chapter 2 approaches to problem solving. section 2a units pages 84-95

Chapter 2Chapter 2Approaches to Problem Approaches to Problem

SolvingSolving

Section 2ASection 2A

UnitsUnitsPages 84-95Pages 84-95

UnitsUnits

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

We can We can addadd or or subtractsubtract numbers numbers ONLY when they have the ONLY when they have the same same unitsunits..

We can We can alwaysalways multiply multiply oror divide divide numbers – we’ll just create new numbers – we’ll just create new units.units.

For example:For example:

Travel 195 Travel 195 milesmiles (distance) (distance) Trip took 3 Trip took 3 hourshours (time) (time)

Average speed (distance/time) =Average speed (distance/time) =195 miles/3 hours 195 miles/3 hours

= = 65 mph (miles per hour)65 mph (miles per hour)

For example:For example:

One side of this floor is One side of this floor is 25 25 feetfeet long long The other side is The other side is 30 30 feetfeet long. long. AreaArea of this floor space = of this floor space =

25 ft 25 ft × × 30 ft = 30 ft = 750 ft750 ft22 (square feet) (square feet)

The room’s height is The room’s height is 12 feet12 feet.. The The volumevolume of this room is of this room is

25ft 25ft ×× 30ft 30ft ×× 12ft = 9000 ft 12ft = 9000 ft33 = 9000 cubic = 9000 cubic feetfeet

Read kilowatts Read kilowatts hours as hours as “kilowatt-hours.”“kilowatt-hours.”

hyphenhyphenMultiplicationMultiplication

Read ft Read ft ft ft ft or ft ft or ft33, as, as

““cubic feet” or “feet cubed”cubic feet” or “feet cubed”cube cube or or cubiccubicRaising to a third Raising to a third

powerpower

Read ft Read ft ft, or ft ft, or ft22, as, as

““square feet” or “feet squared”square feet” or “feet squared”squaresquareRaising to a second Raising to a second

powerpower

Read miles Read miles hours as hours as “miles per hour”“miles per hour”

perperDivisionDivision

ExampleExampleKey word orKey word or symbolsymbol

OperationOperation

2-A

Practice – what unitsPractice – what units??

The price of apples, found by dividing their total The price of apples, found by dividing their total cost in dollars by their total weight in pounds.cost in dollars by their total weight in pounds.

dollars per pound = $/lbdollars per pound = $/lb

The density of a rock, found by dividing its weight The density of a rock, found by dividing its weight in grams by its volume in cubic centimeters.in grams by its volume in cubic centimeters.

grams per cubic centimeter = g/cgrams per cubic centimeter = g/c33 = g/cc = g/cc

A car engine torque, calculated by multiplying a A car engine torque, calculated by multiplying a force in force in pounds by a distance in feet.pounds by a distance in feet.

foot-pounds = ft-lbsfoot-pounds = ft-lbs

Unit ConversionsUnit Conversions Trick = multiply by Trick = multiply by

“1”.“1”.

11 =

1

kg

kg1

4

14

1 81 = =

1 8

2-A

11 =

7

week

days

11 =

12

ft

in12

1 = 1

inches

foot

3651 =

1

days

year

11 =

52

year

weeks

Unit ConversionsUnit Conversions

Convert a distance of 9 feet into inches.Convert a distance of 9 feet into inches.

How many minutes are in one week?How many minutes are in one week?

9 ft = 9 ft 12 in.

1 ft

108 in.

7 days 24 hr 60 min

1 week 10,080 minutes1 week 1 day 1 hr

2-A


Using the fact that there are 1760 yards in Using the fact that there are 1760 yards in a mile and 3 feet in a yard, convert a a mile and 3 feet in a yard, convert a distance of 3 miles into feet.distance of 3 miles into feet.

1760 3

3 miles = 3 miles 15,840 ft.1 mile 1 yard

yards feet

2-A


A football field is 100 yards long and 60 yards wide. A football field is 100 yards long and 60 yards wide. Find its area in (a) square yards and (b) square Find its area in (a) square yards and (b) square feet.feet.

(a)(a)

(b)(b)

2area=100 yards 60 yards 6000 yards

2-A

2 2 23 36000 yards =6000 yards 54,000

1yard 1yard

feet feetft


A car is driving 70 mile per hour. What is A car is driving 70 mile per hour. What is its speed in miles per second?its speed in miles per second?

