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November Problem of the Day Calculations and Calculators: Decimals

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November 1, 2013 The first person to swim across the English Channel was Matthew Webb in 1875. Webbs time was 21.25 hours. The second, third, and fourth people and their times were Thomas Burgess, 22.583 hours; Henry Sullivan, 26.83 hours; and Enrico Tiraboschi, 16.55 hours. Arrange the times in order from greatest to the least. Change the decimals to whole numbers and proper fractions. What would these times be in hours and minutes, rather than fractions of an hour? What is the process to make those conversions?

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November 4, 2013 Maria is ordering lunch at a fast-food restaurant. She estimates her bill as she is ordering. (All costs include sales tax). Following are her estimates for lunch. Soda, $1.25; estimate $1.00 Hamburger Special, $3.39; estimate $3.00 Ice Cream, $0.99; estimate $1.00 Maria has only $5.00. Does she have enough money according to her estimate? Does she really have enough? Why or why not? What are the rules for estimation? Do those rules apply in every instance?

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November 5, 2013 Merchants and store owners are reluctant to round prices down. If canned goods are priced 3 for $1.00 the price of one can is $0.333…but they charge $0.34 for a can if you only buy one. How much do you pay for one item? (a) 2 cans for $1.99 (b) 2 cans for $3.00 (c) 3 cans for $2.00 (d) 8 cans for $5.00 Big Box stores can charge less for each item, but require that you buy a larger quantity (12 or 16 cans), since that is what comes in the box. What are the pros and cons of this method of buying?

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November 6, 2013 Add the following decimals, and then change each decimal to the fractional equivalent. Add them again and discuss the results as compared to the decimal sum: (a) 27.3 + 5.65 (b) 52.0 + 1.345 + 0.54 (c)0.657 + 2.3 + 86.389 (d) 5.678 + 3 + 19.487

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November 7, 2013 Most cash registers provide an itemized receipt. Mary purchases the following items: Potato chips for $1.79 Candy bar for $0.59 Orange Juice for $2.29 Toothpaste for $2.79 Milk for $1.29 How much does Mary have to pay for these items? Why are these decimal numbers and not fractions? Why are the decimals taken out to the hundredths (2 decimal places)? Are there any prices that are normally taken out to the thousandths (3 decimal places)?

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November 8, 2013 Subtract the following decimals and then change each decimal to the fractional equivalent. Subtract them again and discuss the results as compared to the decimal difference: (a) 1.867 – 0.947 (b) 356.2 – 4.7826 (c) 6 – 2.49 (d) 0.09348 – 0.058

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November 11, 2013 Being able to quickly count change is a valuable skill. Determine the change in the fewest bills and coins. Example: Purchase Price, $13.95; amount paid, $15.00; change, $1.05 (one dollar bill, nickel). Explain why the customer chose to pay $60.03 instead of just $60. Does this make sense? (a) Price - $15.89 Paid - $20.00 (b) Price – $2.59 Paid - $5.00 (c) Price - $23.35 Paid – $30.35 (d) Price – 47.63 Paid – $60.03

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November 12, 2013 Each product is correct; however, a decimal point is missing in one or both factors. You may need to add place holders (zeros). Is there more than one way to do this? Explain the process you used to find the correct decimal placement. (a) 36 x 54 = 194.4 (b) 78 x 21 = 0.1638 (c) 324 x 65 = 2,106 (d) 7 x 3 = 0.00021

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November 13, 2013 Which of the problems below are correct? Correct those that are wrong. Explain the errors. Which of the problems below are correct? Correct those that are wrong. Explain the errors. (a) 0.256 x 0.56 = 0.14386 (b) 0.54 x 2.4 = 0.1296 (c) 7.024 x 0.86 = 6.0464 (d) 34.7 x 6.7 = 232.49

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November 14, 2013 Check the quotients by multiplying. If it is incorrect, correct it. Explain the errors. Check the quotients by multiplying. If it is incorrect, correct it. Explain the errors. (a) 6.825 / 0.91 = 7.8 (b) 0.56468 / 7.6 = 0.743 (c) 0.5154 / 0.006 = 8.59 (d) 0.00306 / 0.36 = 0.085

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November 15, 2013 To compute gas mileage, divide the number of miles driven by the number of gallons used. Sergio drove 300.5 miles on 14.8 gallons of gas. What was Sergios mileage rounded to the nearest mile per gallon (mpg)? What is the importance of gas mileage in todays financial and political issues? What about the future?

