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Mastering Decimals and Fractions: Problem-Solving Strategies and Techniques

Dive into the world of multiplying and dividing decimals and fractions with practical strategies and examples. Learn to estimate, choose the best strategy, and verify your answers for reasonable results. From multiplying decimals by whole numbers to dividing mixed numbers, this chapter covers it all to build your mathematical skills.

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Mastering Decimals and Fractions: Problem-Solving Strategies and Techniques

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  1. Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Splash Screen

  2. Multiplying and Dividing Decimals and Fractions 6 Lesson 6-1Multiplying Decimals by Whole Numbers Lesson 6-2Multiplying Decimals Lesson 6-3Problem-Solving Strategy: Reasonable Answers Lesson 6-4Dividing Decimals by Whole Numbers Lesson 6-5Dividing by Decimals Lesson 6-6Problem-Solving Investigation: Choose the Best Strategy Lesson 6-7Estimating Products of Fractions Lesson 6-8Multiplying Fractions Lesson 6-9Multiplying Mixed Numbers Lesson 6-10Dividing Fractions Lesson 6-11Dividing Mixed Numbers Chapter Menu

  3. Multiplying Decimals by Whole Numbers 6-1 Five-Minute Check (over Chapter 5) Main Idea and Vocabulary California Standards Example 1: Multiply Decimals Example 2: Multiply Decimals Example 3: Annex Zeros in the Product Example 4: Annex Zeros in the Product Example 5: Scientific Notation Lesson 1 Menu

  4. Multiplying Decimals by Whole Numbers 6-1 Find 6 – 2 . • 3 1 3 3 1 1 4 4 4 2 2 • 8 • 4 (over Chapter 5) • 4 5Min 1-1

  5. Multiplying Decimals by Whole Numbers 6-1 Find 5 – 3 . • 2 5 1 6 6 4 7 9 3 9 9 9 9 • 1 • 8 • 2 (over Chapter 5) 5Min 1-2

  6. Multiplying Decimals by Whole Numbers 6-1 Find 5 – 3 . 4 2 4 3 2 3 • 1 5 5 5 5 5 5 • 2 • 2 • 8 (over Chapter 5) 5Min 1-3

  7. Multiplying Decimals by Whole Numbers 6-1 Find 15 – 9 . 7 1 3 6 5 3 • 6 4 8 8 8 8 8 • 6 • 5 • 23 (over Chapter 5) 5Min 1-4

  8. Multiplying Decimals by Whole Numbers 6-1 • I will estimate and find the product of decimals and whole numbers. • scientific notation Lesson 1 MI/Vocab

  9. Multiplying Decimals by Whole Numbers 6-1 Standard 5NS2.1Add, subtract, multiply,and divide with decimals;add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results. Lesson 1 Standard 1

  10. Multiplying Decimals by Whole Numbers 6-1 18.9 × 4 19 × 4 or 76 Find 18.9 × 4. One Way: Use estimation. Round 18.9 to 19. 3 3 18.9 Since the estimate is 76, place the decimal point after the 5. × 4 6 7 5 . Lesson 1 Ex1

  11. Multiplying Decimals by Whole Numbers 6-1 Another Way: Count decimal places. 3 3 18.9 × 4 6 7 5 . Answer:75.6 Lesson 1 Ex1

  12. Multiplying Decimals by Whole Numbers 6-1 Find 12.7 × 5. • 64 • 63.5 • 60.35 • 63.35 Lesson 1 CYP1

  13. Multiplying Decimals by Whole Numbers 6-1 0.56 × 7 1 × 7 or 7 Find 0.56 × 7. One Way: Use estimation. Round 0.56 to 1. 3 4 0.56 Since the estimate is 7, place the decimal point after the 3. × 7 2 3 . 9 Lesson 1 Ex2

  14. Multiplying Decimals by Whole Numbers 6-1 Another Way: Count decimal places. 3 4 0.56 × 7 2 3 . 9 Answer:3.92 Lesson 1 Ex2

