Module 2

Module 2: The Imperial System

 

Bringing Ideas Together

 

In Get Started you discovered that there are about 12 thumb widths in a foot. The Romans also divided their foot measure into 12 parts. The word inch comes from the Latin word uncia, which means a 12th part. In some languages the same word is used for thumb and inch. For example, in French, the word for both thumb and inch is pouce.

 

The modern inch is exactly 2.54 cm in length. So, a length of 2 in is about two thumb widths, or 5 cm.

 

The Saxons were a people who settled in Britain after the Romans left. The Saxons used three grains of barley placed end-to-end to define their inch. Barley seeds are very uniform in size. The Saxon inch was very close to today’s inch, but it was longer than a Roman inch. So, as a unit of measure, the Saxon foot of 12 inches was longer than the Roman foot.

 

Do you remember tracing your own foot at the beginning of this lesson? Retrieve your tracing and measure it using your ruler or tape measure. Is your foot more or less than 12 of today’s inches?

 

Does your ruler or tape measure have centimetres marked? If so, check to see how many centimetres there are in one inch. Can you also see how many centimetres there are in one foot?

 

Since 1 in is equal to 2.54 cm, 1 ft is 12 × 2.54 cm, or 30.48 cm. Is that what you found when you looked at 1 ft on your ruler or tape measure?

 

Often measurements are quoted in feet and inches. Do you know your height in feet and inches?

 

Converting Feet and Inches

 

Example 2 shows how feet are converted to inches.

 

Example 2

 

An Iroquois longhouse was 79′11″ long. What was the length of the longhouse in inches?

 

Solution

 

1 ft = 12 in

 

So,

 

 

 

The Iroquois longhouse was 959 in long.

 

Example 3

 

Example 3 shows how inches are converted to feet and inches.

 

Meilin is 53 in tall. What is her height in feet and inches?

 

View the animated “Example 3 Solution.”

 

Note: In this example, a calculator was used to do the division. If long division were used, the quotient would be the number of feet, and the remainder would be the number of inches.

 

Adding Fractions of Inches

 

Example 4

 

John and his mother are finishing their basement. For the outside walls, they plan to use 2-by-4 framing lumber. Framing lumber sold as 2-by-4 pieces actually measure just . The lumber is to be covered with gypsum board measuring in. How thick will this added layer of the wall be?

 

 

Solution

 

 

A 2-by-4 is actually . The total thickness of the framing lumber and wallboard is . These fractions can be added using a ruler. Look at the ruler shown.

 

 

You can also add the fractions using pencil and paper.

 

 

Try this using “Simulated Ruler.” Starting at , move of an inch to the right. Once in this new position, the readout will show the sum.

 

Subtracting Fractions of Inches

 

Example 5

 

Pat wants to plane some wood off the width of a 2-by-6. If a 2-by-6 is in wide, determine what the finished width would be in each of the following cases:

1. if is planed off
2. if is planed off

Solution

1. From in on the scale, move in to the left.
   
   
   
   The final width, as shown on the ruler, is in.
   
   An alternate solution is to subtract.
   
   

    

    

   
   The planed width will be in.
   
   
2. From in on the scale, move in to the left.
   
   
   
   An alternate solution is to subtract.
   
   

    

    

   
   
   The planed width will be in.

 

Adding Feet and Inches

 

Example 6

 

A desk that is 2′9″ in width is pushed against a table measuring 5′6″. What is the total length in feet and inches?

 

Solution

 

One method of finding the solution is to convert everything to inches first.

 

 

So,

 

 

Now change 99″ into feet and inches.

 

 

Because 8 × 12″ = 96″, 99″ = 8′3″.

 

Another method involves adding the feet and inches separately.

 

2′9″ + 5′6″ = 7′15″

 

 

So,

 

 

The total length of the desk and table pushed together is 8′3″.

 

Self-Check

 

This is your opportunity to check your understanding. Answer the questions, and then check your answers.

 

SC 2. State each measure to the nearest fraction of an inch.

 

SC 3. One of the tallest women in the world is De-Fen Yao. She is 93 in tall. How tall is De-Fen Yao in feet and inches?

 

SC 4. The 2008 women’s Olympic record in pole vaulting is . What is this record in inches?

 

SC 5. Janice is cutting 1′3″ off a 7′ board. After the cut, what is the length of the board in feet and inches?

 

SC 6. Add 5′7″, 3′4″, and 6′5″.

 

Compare your answers.

 

Measuring with Yards

 

Have you played golf? Do you follow the PGA Tour? Golf courses in Canada and the United States still measure course distances in yards.

Professional golfers commonly drive golf balls 300 yards off the tee!

 

 

 

 

 

 

 

The word yard comes from the Old English word gyrd, for stick! A yard is about the width of a front door, or the distance from your nose to the tips of your fingers when you stretch your arm to the side. A yard is also close to the length of an adult’s belt or the height of a kitchen stove.

 

Converting from Yards to Feet

 

Example 7

 

On the third hole at the local golf course, the distance from the tee to the green is 174 yd. How many feet is this distance?

 

Solution

 

 

Converting from Feet to Yards

 

Example 8

 

Jack’s driveway is 57 ft long. What is that distance in yards?

 

Solution

 

 

Jack’s driveway is 19 yd long.

 

For longer distances, miles are used. A mile is longer than a kilometre. As a matter of fact, the mile is about 1.6 km. So, approximately how many kilometres would there be in 5 mi?

 

In the United States, distances between cities are posted in miles, and speeds are posted in miles per hour (mph). A speed of 100 km/h is about 60 mph.

