How tall are you? Did you answer in feet and inches or in centimetres? How cold is it outside? Did you answer in degrees Fahrenheit or in degrees Celsius?

metric system • a system of

measurement in which all units are based on multiples of 10

imperial system • a system of

measurement based on British units

Canada’s offi cial measurement system is the metric system . However, most Canadians use both the metric and imperial systems . Th e metric system is used in most countries. Th e United States, Canada’s closest neighbour and largest trading partner, uses a measurement system that is based on the imperial system.

Diff erent measurement systems are used in diff erent industries. In science and medicine, metric is the system of choice around the globe. But in construction and cooking, for example, the imperial system is still commonly used.

Investigate The Relationships Among Imperial Units

Tools gallon container imperial measuring cup imperial measuring spoons

imperial scale pint container quart container sand or water yardstick

Units of measure are grouped into units of length, units of mass/weight, units of volume, and units of temperature. Th e table shows the most common units of imperial measure.*

Category Units of Measure Abbreviation

Length inch, foot, yard, mile in. or ", ft or ', yd, miVolume teaspoon, tablespoon,

fl uid ounce, cup, pint, quart, gallontsp, tbsp, fl oz, c, pt, qt, gal

Weight ounce, pound, ton oz, lb, tnTemperature degree Fahrenheit °F

* Unless otherwise noted, all references to imperial measures in this student text will be U.S.

Imperial Measure1.1

6 MHR • Chapter 1

3221_FOM_CH01_Section1.1.indd 13221_FOM_CH01_Section1.1.indd 1 1/13/07 10:31:11 PM1/13/07 10:31:11 PM

Part A: Units of Length

1. a) Use a yardstick. Determine the number of inches in one foot, and the number of feet in one yard.

b) What is the smallest fraction of an inch shown on the yardstick?

Part B: Units of Volume

The British imperial pints, quarts, and gallons are larger than U.S. pints, quarts, and gallons. The British fl uid ounce is less than the U.S. fl uid ounce.

Math Connect

2. Use a measuring cup, measuring spoons, and pint, quart, and gallon containers. Explore how the units of volume are related to one another. Record your results.

Part C: Units of Weight

3. a) Use a scale. Find the weight of a variety of objects both in pounds and in ounces. How are ounces and pounds related? Record your results.

b) Research the relationship between pounds and tons. Record your fi ndings.

Refl ect Review your fi ndings. Design a table to show how the units of length compare, how the units of volume compare, and how the units of weight compare. Share your fi ndings with a partner. Are your unit comparisons accurate?

Example 1 Measure to a Fraction of an InchFind the length of each object to the smallest fraction of an inch.

A

B

C

DA ruler cannot show 32nds or 64ths of an inch accurately. Calipers are used to make more precise measurements.

Math Connect

1.1 Imperial Measure • MHR 7

3221_FOM_CH01_Section1.1.indd 73221_FOM_CH01_Section1.1.indd 7 1/15/07 5:33:34 PM1/15/07 5:33:34 PM

Solution

Th e bolts/screws measure

a) 1 1 _ 4 in. b) 2 1 _ 2 in.

c) 3 3 _ 8 in. d) 3 3 _ 4 in.

Example 2 Working With VolumeSteve owns a restaurant in Arizona. He bought a 55-gal drum of ketchup at a wholesale store. For the tables, he has 1 _ 2 pint squeezebottles that he fi lls with ketchup from the drum. How many bottlescan Steve fi ll from this drum of ketchup?

Solution

Find the number of pints in the drum.= 55 × 8 There are 8 pt in a gallon, so multiply

the number of gallons by 8.= 440

Th ere are 440 pt in 55 gal.Each bottle will hold half a pint, so the number of bottles that can be fi lled is double the number of pints in the drum. Steve can fi ll 880 squeeze bottles from this drum of ketchup.

Example 3 Find the Cost to Carpet a RoomCalculate the cost, including 17 ft

12 ft

taxes, to carpet the fl oor shown. Th e carpet costs $24 per square yard.

Solution

Calculate the area to be carpeted:A = l × w = 17 × 12 = 204

Th e area to be carpeted is 204 sq ft .

8 MHR • Chapter 1

3221_FOM_CH01_Section1.1.indd 83221_FOM_CH01_Section1.1.indd 8 1/16/07 11:45:32 AM1/16/07 11:45:32 AM

Th ere are 3 ft in a yard and 9 ft in 1 sq yd. Divide by 9 to convert the area in square feet to square yards:

A = 204 ÷ 9= 22 2 _ 3

Th e area to be carpeted is 22 2 _ 3 sq yd.Calculate the cost of the carpet:

= 22 2 _ 3 × 24 The cost is $24 per square yard, so multiply the area by 24.

