Estimate products of decimal tenths and money amounts using a variety of strategies. Suggested answer: Suggested answer: Suggested answer:

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1 1 Estiating Products Estiate products of decial tenths and oney aounts using a variety of strategies. 1. Estiate each product. Show your work. a).6 $9.55 d) 5.7 $ x $0 = $10 or 6 x $1 = $7 or x $0 plus of $0 5 x $1 plus of $1 4 = $90 + $0 = $60 + $9 = $110 = $69 b).4 $16.59 e) 6.6 $4.41 x $16 = $48 or x $16 plus 1 of $16 = $ + $8 7 x $5 = $175 or 6 x $4 plus of $4 = $144 + $16 There are several ways to estiate the cost of an ite. For exaple, to estiate the cost of 1. kg of salon that costs $17.61 per kilogra, use one of these ethods. 1 $0 $0 or 1 $18 plus 1 of $18 $18 $6 $4 Use rounding or nubers that are easier to work with. = $40 = $160 c) 4. $18.86 f) 8.4 $ x $0 = $80 or 8 x $50 = $400 or 4 x $18 plus 1 of $18 8 x $50 plus 1 of $50 = $7 + $6 = $400 + $5 = $78 = $45. Estiate each cost. Use a ethod that will give the answer closest to the actual cost. a) 1. kg at $16.88 per kilogra d) 4. kg at $9.10 per kilogra 1 x $17 = $17 4 x $0 plus 1 of $0 = $10 + $10 = $10 b) 0.6 kg at $1.77 per kilogra e) 5.4 kg at $1.74 per kilogra Suggested of $1 = $14 answer: 5 x $ plus 1 of $ = $160 + $16 = $176 c) 1.8 kg at $18.45 per kilogra f) 8.7 kg at $9.5 per kilogra x $18 = $6 8 x $40 plus 4 of $40 = $0 + $0 = $50 Copyright 006 Nelson Answers Chapter 9: Multiplying Decials 79

2 Multiplying by 1000 and Multiply decial tenths, hundredths, and thousandths by 1000 and Calculate. a) b) c) d) e) f) Deterine the distance in etres. a) 51.4 k b) k 986 c) 8.0 k 80 d) 18.7 k e) 0.00 k 0 00 f) k To ultiply a decial tenth, hundredth, or thousandth by 1000, ove all digits to the left three places. To ultiply by , ove all digits to the left four places. You can see the pattern by ultiplying by 10, 100, 1000, or For exaple, Jaie rides 4.6 k on his bicycle each day. About how far does he ride in years? One year has about 00 days. So years have about 1000 days. I estiate 4.6 k x 1000 = 460 k. 4. Dana walks about 0.76 in each step. How far could she travel if she takes steps? 0.76 x = Answers Chapter 9: Multiplying Decials Copyright 006 Nelson

3 Multiplying Tenths by Whole Nubers Multiply decial tenths by whole nubers using odels, drawings, and sybols. 1. Multiply. Show your work. a) c) x b).8 6 d) tenths x tenths = x tenths x tenths = To ultiply a decial tenth by a whole nuber, you can use regrouping or partial products. For exaple: or tenths tenths A fruit pie uses 1. kg of peaches, 50.5 g of ground alonds, and packages of ricotta. Serina needs to ake 4 pies for a faily gathering. a) How uch of each ingredient is needed? peaches alonds ricotta 1 1. kg g packages x 4 x 4 x 4 5. kg 0. 0 g 8 packages b) One kilogra of peaches costs $6. What is the total cost of the peaches needed? 1 5. x 6 1. The total cost of the peaches is $1.0. Copyright 006 Nelson Answers Chapter 9: Multiplying Decials 81

4 4 Multiplying by 0.1, 0.01, or Multiply by 0.1, 0.01, or using ental ath. 1. Multiply. a) b) c) d) e) To ultiply a whole nuber by 0.1, 0.01, or 0.001, ove the digits to the right. For exaple, f) g) h) Deterine the issing easureent. a) 45 g kg d) k b) c e) 68 g 0.68 kg c) 6 c 0.6 f) 50 5 c. What is each easureent? a) a line of 804 cubes, each 0.01 long, c) a 480 g bag of sunflower seeds, in etres in kilogras kg b) a line of 6 boxes, each 0.1 wide, d) a g candy, in kilogras in etres 0.0 kg 6. 8 Answers Chapter 9: Multiplying Decials Copyright 006 Nelson

5 5 Multiplying Multiples of Ten by Tenths Multiply to calculate the decial portion of a ultiple of Calculate. Show your work. a) d) x 50 = x 800 = 80 x 5 = 75 6 x 80 = 480 b) e) x 640 = 64 5 x 64 = 0 To ultiply a decial tenth by a whole nuber, you can write the decial tenth as a ultiple of 10. For exaple, To ultiply 0.4 0, ultiply Then ultiply c) f) x 50 = x 650 = 65 4 x 5 = 1 8 x 65 = 10. At Neil s faily picnic, 10 people ate 0.6 of 6400 g of roast chicken and 0.5 of a 4500 L container of potato salad. a) How uch roast chicken did Neil s faily eat? 0.1 x 6400 g = 640 g 6 x 640 g = 840 g b) How uch potato salad did Neil s faily eat? 0.1 x 4500 L = 450 L 5 x 450 L = 50 L c) Each person ate the sae aount of potato salad. How uch potato salad did each person eat? 50 L 10 = 5 L. Students fro two schools worked at a food bank. One school had 450 students. The other school had 60 students. Eight-tenths of the students in each school participated. How any ore students participated fro the school of 450 than the school of 60? (school of 450) 0.1 x 450 = 45 (school of 60) 0.1 x 60 = 6 8 x 45 = 60 8 x 6 = 88 difference = = 7 students Copyright 006 Nelson Answers Chapter 9: Multiplying Decials 8

