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 7-1Estimating Products Lesson 7-2Multiplying Fractions Lesson 7-3Multiplying Mixed Numbers Lesson 7-4Dividing Fractions Lesson 7-5Dividing Mixed Numbers Lesson 7-6Sequences

5. Lesson 1 Contents Example 1Estimate Using Compatible Numbers Example 2Estimate Using Compatible Numbers Example 3Estimate by rounding to 0,, or 1 Example 4Estimate With Mixed Numbers

6. Example 1-1a means of 28. Find a number close to 28 that is a multiple of 5. Estimate 30 and 5 are compatible numbers since.

7. Example 1-1a Answer: So, is about 6.

8. Example 1-1b Sample answer: about 9 Estimate

9. Example 1-2a Estimate first. Use 16 since 16 and 4 are compatible numbers. Estimate

10. Example 1-2a If of 16 is 4, then of 16 is Answer: So, is about 12.

11. Example 1-2b Sample answer: about 9 Estimate

12. Example 1-3a Answer: is about Estimate

13. Example 1-3b Sample answer: about Estimate

14. Example 1-4a GEOMETRY Estimate the area of the rectangle. Round each mixed number to the nearest whole number. Answer: So, the area is about 14 square inches.

15. Example 1-4b GEOMETRY Estimate the area of the rectangle. Sample answer:

16. End of Lesson 1

17. Lesson 2 Contents Example 1Multiply Fractions Example 2Multiply Fractions and Whole Numbers Example 3Simplify Before Multiplying Example 4Evaluate Expressions

18. Example 2-1a Simplify. Multiply the numerators. Multiply the denominators. Answer: Find

19. Example 2-1b Answer: Find

20. Example 2-2a Estimate Write 7 as Multiply. Simplify. Compare to the estimate. Answer: Find

21. Example 2-2b Answer: Find

22. Example 2-3a Estimate The numerator 3 and the denominator 9 have a common factor, 3. Divide both the numerator and denominator by 3. Simplify. Compare to the estimate. Answer: Find

23. Example 2-3b Answer: Find

24. Example 2-4a The GCF of 3 and 9 is 3. The GCF of 4 and 8 is 4. Divide both the numerator and denominator by 3 and then by 4. Simplify. Answer: ALGEBRA Evaluate Replace p with and q with 12 3 1

25. Example 2-4b Answer: ALGEBRA Evaluate

26. End of Lesson 2

27. Lesson 3 Contents Example 1Multiply a Fraction and a Mixed Number Example 2Multiply Mixed Numbers Example 3Evaluate Expressions

28. Example 3-1a Divide 45 and 3 by their GCF, 3. Simplify. Compare to the estimate. Estimate Use compatible numbers Answer: Find 15 1

29. Example 3-1b Answer: Find

30. Example 3-2a Estimate DISTANCES Belinda lives times farther from school than Jamie does. If Jamie lives miles from school, how far from school does Belinda live? Belinda lives times farther than miles. So, multiply

31. Example 3-2a First, write mixed numbers as improper fractions. Then, multiply the numerators and multiply the denominators. Simplify. Answer: So, Belinda lives miles from school. Compare this to the estimate.

32. Example 3-2b Answer: WEIGHT A bag of marbles weighs times as much as a bag of pretzels. If the bag of pretzels weighs pounds, how much does the bag of marbles weigh?

33. Example 3-3a Divide the numerator and denominator by 5 and by 2. Simplify. Answer: Replace r with and s with 3 7 1 2 ALGEBRA

34. Example 3-3b Answer: 12 ALGEBRA

35. End of Lesson 3

36. Lesson 4 Contents Example 1Find Reciprocals Example 2Find Reciprocals Example 3Divide by a Fraction Example 4Divide Fractions to Solve a Problem Example 5Divide by a Whole Number

37. Example 4-1a Find the reciprocal of 7. Answer: Since the reciprocal of 7 is.

38. Example 4-1b Find the reciprocal of 4. Answer:

39. Example 4-2a Find the reciprocal of. Answer: Since the reciprocal of

40. Example 4-2b Find the reciprocal of Answer:

41. Example 4-3a Multiply by the reciprocal,. Divide 6 and 3 by the GCF, 3. Multiply numerators. Multiply denominators. Answer: Find 2 1

42. Example 4-3b Answer: Find

43. Example 4-4a PARKING A parking garage charges $1 for every of an hour of parking. How much money will you need to park for 5 hours? Divide 5 by to find the number of thirds of an hour in 5 hours. Multiply by the reciprocal of Simplify. Answer: So, you will need $15 to park for 5 hours.

