Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to multiply decimals by whole numbers and by 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. 4  0.17 17 Multiply as you would with whole numbers.  4 68

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.

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

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.

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

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

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

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

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

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

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

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

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

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

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

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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 21.64 6.432 5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged? $87.40

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

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

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

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

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