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Chapter 4 Fractions and Decimals Click the mouse or press the space bar to continue. Splash Screen. Fractions and Decimals. 4. Lesson 4-1 Greatest Common Factor Lesson 4-2 Problem-Solving Strategy: Make an Organized List Lesson 4-3 Simplifying Fractions

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  1. Chapter 4 Fractions and Decimals Click the mouse or press the space bar to continue. Splash Screen

  2. Fractions and Decimals 4 Lesson 4-1Greatest Common Factor Lesson 4-2Problem-Solving Strategy: Make an Organized List Lesson 4-3Simplifying Fractions Lesson 4-4Mixed Numbers and Improper Fractions Lesson 4-5Least Common Multiple Lesson 4-6Problem-Solving Investigation: Choose the Best Strategy Lesson 4-7Comparing Fractions Lesson 4-8Writing Decimals as Fractions Lesson 4-9Writing Fractions as Decimals Lesson 4-10Algebra: Ordered Pairs and Functions Chapter Menu

  3. Greatest Common Factor 4-1 Five-Minute Check (over Chapter 3) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Example 4 Example 5 Greatest Common Factor Lesson 1 Menu

  4. Greatest Common Factor 4-1 • I will find the greatest common factor of two or more numbers. • common factor • greatest common factor (GCF) Lesson 1 MI/Vocab

  5. Greatest Common Factor 4-1 Preparation for Standard 6NS2.4Determinethe least common multiple and the greatest common divisor of whole numbers;use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Lesson 1 Standard 1

  6. Greatest Common Factor 4-1 Identify the common factors of 20 and 36. First, list the factors by pairs for each number. Answer: The common factors of 20 and 36 are 1, 2, and 4. Lesson 1 Ex1

  7. Greatest Common Factor 4-1 Identify the common factors of 12 and 18. • 1, 2, 3, 6 • 1, 2, 6 • 1, 2, 4, 6 • 1, 2, 3, 4, 6 Lesson 1 CYP1

  8. Greatest Common Factor 4-1 2 × 2 × 12 2 × 2 × 3 × 4 4 × 3 3 2 × 2 2 × 2 × 3 × 2 × 2 × 3 × 3 Find the GCF of 36 and 48. Write the prime factorization. 36 48 2 × 24 12 × 3 Answer: The GCF of 36 and 48 is 2 × 3 or 6. Lesson 1 Ex2

  9. Greatest Common Factor 4-1 Check Use a Venn diagram to show the factors. Notice that the factors 1, 2, 3, 4, 6, and 12 are common factors of 36 and 48 and the GCF is 12. Lesson 1 Ex2

  10. Greatest Common Factor 4-1 Find the GCF of 14 and 21. • 1 • 2 • 3 • 7 Lesson 1 CYP2

  11. Greatest Common Factor 4-1 2 2 × 7 Find the GCF of 21 and 28. 21 28 7 × 3 2 × 14 Answer: The GCF of 21 and 28 is 7. Lesson 1 Ex3

  12. Greatest Common Factor 4-1 Check Use a Venn diagram to show the factors. Notice that the factors 1 and 7 are common factors of 21 and 28 and the GCF is 7. Lesson 1 Ex3

  13. Greatest Common Factor 4-1 Find the GCF of 15 and 25. • 1 • 2 • 5 • 15 Lesson 1 CYP3

  14. Greatest Common Factor 4-1 Ana sells bags of different kinds of cookies. She made $27 selling bags of peanut butter cookies, $18 from chocolate chip cookies, and $45 selling bags of oatmeal cookies. Each bag of cookies costs the same amount. What is the most that Ana could have charged for each bag of cookies? Lesson 1 Ex4

  15. Greatest Common Factor 4-1 Factors of 27: 1, 3, 9, 27 Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 45: 1, 3, 5, 9, 15, 45 Answer: The GCF of 27, 18, and 45 is 9. So, the most Ana could have charged for each bag of cookies is $9. Lesson 1 Ex4

  16. Greatest Common Factor 4-1 Joy bought presents for her three friends. She spent $48 on Jonah, $36 on Louise, and $60 on Brenden. Each gift cost the same amount. What is the most each gift could have cost? • $1 • $4 • $18 • $12 Lesson 1 CYP4

  17. Greatest Common Factor 4-1 Refer to Example 4 of this lesson. How many bags could Ana have sold if each bag cost $9? There is a total of $27 + $18 + $45 or $90. Answer: So, the number of bags of cookies is $90 ÷ $9 or 10. Lesson 1 Ex5

  18. Greatest Common Factor 4-1 If Joy spent $48 on Jonah, $36 on Louise, and $60 on Brenden, and each gift cost $12, how many gifts did she buy? • 48 • 36 • 12 • 60 Lesson 1 CYP5

  19. End of Lesson 1

  20. Problem-Solving Strategy: Make an Organized List 4-2 Five-Minute Check (over Lesson 4-1) Main Idea California Standards Example 1: Problem-Solving Strategy Lesson 2 Menu

  21. Problem-Solving Strategy: Make an Organized List 4-2 • I will solve problems by making an organized list. Lesson 2 MI/Vocab

  22. Problem-Solving Strategy: Make an Organized List 4-2 Standard 5MR1.1Analyze problems byidentifying relationships, distinguishing relevant from irrelevant information, sequencingand prioritizing information,and observing patterns. Standard 5NS1.4 Determine the prime factors of all numbers through 50and write the numbers as the product of their prime factors. Lesson 2 Standard 1

  23. Problem-Solving Strategy: Make an Organized List 4-2 Jessica is setting up four booths in a row for the school carnival. There will be a dart game booth, a ring toss booth, a face-painting booth, and a virtual football booth. In how many ways can the four booths be arranged for the school carnival? Lesson 2 Ex1