1 1min70 .0194

hr 60 min 60 sec sec

170 .0194

hr 3600 sec sec

m hr m

m hr m

2-A


Recall – this room had an area of 25Recall – this room had an area of 25×30 = ×30 = 750ft750ft22..

Convert the area to inConvert the area to in2 2 (square inches).(square inches).

750 ft 2 12 in.

1 ft

12 in.

1 ft

2108,000 in

2-A

Problem Solving with UnitsProblem Solving with Units

Example: You are buying 50 acres of Example: You are buying 50 acres of farm land at a cost of $12,500 per farm land at a cost of $12,500 per acre. What is the total cost?acre. What is the total cost?

The answer should be in dollars. We The answer should be in dollars. We multiply acreage by the cost per multiply acreage by the cost per acre:acre:

$12,500

50 acres $625,0001 acre

2-A


You take a trip in which you drive You take a trip in which you drive 1200 miles in 20 hours. What is your 1200 miles in 20 hours. What is your average speed for the trip?average speed for the trip?

The answer should be in mph. We The answer should be in mph. We divide miles traveled by time (hours) divide miles traveled by time (hours) traveled:traveled:

1200

6020

mmph

hr

2-A


A human heart beats about 60 times A human heart beats about 60 times per minute. If an average human per minute. If an average human being lives to the age of 80, how being lives to the age of 80, how many times does the average heart many times does the average heart beat in a lifetime?beat in a lifetime?

60min 24 36560 80

min 1 1 1

2,522,880,000

beats hr dayyears

hr day year

beats

2-A

Currency Conversions Currency Conversions (Feb. 5, 2007)(Feb. 5, 2007)www.xe.comwww.xe.com ::

2-A

CurrencyCurrency Dollars per Dollars per foreignforeign

Foreign per Foreign per DollarDollar

British poundBritish pound $1.9597$1.9597 .510281.510281Canadian Canadian dollardollar

$0.846067$0.846067 1.181941.18194

European European euroeuro

$1.29262$1.29262 0.7736240.773624

Japanese yenJapanese yen $0.00830818$0.00830818 120.363120.363Mexican pesoMexican peso $0.0915788$0.0915788 10.919610.9196

Buying currencyBuying currency

Which is worth more today – 1 British Which is worth more today – 1 British pound or 1 dollar? Explain.pound or 1 dollar? Explain.

1 $1.9597British pound

2-A


You return from a trip with 2500 You return from a trip with 2500 Mexican pesos. How much are your Mexican pesos. How much are your pesos worth in US $?pesos worth in US $?

$0.0915788

2500 $228.951

pesopeso

2-A


Apples in Japan sell for about 75 yen Apples in Japan sell for about 75 yen each. If you buy 4 apples, how much each. If you buy 4 apples, how much have you spent in dollars?have you spent in dollars?

754 300

1

$0.00830818300 $2.49

1

yenapples yen

apple

yenyen

2-A


How many Canadian dollars can you How many Canadian dollars can you buy for $100?buy for $100?

1.18194

$100 118.194$1

CanadianCanadian

2-A

Example – What went Example – What went wrong?wrong?

You ride your bike up a steep mountain You ride your bike up a steep mountain road at 5 mph. How far do you go in 3 road at 5 mph. How far do you go in 3 hours? hours?

Student solution:Student solution:

Should be 5 miles/hour Should be 5 miles/hour ×3 hours = 15 ×3 hours = 15 milesmiles

5 3 1.7. 1.7 .I rode miles

2-A

Example – What went Example – What went wrong?wrong?

A candy store sells chocolate for $7.70 A candy store sells chocolate for $7.70 per pound. The piece you want to buy per pound. The piece you want to buy weighs 0.11 lb. How much will it cost, weighs 0.11 lb. How much will it cost, to the nearest cent? (Ignore sales tax.) to the nearest cent? (Ignore sales tax.)

Student solution:Student solution:

Should be: $7.77/lb Should be: $7.77/lb × .11 lb = $.85× .11 lb = $.85

0.11 7.70 0.014. It will cost 1.4cents.

2-A

Homework for MondayHomework for Monday

Pages 97-99Pages 97-99

#32, 35, 50*, 53*, 65, 68, 75#32, 35, 50*, 53*, 65, 68, 75

*Use the exchange rates given to *Use the exchange rates given to you in class.you in class.

chapter 2 approaches to problem solving. section 2a units pages 84-95

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