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Name 3.3 ? Number and Operations—5.3.E Also, 5.3.A MATHEMATICAL PROCESSES 5.1.A, 5.1.C Multiplication with Decimals and Whole Numbers Essential Question How can you use properties and place value to multiply a decimal and a whole number? Unlock Unlock the the Problem Problem In 2010, the United States Mint released a newly designed Lincoln penny. A Lincoln penny has a mass of 2.5 grams. If there are 5 Lincoln pennies on a tray, what is the total mass of the pennies? • How much mass does one penny have? • Use grouping language to describe what you are asked to find. Multiply. 5 × 2.5 Estimate the product. Round to the nearest whole number. 5×_=_ Another Way One Way Use the Distributive Property. Show partial products. 5 × 2.5 = 5 × ( _ + 0.5) STEP 1 Multiply the tenths by 5. 2.5 × 5 _ = ( _ × 2) + (5 × _ ) =_+_ =_ Math Talk 2 ones and 5 tenths STEP 2 Multiply the ones by 5. 2.5 × 5 _ 2.5 ← 5 × 2 ones = 10 ones, or 1 ten STEP 3 Add the partial products. Mathematical Processes Explain how the solution would be different if you multiplied $5 × 2.5. © Houghton Mifflin Harcourt Publishing Company ← 5 × 5 tenths = 25 tenths, or 2.5 × 5 _ 2.5 +__ 10 So, 5 Lincoln pennies have a mass of __ grams. Module 3 117 Example Use place value patterns. Having a thickness of 1.35 millimeters, the dime is the thinnest coin produced by the United States Mint. If you stacked 8 dimes, what would be the total thickness of the stack? Multiply. 8 × 1.35 STEP 1 STEP 2 STEP 3 Write the decimal factor as a whole number. Multiply as with whole numbers. Place the decimal point. Think: 0.01 of 135 is 1.35. Find 0.01 of 1,080 and record the product. Think: 1.35 × 100 = 135 1.35 × 8 _ ? × 100 ⎯⎯⎯→ × 100 ⎯⎯⎯→ 135 × 8 __ 1,080 × 0.01 ⎯⎯⎯→ × 0.01 ⎯⎯⎯→ 1.35 × 8 _ A stack of 15 dimes would have a thickness of __ millimeters. Share Share and and Show Show Place the decimal point in the product. 1. 6.81 × 7 __ 47 67 Think: The place value of the decimal factor is hundredths. 2. 3.7 × 2 _ 74 3. 19.34 × 5 __ 96 70 5. 4.5 × 8 _ 6. 40.7 × 5 __ 4. 6.32 × 3 __ Math Talk Mathematical Processes Explain how you can determine if your answer to Exercise 6 is reasonable. 118 © Houghton Mifflin Harcourt Publishing Company Find the product. Name Problem Problem Solving Solving Practice: Copy and Solve Find the product. 7. 8 × 7.2 8. 3 × 1.45 9. 9 × 8.6 10. 6 × 0.79 11. 4 × 9.3 12. 7 × 0.81 13. 6 × 2.08 14. 5 × 23.66 15. Write Math Julie multiplies 6.27 by 7 and claims the product is 438.9. Explain without multiplying how you know Julie’s answer is not correct. Find the correct answer. Problem Problem Solving Solving Use the table for 16–18. 16. Sari has a bag containing 6 half dollars. What is the mass of the half dollars in Sari’s bag? Coin 17. Felicia is running a game booth at a carnival. One of the games requires participants to guess the mass, in grams, of a bag of 9 dimes. What is the actual mass of the dimes in the bag? Nickel 5.00 Dime 2.27 Quarter 5.67 Half Dollar Dollar © Houghton Mifflin Harcourt Publishing Company 18. Mass (in grams) 11.34 8.1 Multi-Step Chance has $2 in quarters. Blake has $5 in dollar coins. Whose coins have the greatest mass? Explain. Module 3 • Lesson 3 119 Mathematical Processes M Model ¥ Reason ¥ Communicate M Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. 19. Apply A hummingbird weighs 5.8 grams. If the hummingbird eats 8 times its body weight each day, how much does the bird eat in four days? A 23.2 grams B 46.4 grams C 185.6 grams D 464 grams 20. Use Symbols Which expression shows how to use the Distributive Property to find 5.17 × 9? A 5.17 + 9 B 9 × (5.1) + 7 C 9 × (5.1 + 7) D 9 × (5 + 0.17) 21. Multi-Step The cost to park a car in a parking lot is $1.10 per hour. Maleek parked his car for 4 hours on Monday, 4 hours on Tuesday, and 4 hours on Wednesday. How much did he spend on parking in all? A $4.10 B $4.40 C $13.10 D $13.20 TEXAS Test Prep If he walks to school 5 days, how many miles will Milo have walked? 120 A 1,825 miles B 18.25 miles C 182.5 miles D 1.825 miles © Houghton Mifflin Harcourt Publishing Company 22. Every day on his way to and from school, Milo walks a total of 3.65 miles. Number and Operations—5.3.E Also, 5.3.A MATHEMATICAL PROCESSES 5.1.A, 5.1.C H o mewo rk and Practice 3.3 Name Multiplication with Decimals and Whole Numbers Find the product. 1. 4 × 7.12 2. 3 × 0.29 3. 8 × 2.19 4. 7 × 18.3 5. 5 × 9.29 6. 2 × 42.1 7. 7 × 0.34 8. 9 × 7.21 9. 4 × 5.2 10. 7 × 17.2 11. 4 × 3.92 12. 8 × 0.21 13. Logan multiplies 5.31 by 3 and says the product is 159.3. Explain why Logan’s answer is not correct. © Houghton Mifflin Harcourt Publishing Company Problem Problem Solving Solving 14. Minnie rides her bike 2.76 miles each day. How many miles will she bike in 7 days? 15. Dominick buys a package of soup mix that is 1.38 ounces. How many ounces are 6 packages of soup mix? Module 3 • Lesson 3 121 TEXAS Test Prep Lesson Lesson Check Check Fill in the bubble completely to show your answer. If she triples the recipe, how many ounces of beans will Sandra need? A 17.29 ounces B 18.83 ounces C 19.17 ounces D 20.19 ounces 17. Kip uses the Distributive Property to rewrite an expression. (4 × 3) + (4 × 0.7) What is the value of the expression? A 3.07 B 11.7 C 14.8 D 29.6 18. Manny charges $1.25 for a cup of lemonade 19. Fabric costs $11.99 a yard. Leo buys 4 yards at the lemonade stand. He sells 9 cups. How much money does Manny collect? of red fabric and 3 yards of blue fabric. How much does Leo spend on fabric? A $10.75 A $47.96 B $11.00 B $35.97 C $11.25 C $77.33 D $11.75 D $83.93 20. Multi-Step On the first day of summer, a 122 21. Multi-Step Nicky bought 14.2 pounds of rainstorm brought 2.29 inches of rain to the area. During the rest of the summer, there was 3 times as much rain as on the first day. What was the total number of inches of rainfall for the summer? coffee for the coffee shop. The shop usually uses 5 times that amount of coffee during one week. How much more coffee will Nicky need to purchase to get the right amount of coffee for the week? A 6.29 inches A 71 pounds B 5.67 inches B 56.8 pounds C 6.87 inches C 85.2 pounds D 9.16 inches D 50 pounds © Houghton Mifflin Harcourt Publishing Company 16. Sandra uses 6.39 ounces of beans in a recipe.