  24. Problem-Solving Strategy: Make an Organized List 4-2 Understand What facts do you know? • There are four different booths: dart game, ring toss, face-painting, and virtual football. • The booths will be set up in a row. What do you need to find? • Find how many different ways the booth can be arranged. Lesson 2 Ex1

  25. Problem-Solving Strategy: Make an Organized List 4-2 Plan Make a list of all the different possible arrangements. Use D for darts, R for ring toss, F for face-painting, and V for virtual football. Organize your list by listing each booth first as shown below. D_ _ _R_ _ _F_ _ _V_ _ _ Lesson 2 Ex1

  26. Problem-Solving Strategy: Make an Organized List 4-2 Plan Then fill in the remaining three positions with the other booths. Continue this process until all the different arrangements are listed in the second, third, and fourth positions. Lesson 2 Ex1

  27. Problem-Solving Strategy: Make an Organized List 4-2 Solve Listing R first: Listing D first: D R F V D R V F D F R V D F V R D V R F D V F R R F V D R F D V R V D F R V F D R D F V R D V F Lesson 2 Ex1

  28. Problem-Solving Strategy: Make an Organized List 4-2 Solve Listing V first: Listing F first: F V D R F V R D F D R V F D V R F R V D F R D V V D R F V D F R V R F D V R D F V F D R V F R D Answer: There are 24 different ways the booths can be arranged. Lesson 2 Ex1 Lesson 2 Ex1

  29. Problem-Solving Strategy: Make an Organized List 4-2 Check Look back. Is each booth accounted for six times in the first, second, third, and fourth positions? Lesson 2 Ex1

  30. End of Lesson 2

  31. Simplifying Fractions 4-3 Five-Minute Check (over Lesson 4-2) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Example 4 Lesson 3 Menu

  32. Simplifying Fractions 4-3 • I will express fractions in simplest form. • ratio • equivalent fractions • simplest form Lesson 3 MI/Vocab

  33. Simplifying Fractions 4-3 Preparation for Standard 5NS2.3Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form. Lesson 3 Standard 1

  34. Simplifying Fractions 4-3 x x 6 6 = = 52 52 13 13 Replace the x with a number so the fractions are equivalent. Since 13 × 4 = 52, multiply the numerator and denominator by 4. Answer: So, x = 24. Lesson 3 Ex1

  35. Simplifying Fractions 4-3 x 7 = 48 12 Solve for x. Choose the correct answer. • 24 • 28 • 30 • 7 Lesson 3 CYP1

  36. Simplifying Fractions 4-3 3 3 24 24 = = x x 40 40 Replace the x with a number so the fractions are equivalent. Since 24 ÷ 8 = 3, divide the numerator and denominator by 8. Answer: So, x = 5. Lesson 3 Ex2

  37. Simplifying Fractions 4-3 1 5 = x 25 Solve for x. Choose the correct answer. • 5 • 10 • 20 • 15 Lesson 3 CYP2

  38. Simplifying Fractions 4-3 Write in simplest form. 14 42 7 14 1 21 42 3 One Way: Divide by common factors. A common factor of 14 and 42 is 2. = = A common factor of 7 and 21 is 7. Lesson 3 Ex3

  39. Simplifying Fractions 4-3 1 14 3 42 Another Way: 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. = Lesson 3 Ex3

  40. Simplifying Fractions 4-3 Write in simplest form. 48 24 14 48 9 50 25 10 15 50 Lesson 3 CYP3

  41. Simplifying Fractions 4-3 Lin practices gymnastics 3 hours each day. There are 24 hours in a day. Express the fraction in simplest form. 3 24 1 3 = 8 24 Answer: So, Lin spends or 1 out of every 8 hours practicing gymnastics. 1 8 The GCF of 3 and 24 is 3. 1 Mentally divide both the numerator and denominator by 3. 8 Lesson 3 Ex4

  42. Simplifying Fractions 4-3 Mark spends $10 of the $50 bill his mom gave him. Express in simplest form. 10 5 1 1 1 10 50 25 2 5 Lesson 3 CYP4

  43. End of Lesson 3

  44. Mixed Numbers and Improper Fractions 4-4 Five-Minute Check (over Lesson 4-3) Main Idea and Vocabulary California Standards Example 1 Example 2 Lesson 4 Menu

  45. Mixed Numbers and Improper Fractions 4-4 • I will write mixed numbers as improper fractions and vice versa. • mixed number • proper fraction • improper fraction Lesson 4 MI/Vocab

  46. Mixed Numbers and Improper Fractions 4-4 Standard 5NS1.5Identify and represent on a number linedecimals, fractions, mixed numbers,and positive and negative integers. Lesson 4 Standard 1

  47. Mixed Numbers and Improper Fractions 4-4 If a spaceship lifts off the Moon, it must travel at a speed of 2 kilometers per second in order to escape the pull of the Moon’s gravity. Write this speed as an improper fraction. Then graph the improper fraction on a number line. 2 5 Lesson 4 Ex1

  48. Mixed Numbers and Improper Fractions 4-4 = 12 12 2 2 5 5 5 5 (2 × 5) + 2 2 Answer: So, 2 = . 5 = Lesson 4 Ex1

  49. Mixed Numbers and Improper Fractions 4-4 Since is between 2 and 3, draw a number line using increments of one fifth. Then, draw a dot at . 12 12 5 5 Lesson 4 Ex1

  50. Mixed Numbers and Improper Fractions 4-4 The average height of an adult man is 5 feet tall. Choose the answer that shows 5 as an improper fraction. 9 59 69 9 9 9 108 12 12 12 60 60 Lesson 4 CYP1

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