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3-5 Multiplying Decimals Warm Up Problem of the Day Lesson Presentation Course 1 3-5 Multiplying Decimals Warm Up Multiply. 1. 87 320 27,840 2. 943 800 754,400 3. 3,806 10 4. 1,207 100 38,060 120,700 5. 72 196 14,112 6. 120 523 62,760 Course 1 3-5 Multiplying Decimals 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 Course 1 3-5 Multiplying Decimals Learn to multiply decimals by whole numbers and by decimals. Course 1 3-5 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? 4 0.17 17 4 68 Course 1 Multiply 4 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon. Multiply as you would with whole numbers. 3-5 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? Place the decimal point by adding the number of decimal places in the numbers multiplied. 0.17 4 0.68 2 decimal places + 0 decimal places 2 decimal places A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon. Course 1 3-5 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? 7 0.17 17 7 119 Course 1 Multiply 7 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon. Multiply as you would with whole numbers. 3-5 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? Place the decimal point by adding the number of decimal places in the numbers multiplied. 0.17 7 1.19 2 decimal places + 0 decimal places 2 decimal places A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon. Course 1 3-5 Multiplying Decimals Helpful Hint You can use a decimal grid to model multiplication of decimals. Course 1 3-5 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 1 decimal place 0.4 + 1 decimal place 0.12 Course 1 2 decimal places 3-5 Multiplying Decimals Additional Example 2B: Multiplying a Decimal by a Decimal 0.07 0.8 0.07 1 = 0.07 Estimate the product. 0.8 is close to 1. 0.07 0.8 0.056 Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places; use a placeholder zero 0.056 is close to the estimate of 0.07. The answer is reasonable. Course 1 3-5 Multiplying Decimals Additional Example 2C: Multiplying a Decimal by a Decimal 1.34 2.5 13=3 1.34 2.5 670 2680 3.350 Estimate the product. Round each factor to the nearest whole number. Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places 3.350 is close to the estimate of 3. The answer is reasonable. Course 1 3-5 Multiplying Decimals Check It Out: Example 2A Find the product. 0.5 0.2 Multiply. Then place the decimal point. 0.5 1 decimal place 0.2 + 1 decimal place 0.10 Course 1 2 decimal places 3-5 Multiplying Decimals 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 0.9 0.027 Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places; use a placeholder zero 0.027 is close to the estimate of 0.03. The answer is reasonable. Course 1 3-5 Multiplying Decimals Check It Out: Example 2C 3.80 3.3 4 3 = 12 3.80 3.3 1140 11400 12.540 Estimate the product. Round each factor to the nearest whole number. Multiply. Then place the decimal point. 2 decimal places + 1 decimal places 3 decimal places 12.54 is close to the estimate of 12. The answer is reasonable. Course 1 3-5 Multiplying Decimals Additional Example 3A: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 3.062 5x = 5(3.062) Substitute 3.062 for x. 3.062 3 decimal places 5 + 0 decimal places 15.310 3 decimal places Remember! These notations all mean multiply 3 times x. 3•x Course 1 3x 3(x) 3-5 Multiplying Decimals Additional Example 3B: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 4.79 5x = 5(4.79) Course 1 Substitute 4.79 for x. 4.79 2 decimal places 5 + 0 decimal places 23.95 2 decimal places 3-5 Multiplying Decimals Check It Out: Example 3A Evaluate 5x for the value of x. x = 2.012 5x = 5(2.012) Substitute 2.012 for x. 2.012 3 decimal places 5 + 0 decimal places 10.060 3 decimal places Course 1 3-5 Multiplying Decimals Check It Out: Example 3B Evaluate 5x for the value of x. x = 6.22 5x = 5(6.22) 6.22 2 decimal places 5 + 0 decimal places 31.10 2 decimal places Course 1 Substitute 6.22 for x. 3-5 Multiplying Insert Lesson Decimals Title Here Lesson Quiz Find each product. 1. 0.8 0.07 0.056 2. 0.006 0.07 0.00042 Evaluate 8x for each value of x. 3. x = 2.705 21.64 4. x = 0.804 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 Course 1