44. Example 4-4b Answer: $24 EQUIPMENT RENTAL A hardware store charges $3 for every hour a tool is rented. How much would it cost to rent the tool for 4 hours?

45. Example 4-5a Read the Test Item You need to find the distance each runner will run. To do so, divide into 4 equal parts. GRID-IN TEST ITEM A relay race is of a mile long. There are 4 runners in the race. What portion of a mile will each racer run?

46. Example 4-5a Solve the Test Item Multiply by the reciprocal. Simplify. Each racer will run of a mile.

47. Example 4-5a Answer:

48. Example 4-5b Answer: GRID-IN TEST ITEM A bag of jelly beans that is of a pound is to be divided evenly among 4 friends. How much of the bag does each of the friends get?

49. End of Lesson 4

50. Lesson 5 Contents Example 1Divide by a Mixed Number Example 2Evaluate Expressions Example 3Solve Problems with Mixed Numbers Example 4Solve Problems with Mixed Numbers

51. Example 5-1a Write mixed numbers as improper fractions. Multiply by the reciprocal. Divide out the common factors Compare to the estimate. Estimate Find 5 1 1 2

52. Example 5-1a Answer:

53. Example 5-1b Answer: Find

54. Example 5-2a Write the mixed number as an improper fraction. Multiply by the reciprocal. Simplify. Answer: Replace f with and g with ALGEBRA

55. Example 5-2b Answer: 6 ALGEBRA

56. Example 5-3a Estimate ADVENTURE RACING A team took days to complete 180 miles of an adventure race consisting of hiking, biking, and river rafting. How many miles did they average each day?

57. Example 5-3a Write the mixed number as an improper fraction. Multiply by the reciprocal. Divide 180 and 15 by the GCF, 15. Simplify. Compare to the estimate. Answer: So, the team averaged 48 miles each day. 12 1

58. Example 5-3b Answer: 60 miles TRAVEL Mario took days to travel a distance of 260 miles. How many miles did he average each day?

59. Example 5-4a ADVENTURE RACING A team took days to complete 180 miles of an adventure race consisting of hiking, biking, and river rafting. How far would they travel in day at the same rate? Write the whole number as a fraction. Divide 4 and 48 by their GCF, 4. Simplify. 12 1

60. Example 5-4a Answer: So, the team would travel 36 miles in day.

61. Example 5-4b Answer: 40 miles TRAVEL Mario took days to travel a distance of 260 miles. How far would Mario travel in day at the same rate?

62. End of Lesson 5

63. Lesson 6 Contents Example 1Extend a Sequence by Adding Example 2Extend a Sequence by Multiplying Example 3Use Sequences to Solve a Problem

64. Example 6-1a Describe the pattern. Then find the next two numbers in the sequence. 24, 30, 36, 42, … Each number is 6 more than the number before it. 24,30,36,42, … Answer: In this sequence, 6 is added to each number. The next two numbers are or 48, and or 54.

65. Example 6-1b Describe the pattern. Then find the next two numbers in the sequence. 17, 21, 25, 29, … Answer: Add 4 to each number; 33, 37.

66. Example 6-2a Describe the pattern. Then find the next two numbers in the sequence. 4, 20, 100, 500, … Answer: Each number is multiplied by 5. The next two numbers are 500  5, or 2,500 and 2,500  5, or 12,500.

67. Example 6-2b Answer: Multiply each number by 4; 1,792, 7,168. Describe the pattern. Then find the next two numbers in the sequence. 7, 28, 112, 448, …

68. Example 6-3a GARDENING A gardener is making a triangular pattern of tulips, starting with 4 tulips in the first row. The second row has 7 tulips, and the third row has 10. How many tulips will be in the fifth row? Write the sequence. Find the fifth number. 4,7, 10,13,16 Answer: There are 16 tulips in the fifth row.

69. Example 6-3b SEATING Julie is setting up a seating arrangement for a performance. She has placed 10 chairs in the first row, 14 chairs in the second row, and 18 chairs in the third row. How many chairs will be in the sixth row? Answer: 30 chairs

70. End of Lesson 6

71. Online Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 1 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath1.net/extra_examples.

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