= 544

Find the total aft er adding 14% tax (8% PST plus 6% GST):= 544 × 1.14= 620.16

It will cost $620.16 to carpet this room.

Key Concepts

• The basic units of imperial measure are the foot, gallon, pound, and degree Fahrenheit.

• There are fi xed relationships among the diff erent units for length, volume, and weight.

Discuss the Concepts

D1. List the imperial measures and their abbreviations that are used to measure the following.

a) length b) volume c) weight d) temperature

D2. Describe how the imperial units for length are related.

D3. Describe how the imperial units for weight are related.

Practise the Concepts AFor help with question 1, see Example 1.

1. Measure the perimeter of each fi gure as precisely as possible. a) b) c)

1.1 Imperial Measure • MHR 9

3221_FOM_CH01_Section1.1.indd 93221_FOM_CH01_Section1.1.indd 9 1/16/07 11:46:00 AM1/16/07 11:46:00 AM

For help with questions 2, 3, and 4, refer to Example 2. All measures are in U.S. imperial units.

2. Convert each measure to pints and to quarts. a) 32 fl oz b) 24 c c) 10 c d) 108 fl oz

3. Convert each measure to gallons. a) 64 qt b) 104 c c) 50 pt

4. Express each measure in fl uid ounces. a) 5 qt b) 16 c c) 3 gal d) 5 pt

5. Convert each measure to pounds. a) 32 oz b) 456 oz

6. Express each weight in ounces. a) 3 lb b) 5.6 lb

7. Work with a partner. Discuss which units you would use to measure in each case. Explain your choices.

a) the size of a book, a desk, a lawn, an airfi eld b) the volume contained in a thimble, a glass, a swimming pool,

an ocean c) the weight of a sheet of paper, a book, a person, a car

Apply the Concepts B 8. A recipe calls for 7 tbsp of oil. How many fl uid ounces of oil

do you need?

9. Chris is sewing drapes and needs 20 ft of fabric. Th e local fabric store sells fabric by the yard. How many yards of fabric does Chris need?

10. Cindy is catering a dinner for a conference with 225 guests. She plans to serve a pasta course and fi gures she needs 6 oz of pasta per guest. How many pounds of pasta will she need to order?

11. A Canadian football fi eld is 110 yd long and an American football fi eld is 100 yd long. How many feet longer is the Canadian fi eld?

For help with question 12, refer to Example 3.

12. Jamila’s dining room is 13 ft long by 10 ft wide. She plans to install bamboo fl ooring that costs $18.50 per square yard. How much will Jamila pay for the fl ooring, including taxes?

10 MHR • Chapter 1

3221_FOM_CH01_Section1.1.indd 53221_FOM_CH01_Section1.1.indd 5 1/13/07 10:31:47 PM1/13/07 10:31:47 PM

Literacy Connect 13. Although the metric system is Canada’s offi cial measurement system, many Canadians know their weight and height in imperial measure. With a partner, discuss why this is the case.

Chapter Problem 14. Darren has to remove some dead branches at the top of a tree. Th e tree is approximately 15' tall. Darren stands 5' 10" tall. He has a ladder that reaches up 8' 5". Will Darren be able to use his ladder to trim the branches or will he need to rent scaff olding?

Extend the Concepts CUse this fl oor plan for questions 15 to 17.

15. You plan to put carpet in the bedroom of your new home, hardwood fl oors in the living room, and ceramic tile in the kitchen, bathroom, and laundry room. Calculate the number of square feet of each type of fl ooring you will need.

a) carpet b) tile c) hardwood

16. Tile costs $3.60 per square foot, carpet costs $28.00 per square yard, and hardwood costs $6.99 per square foot. What will your total cost be?

17. You need to buy primer to paint the three walls in the garage. Th e walls are 8' high. Th e garage door, the fourth wall, will not be painted.

a) Calculate the total area to be primed. b) Suppose one quart of primer covers 110 sq ft . How many

gallons of primer will you need?

1.1 Imperial Measure • MHR 11

3221_FOM_CH01_Section1.1.indd 63221_FOM_CH01_Section1.1.indd 6 1/13/07 10:31:49 PM1/13/07 10:31:49 PM