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November 18, 2013 The average lengths of the three longest bones (all leg bones) in the human body are listed below. Femur – 19.88 Tibia – 16.94 Fibula – 15.94 Find the average length of the human leg. What do you need to know about the bones of the body to solve this problem? What are some factors that would influence these averages? What do you think about the accuracy of this average (an average of averages)?

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November 19, 2013 A unit price or unit rate is the amount charged per unit. A unit may be single item, a measurement, or some other quantity depending, on the product. You can compare the cost of similar items by comparing unit prices. A lower unit price is usually a better buy. A 35-ounce box of cereal sells for $6.49. A 20-ounce box of the same cereal sells for $3.99. Which is the better buy? What would be some instances when a lower unit price might not be the best buy? Do you check unit prices when you purchase items, why or why not?

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November 20, 2013 A local restaurant pays cashiers $7.75 per hour, with time and a half (1.5 times the hourly wage) for overtime. This restaurant pays overtime for any hours more than 40 worked per week. Casey worked 43.5 hours last week. How much money did Casey earn? Does rounding figure into his pay? Casey needs to make at least $375 a week to pay his bills, so how many hours does he need to work?

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November 21, 2013 Eat Rite Supermarket is having a buy one get one free sale on the 20-ounce box of Toasties cereal. One box sells for $3.99. Samantha has a coupon that is worth $0.75 off the 35-ounce box of Toasties. This box normally sells for $6.49. Which is the better buy? Why? Should she take advantage of both offers? Why or why not?

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November 22, 2013 Vinnys Pizza sells a 10-inch pizza for $8.49. The plan pie comes with tomato sauce and cheese. A special combination of any three additional toppings is $2.00 extra. If a fourth, fifth or sixth topping is selected; the cost is $0.45 per topping. What is the cost of a 10-inch pizza with anchovies, onions, peppers, and pepperoni? What do you think about the value of a pizza with the 3 toppings special price versus the value of the four or five topping pie for the extra 45 cents each? Do you really get more for the extra money or is there a limit to the amount of toppings a 10-inch pizza can hold?

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November 25, 2013 Electricians often charge a set amount for each hour they work, plus a service charge. The service charge doesnt vary and is charged regardless of how long a job takes. How much would an electrician charge for doing 4.5 hours of work if the rate is $25 per hour, plus a service charge of $45? What do you think about the fairness of a service charge in addition to the hourly rate? What about a fuel charge, off hours/weekend rate, or adding 20% on to the cost of parts? How does this affect the cost of service? Is there a limit to what the customer will pay?

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November 26, 2013 Long distance phone calls are based on the rates, calling point, and the time the call was made. A 15- minute long-distance call is calculated in the following manner: Up to and including the first 10 minutes, the cost is $0.09 per minute. Each additional minute is $0.03. Find the total cost of a 15-minute call and a 30-minute call. Is the price double since the time is doubled? If you called long distance frequently what should you do to reduce your costs?

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November 27, 2013 An operator-assisted long-distance phone call is a call in which an operator assists, or helps, a person complete the call. Such calls are usually more expensive than calls the caller completes her- or himself. Dana was told that an operator-assisted call costs 1.5 times the cost of a direct dial call to the same city. Find the cost of the direct-dial call if the operator-assisted call costs $5.45 and round your answer to the nearest cent. How has the use of cell phones changed our calling habits? Do you think it costs more now than it did before the cell phone and all the calling plans.

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