1. 3-4 Multiplying Decimals Estimating & Multiplying Decimals

2. 3-4 Multiplying Decimals MA.6.A.1.2 Multiply…decimals efficiently. MA.6.A.1.3 Solve real-world problems involving multiplication…of…decimals. Also MA.6.A.1.1 Sunshine State Standards

3. 3-4 Multiplying Decimals Reading Decimal Place Value How would you say the following decimals? 0.3

4. 3-4 Multiplying Decimals Reading Decimal Place Value How would you say the following decimals? 0.3three tenths

5. 3-4 Multiplying Decimals Reading Decimal Place Value How would you say the following decimals? 0.3three tenths 0.27

6. 3-4 Multiplying Decimals Reading Decimal Place Value How would you say the following decimals? 0.3three tenths 0.27twenty-seven hundredths

7. 3-4 Multiplying Decimals Reading Decimal Place Value How would you say the following decimals? 0.3three tenths 0.27twenty-seven hundredths 5.238

8. 3-4 Multiplying Decimals Reading Decimal Place Value How would you say the following decimals? 0.3three tenths 0.27twenty-seven hundredths 5.238five and two hundred thirty-eight thousandths

9. 3-4 Multiplying Decimals How do you determine place value for decimals?

10. 3-4 Multiplying Decimals How do you determine place value for decimals? When in doubt, place a one under the decimal and a zero for each digit past the decimal.

11. 3-4 Multiplying Decimals How do you determine place value for decimals? When in doubt, place a one under the decimal and a zero for each digit past the decimal. 0.375

12. 3-4 Multiplying Decimals How do you determine place value for decimals? When in doubt, place a one under the decimal and a zero for each digit past the decimal. 0.375 1

13. 3-4 Multiplying Decimals How do you determine place value for decimals? When in doubt, place a one under the decimal and a zero for each digit past the decimal. 0.375 1000

14. 3-4 Multiplying Decimals How do you determine place value for decimals? When in doubt, place a one under the decimal and a zero for each digit past the decimal. 0.375 1000 Read the whole number on top and the number you see on the bottom as a “spit number”

15. 3-4 Multiplying Decimals How do you determine place value for decimals? When in doubt, place a one under the decimal and a zero for each digit past the Decimal. 0.375 1000 Read the whole number on top and the number you see on the bottom as a “spit number” – three hundred seventy-five thousandths

16. 3-4 Multiplying Decimals How do you read the following decimals? 3.78

17. 3-4 Multiplying Decimals How do you read the following decimals? 3.78three and seventy-eight hundredths

18. 3-4 Multiplying Decimals How do you read the following decimals? 3.78three and seventy-eight hundredths 2.003

19. 3-4 Multiplying Decimals How do you read the following decimals? 3.78three and seventy-eight hundredths 2.003two and three thousandths

20. 3-4 Multiplying Decimals Model the following decimals: 0.18

21. 3-4 Multiplying Decimals Model the following decimals: 0.18

22. 3-4 Multiplying Decimals Model the following decimals: 0.18 · 3

23. 3-4 Multiplying Decimals Model the following decimals: 0.18 · 3

24. 3-4 Multiplying Decimals Model the following decimals: 0.18 · 3 = 0.54

25. 3-4 Multiplying Decimals Model the following decimal 0.3

26. 3-4 Multiplying Decimals Model the following decimal 0.3

27. 3-4 Multiplying Decimals Model the following decimals 0.3 · 0.70

28. 3-4 Multiplying Decimals Model the following decimals 0.3 · 0.70

29. 3-4 Multiplying Decimals Model the following decimals 0.3 · 0.70 = 0.21

30. 3-4 Multiplying Decimals Additional Example 1: Science Application Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon? Multiply 4 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon. 17  4 68 Multiply as you would with whole numbers. 4  0.17

31. 3-4 Multiplying Decimals Additional Example 1 Continued Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon? 0.17  4 0.68 Place the decimal point by adding the number of decimal places in the numbers multiplied. A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon. 2 decimal places + 0 decimal places 2 decimal places

32. 3-4 Multiplying Decimals Check It Out: Example 1 Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon? Multiply 7 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon. 17  7 119 Multiply as you would with whole numbers. 7  0.17

33. 3-4 Multiplying Decimals Check It Out: Example 1 Continued Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon? 0.17  7 1.19 Place the decimal point by adding the number of decimal places in the numbers multiplied. A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon. 2 decimal places + 0 decimal places 2 decimal places

34. 3-4 Multiplying Decimals Additional Example 2A: Multiplying a Decimal by a Decimal Find the product. 0.3  0.4 Multiply. Then place the decimal point. 0.3 0.4  1 decimal place + 1 decimal place2 decimal places 0.12

35. 3-4 Multiplying Decimals Estimating Decimals

36. 3-4 Multiplying Decimals Estimating Decimals ClusteringRoundingCompatible Numbers

37. 3-4 Multiplying Decimals Clustering What is clustering? When would you use clustering to estimate the solution to a problem involving decimals?