  15. Multiplying Decimals by Whole Numbers 6-1 Find 0.47 × 8. • 8 • 5.76 • 3.76 • 0.392 Lesson 1 CYP2

  16. Multiplying Decimals by Whole Numbers 6-1 Find 3 × 0.016. 1 0.016 × 3 8 0. 0 4 Answer:0.048 Lesson 1 Ex3

  17. Multiplying Decimals by Whole Numbers 6-1 Find 0.026 × 2. • 0.052 • 0.52 • 0.0052 • 0.502 Lesson 1 CYP3

  18. Multiplying Decimals by Whole Numbers 6-1 ALGEBRA Evaluate 5g if g = 0.0091. 5g = 5 × 0.0091 Replace g with 0.0091. 4 0.0091 × 5 5 0 4 0. 5 Answer:0.0455 Lesson 1 Ex4

  19. Multiplying Decimals by Whole Numbers 6-1 ALGEBRA Evaluate 3h if h = 0.0054. • 1.62 • 0.162 • 0.00162 • 0.0162 Lesson 1 CYP4

  20. Multiplying Decimals by Whole Numbers 6-1 The average distance from Earth to the Sun is 1.5 × 108 kilometers. Write the distance in standard form. Lesson 1 Ex5

  21. Multiplying Decimals by Whole Numbers 6-1 One Way: Use order of operations. Evaluate 108 first. Then multiply. 1.5 × 108 = 1.5 × 100,000,000 = 150,000,000 kilometers Lesson 1 Ex5

  22. Multiplying Decimals by Whole Numbers 6-1 Another Way: Use mental math. Move the decimal point to the right the same number of places as the exponent of 10, or 8 places. 1.5 × 108 = 1.50000000 = 150,000,000 Lesson 1 Ex5

  23. Multiplying Decimals by Whole Numbers 6-1 Answer: The average distance from Earth to the Sun is 150,000,000 kilometers. Lesson 1 Ex5

  24. Multiplying Decimals by Whole Numbers 6-1 The average distance from the Sun to the planet Jupiter is 5.88 × 108 kilometers. Choose the answer showing the distance written in standard form. • 588,000,000 kilometers • 58,000,000 kilometers • 5,880,000,000 kilometers • 5,800,000 kilometers Lesson 1 CYP5

  25. End of Lesson 1

  26. Multiplying Decimals 6-2 Five-Minute Check (over Lesson 6-1) Main Idea California Standards Example 1: Multiply Decimals Example 2: Multiply Decimals Example 3: Evaluate an Expression Example 4: Real-World Example Lesson 2 Menu

  27. Multiplying Decimals 6-2 (over Lesson 6-1) Find 3.8 × 2. • 5.8 • 7.6 • 5.6 • 5 5Min 2-1

  28. Multiplying Decimals 6-2 (over Lesson 6-1) Find 0.6 × 25. • 15 • 25 • 10 • 4 5Min 2-2

  29. Multiplying Decimals 6-2 (over Lesson 6-1) Find 0.038 × 15. • 0.63 • 1.35 • 0.57 • 1 5Min 2-3

  30. Multiplying Decimals 6-2 (over Lesson 6-1) Find 0.0003 × 17. • 0.0021 • 0.0034 • 0.0051 • 0.21 5Min 2-4

  31. Multiplying Decimals 6-2 (over Lesson 6-1) Mercury is approximately 3.6 × 107 miles from the Sun. How far is this? • 360 mi • 1,800,000 mi • 36,000,000 mi • 3,000,000 mi 5Min 2-5

  32. Multiplying Decimals 6-2 • I will multiply decimals by decimals. Lesson 2 MI/Vocab

  33. Multiplying Decimals 6-2 Standard 5NS2.1Add, subtract,multiply, and dividewith decimals; add with negative integers; subtract positive integers from negative integers;and verify the reasonableness of results. Standard 5MR2.1 Use estimation to verify the reasonableness of calculated results. Lesson 2 Standard 1

