3-2 Estimate Products. Estimate the product SOLUTION: Use rounding. So, is about SOLUTION: Use rounding.
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1 Estimate the product So, is about So, is about So, is about So, is about So, is about 240. esolutions Manual - Powered by Cognero Page 1
2 So, is about On average, the U.S. produces 36.5 million tons of fruit each year. About how much fruit does it produce in 2.25 years? The U.S. would produce about 80 million tons in 2.25 years. 8. Lisha is making headbands using ribbon. She would like to make 12 headbands. Each one requires 15.5 inches of ribbon. She estimates that she will need to buy 160 inches of ribbon. Is her estimate reasonable? Explain your reasoning. If 15.5 is rounded to 16 and 12 is rounded to 10, Lisha would need or 160 centimeters of ribbon. Her estimate is not reasonable. esolutions Manual - Powered by Cognero Page 2
3 9. Financial Literacy Hannah s hourly wage at the ice cream shop is $5.85. The table shows the number of hours she worked. She estimates her earnings to be $120. Without calculating her actual earnings, determine if her estimate is more or less than her actual earnings. Explain your reasoning. First find the total number of hours Hannah worked. Then Hannah used rounding to estimate her hourly wages, by rounding $5.85 up to $6.00. She also rounded the number of hours up to 20. So, because both her hourly wage and number of hours worked were rounded up, the actual total that she earned is less than the estimate. 10. A car releases 19.6 pounds of carbon dioxide for every 1 gallon of gasoline burned. Estimate the number of pounds of carbon dioxide released if 14.5 gallons is burned. About 300 pounds of carbon dioxide is released if 14.5 gallons of gasoline is burned. esolutions Manual - Powered by Cognero Page 3
4 11. Model with Mathematics Refer to the graphic novel frame below for Exercises a b. a. How much more does Raj need until he has enough to buy the video game system? b. Raj estimates that if he works for 20 hours, he will have enough to buy the video game system. Is he correct? Explain. a. The cost of the video game system is $200, and Raj has saved $68. So, Raj will need to save $200 $68 or $132 more to buy the game. b. Raj makes $5.50 per hour, which is rounded to $6. Estimate using $6. $6 20 = $120 Since you rounded up to $6, the actual amount Raj would earn is less than $120. Raj needs to make $132, so he will not have enough to buy the video game system. 12. Reason Abstractly Name three decimals with a product that is about 40. Sample answer: So, is about 40. esolutions Manual - Powered by Cognero Page 4
5 13. Persevere with Problems A scooter can travel between 22 and 28 miles on each gallon of gasoline. If one gallon of gasoline costs between $3.75 and $3.95 per gallon, about how much will it cost to travel 75 miles? A scooter can travel between 22 and 28 miles on each gallon of gasoline, or about 25 miles on each gallon. If the total distance is 75 miles, then the scooter will need or 3 gallons of gasoline. One gallon of gasoline costs between $3.75 and $3.95 per gallon, or about $3.85. Use rounding to estimate the cost. So, it will cost about $12 to travel 75 miles. 14. Justify Conclusions Suppose your friend multiplied 1.2 and 2.6 and got 31.2 as the product. Is your friend s answer reasonable? Justify your response. So, is about 3. The answer of 31.2 is not close to 3 so it is not reasonable. 15. Reason Inductively Green peppers are on sale for $2.89 per pound. Mrs. Moseley bought 1.75 pounds of peppers. Is it more reasonable to say that she spent between $5 and $6 or between $6 and $7 on the peppers? Explain your reasoning. Round 1.75 lbs to 2 lbs Round $2.89 to $3 The cost is 2 X $3 = $6. Since both values were rounded up, the cost will be less than the estimate. 16. Estimate the product. So, is about 260. esolutions Manual - Powered by Cognero Page 5
6 So, is about 2,400. So, is about 1, A single year on Saturn is equal to 29.4 years on Earth. About how many Earth-years are equal to 3.2 years on Saturn? About 90 Earth-years are equal to 3.2 years on Saturn. 20. Miguel received a $50 gift card to a bookstore. He would like to buy 3 books that cost $15.75 each. He estimates that he cannot buy all three books because each book costs about $20, and all three books would cost $60. Is his estimate reasonable? Explain your reasoning. Miguel s estimate is not reasonable. He rounded $15.75 to $20. This gave him a high estimate of $60. Suppose he rounded $15.75 to $16. The estimate of the cost of the three books would be $48, so he would have enough money on the gift card. esolutions Manual - Powered by Cognero Page 6
7 Use estimation to determine whether the answer is reasonable. If the answer is reasonable, write yes. If not, write no and provide a reasonable estimate = The answer is close to 100. So yes, the answer is reasonable = The answer is not close to 70, so no, it is not reasonable. A reasonable estimate of the product is about = 50 The answer 50 is not close to 32, so no, it is not reasonable. A reasonable estimate of the product is about = The answer is close to 360. So yes, the answer is reasonable. esolutions Manual - Powered by Cognero Page 7
8 25. Use Math Tools The table shows some nutritional facts about orange juice. Estimate each value for 1 quart of orange juice. (Hint: 4 cups is equal to 1 quart.) For the number of Calories, round 112 to 100. So, there are about 400 Calories in 1 quart of orange juice. For the amount of Vitamin C, round 96.9 to 100. So, there are about 400 mg of Vitamin C in 1 quart of orange juice. For the amount of carbohydrates, round 26.8 to 25. So, there are about 100 g of Carbohydrates in 1 quart of orange juice. For the amount of calcium, round 22.4 to 20. So, there are about 80 mg of calcium in 1 quart of orange juice. esolutions Manual - Powered by Cognero Page 8
9 26. Medina s school lunch menu is shown. Estimate the cost for the following combinations. 2 slices of pizza, salad, fruit punch fish and fries, pudding, milk 1 slice of pizza, salad, pudding, fruit punch Which combination is the least expensive? Use rounding for each. Pizza rounds to $2 Fish and Fries rounds to $2 Salad rounds to $1 Fruit Punch rounds to $1 Milk rounds to $1 Pudding rounds to $1 Find the cost for each combination 2 slices of pizza, salad, fruit punch fish and fries, pudding, milk 1 slice of pizza, salad, pudding, fruit punch esolutions Manual - Powered by Cognero Page 9
10 27. Mario and Andrew s hourly charge for mowing lawns is shown. Suppose Mario and Andrew each worked 25 hours. About how much more money did Mario earn? Use rounding to estimate how much money they each made. Mario made $8.25 per hour for 25 hours. $8.25 is about $8. So, Mario made about $200 Andrew made $5.60 per hour for 25 hours. Andrew made about $6 per hour So, Andrew made about $150. Therefore, Mario earned about $200 $150 or $50 more. Multiply. 28. esolutions Manual - Powered by Cognero Page 10
11 Marissa spent $15.63 at the bookstore. She paid with a $20 bill. How much change will she receive? Subtract $15.63 from $20 to find how much change Marissa will receive. Marissa will receive $4.37. esolutions Manual - Powered by Cognero Page 11
12 32. Cristian is placing photos onto scrapbook paper for his photo album. The scrapbook paper is 12 inches long and 12 inches wide. What is the area of the paper? (Hint: area = length width) To find the area of the paper, multiply the length by the width. Remember that area is measured in square units. 12 inches 12 inches = 144 square inches So, the area of the paper is 144 square inches. esolutions Manual - Powered by Cognero Page 12
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