Warm Up

1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2. Warm Up Multiply. 1.87  320 27,840 2. 943  800 754,400 3. 3,806  10 38,060 4. 1,207  100 120,700 5. 72  196 14,112 6. 120  523 62,760

3. Problem of the Day Carmen and Rita sold homemade oatmeal cookies. After 8 days, they had sales totaling $70. Each day, their sales were $0.50 higher than the previous day. What were their sales on the first day? $7.00

4. Learn to multiply decimals by whole numbers and by decimals.

5. 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. 4  0.17 17 Multiply as you would with whole numbers.  4 68

6. 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? Place the decimal point by adding the number of decimal places in the numbers multiplied. 0.17 2 decimal places  4 + 0 decimal places 0.68 2 decimal places A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.

7. 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. 7  0.17 17 Multiply as you would with whole numbers.  7 119

8. 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? Place the decimal point by adding the number of decimal places in the numbers multiplied. 0.17 2 decimal places  7 + 0 decimal places 1.19 2 decimal places A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.

9. Helpful Hint You can use a decimal grid to model multiplication of decimals.

10. Multiply. Then place the decimal point. 1 decimal place + 1 decimal place 2 decimal places Additional Example 2A: Multiplying a Decimal by a Decimal Find the product. 0.3  0.4 0.3  0.4 0.12

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

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

13. Multiply. Then place the decimal point. 1 decimal place + 1 decimal place 2 decimal places Check It Out: Example 2A Find the product. 0.5  0.2 0.5  0.2 0.10

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

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

16. Remember! These notations all mean multiply 3 times x. 3 •x 3x 3(x) 3 decimal places + 0 decimal places 3 decimal places Substitute 3.062 for x. Additional Example 3A: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 3.062 5x = 5(3.062) 3.062  5 15.310

17. 2 decimal places + 0 decimal places 2 decimal places Substitute 4.79 for x. Additional Example 3B: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 4.79 5x = 5(4.79) 4.79  5 23.95

18. 3 decimal places + 0 decimal places 3 decimal places Substitute 2.012 for x. Check It Out: Example 3A Evaluate 5x for the value of x. x = 2.012 5x = 5(2.012) 2.012  5 10.060

19. 2 decimal places + 0 decimal places 2 decimal places Substitute 6.22 for x. Check It Out: Example 3B Evaluate 5x for the value of x. x = 6.22 5x = 5(6.22) 6.22  5 31.10

20. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

21. Lesson Quiz Find each product. 1. 0.8  0.07 2. 0.006  0.07 Evaluate 8x for each value of x. 0.056 0.00042 3.x = 2.705 4.x = 0.804 6.432 21.64 5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged? $87.40

22. Lesson Quiz for Student Response Systems 1. Identify the product. 0.29  0.01 A. 0.29 B. 0.029 C. 0.0029 D. 0.00029

23. Lesson Quiz for Student Response Systems 2. Identify the product. 0.052  0.03 A. 1.0056 B. 0.1056 C. 0.0156 D. 0.00156

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

25. Lesson Quiz for Student Response Systems 4. Evaluate 9x for x = 0.012. A. 10.8 B. 1.08 C. 0.108 D. 0.0108

26. Lesson Quiz for Student Response Systems 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