  34. Multiplying Decimals 6-2 Estimate 8.3 × 2.9 8 × 3 or 24 one decimal place one decimal place two decimal places Find 8.3 × 2.9. 8.3 × 2.9 747 + 166 24.07 Answer: So, the product is 24.07. Lesson 2 Ex1

  35. Multiplying Decimals 6-2 Check for Reasonableness Compare 24.07 to the estimate. 24.07 is about 24. Lesson 2 Ex1

  36. Multiplying Decimals 6-2 Find 4.5 × 3.9. • 17.55 • 20 • 18.44 • 19.45 Lesson 2 CYP1

  37. Multiplying Decimals 6-2 Estimate 0.12 × 5.3 0 × 5 or 0 two decimal places one decimal place three decimal places Find 0.12 × 5.3. 0.12 × 5.3 36 + 60 0.636 Answer: So, the product is 0.636. Lesson 2 Ex2

  38. Multiplying Decimals 6-2 Check for Reasonableness Compare 0.636 to the estimate. 0.636 is about 0. Lesson 2 Ex2

  39. Multiplying Decimals 6-2 Find 0.14 × 3.3. • 0.636 • 0.543 • 0.462 • 0.723 Lesson 2 CYP2

  40. Multiplying Decimals 6-2 one decimal place three decimal places Annex a zero to make four decimal places. ALGEBRA Evaluate 1.8r if r = 0.029. 1.8r = 1.8 ×0.029 Replace r with 0.029. 0.029 × 1.8 232 + 29 0.0522 Answer: So, the product is 0.0522. Lesson 2 Ex3

  41. Multiplying Decimals 6-2 ALGEBRA Evaluate 2.7x if x = 0.038. • 2.738 • 0.1026 • 0.0126 • 0.2106 Lesson 2 CYP3

  42. Multiplying Decimals 6-2 Estimate 14.60 × 15.75 15 × 16 or 240 two decimal places two decimal places Carmen earns $14.60 per hour as a painter’s helper. She worked a total of 15.75 hours one week. How much money did she earn? $14.60 × 15.75 7300 10220 7300 + 1460 229.9500 Lesson 2 Ex4

  43. Multiplying Decimals 6-2 Answer: So, Carmen earned $229.95. Check for Reasonableness Compare $229.95 to the estimate. $229.95 is about $240. Lesson 2 Ex4

  44. Multiplying Decimals 6-2 Alex went shopping for 6.5 hours and spent $32.50 per hour. How much did she spend? • $211.25 • $225 • $250.25 • $211.50 Lesson 2 CYP4

  45. End of Lesson 2

  46. Problem-Solving Strategy: Reasonable Answers 6-3 Five-Minute Check (over Lesson 6-2) Main Idea California Standards Example 1: Problem-Solving Strategy Lesson 3 Menu

  47. Problem-Solving Strategy: Reasonable Answers 6-3 (over Lesson 6-2) Find 75.4 × 2.9. • 150.36 • 77.36 • 125 • 218.66 5Min 3-1

  48. Problem-Solving Strategy: Reasonable Answers 6-3 (over Lesson 6-2) Find 0.05 × 0.123. • 0.15 • 0.00615 • 0.00506 • 1 5Min 3-2

  49. Problem-Solving Strategy: Reasonable Answers 6-3 (over Lesson 6-2) Evaluate 2.5y if y = 4.8. • 4.8 • 10.48 • 8.5 • 12 5Min 3-3

  50. Problem-Solving Strategy: Reasonable Answers 6-3 (over Lesson 6-2) Selam makes $6.75 an hour. Last week, she worked 12.4 hours. How much did she earn? • $36.75 • $48.55 • $48.50 • $83.70 5Min 3-4

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