38. 3-4 Multiplying Decimals Clustering Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.) In this example, why would each of the three addends (numbers being added) be rounded to 170? What operation could you use rather than adding 170 plus 170 plus 170?

39. 3-4 Multiplying Decimals Rounding When rounding a decimal, how do you know which digit to look at? Explain the rules for rounding a decimal. If you rounded all the numbers “up”, how would your estimated answer compare to the actual answer to the problem?

40. 3-4 Multiplying Decimals Compatible Numbers What is a compatible number? Given the expression 33.83 · 1.98, how does the estimated product compare to the actual product? Explain. Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26? What would you use?

41. 3-4 Multiplying Decimals Estimating Decimals Clustering 31.2 · 28.7 · 30.5 Rounding 7.6 · 9.2 Compatible Numbers 18.89 · 5.11

42. 3-4 Multiplying Decimals Additional Example 2B: Multiplying a Decimal by a Decimal 0.07  0.8 Multiply. Then place the decimal point. 0.07  0.8 2 decimal places + 1 decimal place3 decimal places; use a placeholder zero 0.056 Estimate the product. 0.8 is close to 1. 0.07  1 = 0.07 0.056 is close to the estimate of 0.07. The answer is reasonable.

43. 3-4 Multiplying Decimals Additional Example 2C: Multiplying a Decimal by a Decimal 1.34  2.5 Multiply. Then place the decimal point. 1.34 2.5  2 decimal places + 1 decimal place3 decimal places 670 Estimate the product. Round each factor to the nearest whole number. 1  3 = 3 3.350 is close to the estimate of 3. The answer is reasonable. 2680 3.350

44. 3-4 Multiplying Decimals Check It Out: Example 2A Find the product. 0.5  0.2 Multiply. Then place the decimal point. 0.5 0.2  1 decimal place + 1 decimal place2 decimal places 0.10

45. 3-4 Multiplying Decimals Check It Out: Example 2B 0.03  0.9 Multiply. Then place the decimal point. 0.03 0.9  2 decimal places + 1 decimal place3 decimal places; use a placeholder zero 0.027 Estimate the product. 0.9 is close to 1. 0.03  1 = 0.03 0.027 is close to the estimate of 0.03. The answer is reasonable.

46. 3-4 Multiplying Decimals Check It Out: Example 2C 3.80  3.3 Multiply. Then place the decimal point. 3.80 3.3  2 decimal places + 1 decimal places3 decimal places 1140 Estimate the product. Round each factor to the nearest whole number. 4  3 = 12 12.54 is close to the estimate of 12. The answer is reasonable. 11400 12.540

47. 3-4 Multiplying Decimals Additional Example 3A: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 3.062 3.062 5  3 decimal places + 0 decimal places3 decimal places 15.310 Substitute 3.062 for x. 5x = 5(3.062) These notations all mean multiply 3 times x. 3 x3x3(x) Remember!

48. 3-4 Multiplying Decimals Additional Example 3B: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 4.79 4.79 5  2 decimal places + 0 decimal places2 decimal places 23.95 Substitute 4.79 for x. 5x = 5(4.79)

49. 3-4 Multiplying Decimals Check It Out: Example 3A Evaluate 5x for the value of x. x = 2.012 2.012 5  3 decimal places + 0 decimal places3 decimal places 10.060 Substitute 2.012 for x. 5x = 5(2.012)

50. 3-4 Multiplying Decimals Check It Out: Example 3B Evaluate 5x for the value of x. x = 6.22 6.22 5  2 decimal places + 0 decimal places2 decimal places 31.10 Substitute 6.22 for x. 5x = 5(6.22)

51. 3-4 Multiplying Decimals Lesson Quiz Find each product. 1. 0.8  0.07 2. 0.006  0.07 Evaluate 8x for each value of x. 0.00042 0.056 21.64 6.432 $87.40 3. x = 2.7054. x = 0.804 5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged?

52. 3-4 Multiplying Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

53. 3-4 Multiplying Decimals 1. Identify the product. 0.29  0.01 A. 0.29 B. 0.029 C. 0.0029 D. 0.00029 Lesson Quiz for Student Response Systems

54. 3-4 Multiplying Decimals 2. Identify the product. 0.052  0.03 A. 1.0056 B. 0.1056 C. 0.0156 D. 0.00156 Lesson Quiz for Student Response Systems

55. 3-4 Multiplying Decimals 3. Evaluate 4x for x = 5.325. A. 21 B. 21.2 C. 21.28 D. 21.3 Lesson Quiz for Student Response Systems

56. 3-4 Multiplying Decimals 4. Evaluate 9x for x = 0.012. A. 10.8 B. 1.08 C. 0.108 D. 0.0108 Lesson Quiz for Student Response Systems

57. 3-4 Multiplying Decimals 5. Strawberry lemonade costs $0.89 per packet. Karen bought 58 packets of strawberry lemonade for a picnic. How much did she pay for it? A. $51.62 B. $51.86 C. $52.54 D. $52.93 Lesson Quiz for Student Response Systems