6 6 Counicate About Proble Solving Explain how to solve probles involving decial ultiplication. 1. Janice exercises for 60 in each week. She walks for 0.6 of the tie, and rides her bicycle for the rest of the tie. a) For how any inutes does Janice walk? Understand the Proble I need to find out how any inutes Janice spends walking. Make a Plan 6 I will odel 0.6 using a rectangle. 0.6 is the sae as. 1 0 So I divide the rectangle into 10 equal parts and shade 6 of the. 60 in b) For how any inutes does Janice ride her bicycle? When writing a solution to a proble, use the proble-solving odel. Understand the Proble Make a Plan Carry Out the Plan Look Back Make sure you counicate your thinking clearly. Use the Counication Checklist. I will deterine how any inutes are represented by each part. Then I will ultiply that nuber by 6, because 6 parts are shaded. Carry Out the Plan Since 60 is divided into 10 parts, each part represents = 6 in. 6 x 6 in = 16 in Janice walks for 16 in each week. Understand the Proble I need to find how any inutes Janice rides her bicycle. Make a Plan I know that the total tie Janice exercises is 60 in. Since she walks for 16 in, the rest of the tie she rides her bicycle. So I need to subtract. Carry Out the Plan 60 in 16 in = 144 in Janice rides her bicycle for 144 in. Counication Checklist Did you odel the problesolving process? Did you show all your steps? Did you use a odel or diagra? Did you explain your thinking? Did you state your solution clearly? 84 Answers Chapter 9: Multiplying Decials Copyright 006 Nelson

7 7 Choosing a Multiplication Method Justify the choice of a ultiplication ethod. 1. Multiply. Did you use ental ath, pencil and paper, or a calculator? a) e).9 4 ental ath b) f) x pencil and paper x 4 = x 4 = = 11.6 pencil and paper 570 ental ath If nubers are siple to ultiply, you can use ental ath. Multiplying by 0.001, 0.01, 0.1, 10, 100, and 1000 can be done entally. For exaple, If you can ultiply nubers without a lot of partial products, use pencil and paper. For exaple, If you have to use a lot of partial products, use a calculator. For exaple, c) g) x 4 ental ath.0 8 pencil and paper d) h) ental ath ental ath. Explain why you chose the ethod you did for three parts in Question 1. Part a): I used ental ath because I know that 6 x 5 = 0. So 0.6 x 5 =. Part b): I used pencil and paper because the nubers were too hard to ultiply in y head. Part e): I used pencil and paper because I had to keep track of the partial products. Then I added the partial products in y head. Copyright 006 Nelson Answers Chapter 9: Multiplying Decials 85

8 Test Yourself Page 1 Circle the correct answer. 1. Which estiate would be closest to the actual product? A. 8 1 C. 8 1 plus 1 of 1 B. 9 D. 9 4 plus 1 of 4. Which is the best estiate for 0.8 kg at $8.95 per kilogra? A. $16 B. $18 C. $9 D. $. What is the product of 1000 and 5.064? A B C D What is the product of and 1000? A B C. 891 D What is k in etres? A B C D What is the product of 6. and 7? A. 4. B. 4.4 C D What is the product of 50 and 0.01? A B. 5.0 C. 50. D What is the product of 0.1 and 87? A. 870 B. 87 C. 8.7 D One uffin has a ass of 0.05 kg. What is the ass in gras? A. 50 g B. 0.5 g C..5 g D. 5 g 10. What is the product of 0.4 and 60? A. 65 B. 978 C. 104 D Answers Chapter 9: Multiplying Decials Copyright 006 Nelson

9 Test Yourself Page 11. A library has 5460 books. Three-tenths of the books are ysteries. How any ystery books are there? A. 546 books B. 168 books C. 180 books D. 70 books 1. Jason wants to ultiply 0.6 by 90. He wrote What are the issing nubers? A. 9, 6, 55 B. 9., 6, 55. C. 9, 60, 550 D. 9, 60, Lina saved $40 planting trees. She spent 0.4 of that aount on a new jacket. How uch did she spend on the jacket? A. $60 B. $96 C. $10 D. $ Which product is greatest? A B C D Mitch bought 0.6 kg of grapes. One kilogra cost $.00 on sale. The regular price was $4.00 per kilogra. How uch did Mitch save? $.00 A. $1.80 C. $.40 B. $0.80 D. $0.60 Copyright 006 Nelson Answers Chapter 9: Multiplying Decials 87