mixed Numbers as Improper Fractions Example 2Mixed Numbers as Improper Fractions Example 3Improper Fractions as Mixed Numbers

30. Example 3-1a Draw a model for Then write as an improper fraction. Answer: There are twenty-seven So, can be written as Since the mixed number is greater than 3, draw four models that are divided into eight equal sections to show eighths. Then shade three wholes and three eighths.

31. Example 3-1b Draw a model for Then write as an improper fraction. Answer:

32. Example 3-2a ASTRONOMY If a spaceship lifts off the Moon, it must travel at a speed of kilometers per second in order to escape the pull of the Moon’s gravity. Write this speed as an improper fraction. 2 Answer: The speed is kilometers per second.

33. Example 3-2b EXERCISE As part of a regular exercise program, Max walks miles each morning. Write this distance as an improper fraction. Answer:

34. Example 3-3a Write as a mixed number. Divide 23 by 4. Use the remainder as the numerator of the fraction.

35. Example 3-3a Answer:

36. Example 3-3b Answer: Write as a mixed number.

37. End of Lesson 3

38. Lesson 4 Contents Example 1Find the LCM by Making a List Example 2Find the LCM by Using Prime Factors Example 3Use the LCM to Solve a Problem

39. Example 4-1a Find the LCM of 4 and 9 by making a list. Step 1 List the nonzero multiples. multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, … multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, … Step 2 Identify the LCM from the common multiples. Answer: The LCM of 4 and 9 is 36.

40. Example 4-1b Find the LCM of 6 and 14 by making a list. Answer: 42

41. Example 4-2a Find the LCM of 8 and 18 by using prime factors. Step 1 Write the prime factorizations of each number. 818

42. Example 4-2b Step 3 Find the product of the prime factors using each common prime factor once and any remaining factors. Answer: Step 2 Identify all common prime factors.

43. Example 4-2c Find the LCM of 9 and 21 by using prime factors. Answer: 63

44. Example 4-3a MONEY Liam, Eva, and Brady each have the same amount of money. Liam has only nickels, Eva has only dimes, and Brady has only quarters. What is the least amount of money that each of them could have? Find the LCM of 5, 10, and 25 using prime factors. 51025 Answer: The least amount of money that each of them could have is or 50 cents.

45. Example 4-3b CANDY Michael, Logan, and Diego each have bags of candy that have the same total weight. Michael’s bag has candy bars that each weigh 4 ounces, Logan’s bag has candy bars that each weigh 6 ounces, and Diego’s bag has candy bars that each weigh 9 ounces. What is the least total weight that each of them could have? Answer: 36 ounces

46. End of Lesson 4

47. Lesson 5 Contents Example 1Compare Fractions Example 2Order Fractions Example 3Compare and Order Fractions

48. Example 5-1a First, find the LCD; that is, the LCM of the denominators. The LCM of 21 and 7 is 21. So, the LCD is 21. Next, rewrite each fraction with a denominator of 21. Then compare the numerators. Replace with or = to make true. Answer:

49. Replace with or = to make true. Example 5-1b Answer:

50. Example 5-2a The LCD of the fractions is 15. So, rewrite each fraction with a denominator of 15. Order the fractions and from least to greatest.

51. Example 5-2b Answer: The order of the fractions from least to greatest is

52. Example 5-2c Order the fractions and from least to greatest. Answer:

53. Example 5-3a A as arable land B as permanent pastures C as forests and woodland D B and C are equal MULTIPLE-CHOICE TEST ITEM According to the table, how is most land in the United States used? Source: CIA World Fact Book other forests and woodlands permanent pastures arable (cropland) Land Use in the United States

54. Example 5-3b Read the Test Item You need to compare the fractions. Solve the Test Item Rewrite the fractions with the LCD, 100.

55. Example 5-3c So, is the greatest fraction. Answer: C

56. Example 5-3d MULTIPLE-CHOICE TEST ITEM According to a survey data, what did most people say should be done with the length of the school year? keep the length the same shorten the school year lengthen the school year How long should the school year be? A lengthen the school year B shorten the school year C keep the length the same D cannot tell from the data Answer: A

57. End of Lesson 5

58. Lesson 6 Contents Example 1Write Decimals as Fractions Example 2Write Decimals as Fractions Example 3Write Decimals as Fractions Example 4Write Decimals as Mixed Numbers

59. Example 6-1a Write the decimal 0.4 as a fraction in simplest form. The place-value chart shows that the place value of the last decimal place is tenths. So, 0.4 means four tenths.

60. 5 Example 6-1b 0.4 means four tenths. Simplify. Divide the numerator and denominator by the GCF, 2. Answer: In simplest form, 0.4 is written as 2

61. Example 6-1c Write the decimal 0.8 as a fraction in simplest form. Answer:

62. Example 6-2a Write the decimal 0.38 as a fraction in simplest form.

63. 50 19 Example 6-2a 0.38 means thirty-eight hundredths. Simplify. Divide by the GCF, 2. Answer:

64. Example 6-2b Write the decimal 0.64 as a fraction in simplest form. Answer:

65. Example 6-3a Write the decimal 0.264 as a fraction in simplest form.

66. Example 6-3a 0.264 means two hundred sixty-four thousandths. Simplify. Divide by the GCF, 8. Answer: 125 33

67. Example 6-3b Write the decimal 0.824 as a fraction in simplest form. Answer:

68. Example 6-4a RAINFALL In 1955, Hurricane Diane moved through New England and produced one of the region’s heaviest rainfalls in history. In a 24-hour period, 18.15 inches of rain were recorded in one area. Write this amount as a mixed number in simplest form. Simplify. 20 3

69. Example 6-4b Answer:

70. Example 6-4c BICYCLING While training for a bicycle race, Ted rides an average of 23.56 miles per day. Write this distance as a mixed number in simplest form. Answer:

71. End of Lesson 6

72. Lesson 7 Contents Example 1Write Fractions as Terminating Decimals Example 2Write Fractions as Repeating Decimals Example 3Write Fractions as Repeating Decimals

73. Example 7-1a Write as a decimal. Method 1 Use paper and pencil. 0 Divide 3 by 8.

74. Example 7-1b Method 2 Use a calculator. Answer: 380.375 ENTER

75. Example 7-1c Write as a decimal. Answer: 0.625

76. Example 7-2a Write as a decimal. Method 1 Use paper and pencil. The pattern will continue. Divide 5 by 12.

77. Example 7-2b Method 2 Use a calculator. Answer: 5120.41666666666… ENTER

78. Example 7-2c Write as a decimal. Answer:

79. Example 7-3a Answer: At the meeting, six-packs of soda were drunk. BEVERAGES At a meeting, people drank 23 cans of soda. This makes six-packs. Write this number as a decimal. You can use a calculator to write as a decimal. 353.833333336 ENTER

80. Example 7-3b Answer: 4.375 PIZZA PARTY At a pizza party, people ate 35 slices of pizza. This makes pizzas. Write this number as a decimal.

81. End of Lesson 7

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