Chapter 2Approaches to Problem Solving

Section 2AThe Problem Solving Power of Units

Pages 84-95

Units

• The units of a quantity describe what is being measured or counted.

• We can add or subtract numbers ONLY when they have the same units.

• We can always multiple or divide numbers – we’ll just create new units.

Units

• Do NOT disregard units.

• ALWAYS pay attention to units.

• Units are your FRIENDS!

For example:

• Travel 195 miles (distance)• Trip took 3 hours (time)

Average speed (distance/time) = 195 miles/3 hours = 65 mph (miles per hour)

For example:• One side of the floor is 25 feet long• The other side is 30 feet long.• The area of the floor space =

25 ft × 30 ft = 750 ft2 (square feet)

• The room’s height is 12 feet.• The volume of the room is 25ft × 30ft × 12ft = 9000 ft3 = 9000 cubic feet

1 inch

1 inch

1 inch1 square inch

1 inch

1 inch

1 in

ch

1 cubic inch

Read kilowatts hours as “kilowatt-hours.”

hyphenMultiplication

Read ft ft ft or ft3, as“cubic feet” or “feet cubed”

cube or cubicRaising to a third power

Read ft ft, or ft2, as“square feet” or “feet squared”

squareRaising to a second power

Read miles hours as “miles per hour”

perDivision

ExampleKey word or symbol

Operation

2-A

Practice – what units?29/96 The price of apple juice , found by dividing itstotal cost in dollars by its volume in ounces.

– dollars per ounce = $/oz

1b/85 The area of a circle, found with the formulawhere r is the radius of the circle measured in centimeters.

- square centimeters = cm2

35/97 The gas mileage of a car, found by dividing the distance in miles that it travels by the amount of gas in gallons that it uses. -miles per gallon = m/gal = mpg

pg85 The energy used by a light bulb found by multiplying the power rating in kilowatts by the number of hours it is turned on.- kilowatt X hours = kilowatt-hours

2r

Unit Conversionsconverting one set of units to another

• Trick = multiply by “1”.

1

4

14

1 81 = =

1 8

2-A

11 =

7

week

days

11 =

12

ft

in12

1 = 1

inches

foot12 inches = 1 foot

1 week = 7 days 7days1 =

1week

Unit Conversions

43/97 Convert 2 weeks to units of minutes.

2-A

44*/97 A car is driving at 100 44*/97 A car is driving at 100 kilometers per hour. What is its speed kilometers per hour. What is its speed in kilometers per second?in kilometers per second?

53/98 A box-shaped water tank measures 12 53/98 A box-shaped water tank measures 12 feetfeetby 8 feet by 4 feet. Find its volume in cubic by 8 feet by 4 feet. Find its volume in cubic yards. yards. (Careful with square and cubic units!)(Careful with square and cubic units!)

(Careful with square and cubic (Careful with square and cubic units!)units!)

1 square yard = 9 square feet1 square yard = 9 square feet

1 square foot = 144 square inches1 square foot = 144 square inches

1 cubic yard = 27 cubic feet1 cubic yard = 27 cubic feet

1 cubic foot = 1728 cubic inches1 cubic foot = 1728 cubic inches

WHY???WHY???

WHY???WHY???

Currency Conversions (September 2008):(www.xe.com)

2-A

Currency dollars per foreign foreign per dollar

British pound 1.7834 0.5607

Canadian dollar

0.9360 1.0684

European euro 1.4518 0.6888

Japanese yen 0.0092 108.7510

Mexican peso 0.09653 10.3593

Currency Conversions

57/98 Which is worth more today – 1 Mexican peso or 1 US dollar? Explain.

2-A

61/98 61/98 How many US dollars can you buy How many US dollars can you buy with 12,000 Japanese yen?with 12,000 Japanese yen?

Problem Solving with Units

65/98 A car travels 13 miles in 15 minutes. How fast is it going in miles per hour?

69/98 You are buying 4.7 pounds of apples priced at $1.29 per pound. How much do you pay?

77/98 If you sleep an average of 7 hours each night, how many hours do you sleep in a year?

2-A

Problem Solving with Units

83/98 Suppose you drive a car with an average gas mileage of 28 miles per gallon. If you plan to take a 2500-mile cross country trip, how many gallons of gasoline should you expect to use.

2-A

Homework

Pages 97-99: #1-93

TURN IN: 38,44,52,56,60,66,70,76,78,84

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