 

 

Converting from Miles to Yards

 

Example 9

 

First Nations peoples who lived on the Plains, like the Cree and the Blackfoot, were nomadic and often travelled tens of miles a day. How many yards are there in a mile?

 

Solution

 

 

A mile is 5280 ft, or 1760 yd.

 

The multimedia tool “Imperial System Length Conversion” can be used to convert one unit of length in the imperial system to another unit. Move the left slider according to the unit you are starting with and the right slider to the unit you are converting to.

 

Use “Imperial System Length Conversion” to help summarize the conversion equivalents used so far in this lesson. Fill in the following blanks:

 

 

Use this multimedia tool to answer Example 9, which you have already tried answering. You may also use the tool to confirm your answers for the following Self-Check questions.

 

Self-Check

 

Respond to the questions that follow.

 

SC 6.

 

 

SC 7. On golf courses, white tees are placed a little closer to the green than the blue tees. If you are playing from the white tees, the Mountain View Golf Course in Whitehorse, Yukon, is 6114 yd long. How many miles long is that length? Round your answer to the nearest tenth of a mile.

 

SC 8. Marcie is driving to her friend’s farm. Her friend’s father said their house was a quarter mile off the main road. How many yards off the main road does Marcie’s friend live?

 

SC 9. A quarter section of land is a square one-half mile on each side. How many feet of fencing would be needed to fence a quarter section?

 

SC 10. A Canadian Football League field is 110 yd from goal line to goal line. How many feet is 110 yd?

 

SC 11. Barbara is fencing a quarter mile of pasture on her farm. If Barbara decides to use three strands of barbed wire, how many feet of wire will she need altogether?

 

Compare your answers.

 

Because of trade and travel with the United States, which uses imperial measures for length and distance, more than tradespeople should be familiar with translating between systems—in fact, most Canadians should be able to translate between systems. Conversion is just a matter of using proportional reasoning—reasoning based on relations that can be represented by proportions.

 

Converting Between Imperial and Metric Units Using Proportions

 

Example 10

1. Convert 1 ft to centimetres.

2. Convert 1 ft to metres.

Solution

1. You know that 1 in = 2.54 cm, and 1 ft = 12 in.
   
   So, in 1 ft there will be 12 times as many centimetres as in 1 in.
   
   

    

    

   
   
   Of course, you could have used a proportion—two ratios equated to each other—to apply proportional reasoning more formally.
   
   Let the number of centimetres in a foot be n.
   
   Set up the proportion.
   
   

    

    

   
   
   

    

    

   
   
   So, 1 ft = 30.48 cm.

2. Since 1 m = 100 cm,
   
   

    

    

   
   
   So, 1 ft = 0.3048 m.

Look at two more examples.

 

Converting Kilometres to Miles

 

Example 11

 

How many kilometres are there in 1 mi? Round your answer to 4 decimal places.

 

Solution

 

You know that 1 mi = 5280 ft and 1 ft = 0.3048 m.

 

So,

 

 

The following shows an alternate solution using a proportion.

 

To change miles to metres, use a proportion.

 

Let the number of metres in a mile be n.

 

Set up the proportion.

 

 

But 1 km = 1000 m.

 

So,

 

 

Therefore, 1 mi is about 1.6093 km.

 

Converting Metres to Yards

 

Example 12

 

Convert 1 m to yards. Round your answer to 4 decimal places.

 

Solution

 

You know that 1 m = 100 cm, 2.54 cm = 1 in, and 36 in = 1 yd.

 

Each of these equations has a unit in common. Therefore, you can use these equations to make the conversion into yards in this order: metres to centimetres; centimetres to inches; and, finally, inches to yards.

 

So,

 

 

Self-Check

 

Respond to the following questions, and then check your answers.

 

SC 12. Complete a table like the following. Round your answers to 4 decimal places when necessary. Some of the entries have been done for you!

 

Metric	Imperial
1 mm	________ in
1 cm	________ in
1 m = 100 cm	1.0936 yd
1 km	________ mi

 

SC 13. Complete a table like the following. Round your answers to 4 decimal places when necessary. Some of the entries are done for you!

 

Imperial	Metric
1 in	________ cm
1 ft = 12 in	30.48 cm or 0.3048 m
1 yd = 3 ft = 36 in	________ m
1 mi = 5280 ft = 1760 yd	1.6093 km

 

Check your answers.

 

Next, you will use these tables to make conversions even simpler!

 

Converting Kilometres to Miles Using Tables

 

Example 13

 

The speed limit on the QE2 is 110 km/h. A friend has driven up from the United States. What would you tell him the speed limit is in miles per hour? Round your answer to the nearest mile per hour.

 

Solution

 

You must convert 110 km to miles.

 

From the tables, .

 

So,

 

 

A highway speed of 110 km/h is approximately 71 mph.

 

Example 14

 

Mei Lei’s house is on a lot 55 ft wide. What is the lot width in metres?

 

Solution

 

You must convert 55 ft to metres.

 

From the tables, 1 ft = 0.3048 m.

 

So,

 

 

Mei Lei’s lot is 16.764 m wide.

 

Your turn!

 

Self-Check

 

Respond to the following questions. Then check your answers.

 

SC 14. A television screen measures 21 in on the diagonal. How many centimetres is the screen’s diagonal?

 

SC 15. Jack is 6 ft 2 in tall. What is his height to the nearest centimetre?

 

SC 16. The distance from Michael’s house to the Red Pheasant First Nation is 12.3 km. How far is this distance in miles? Round your answer to 1 decimal place.

 

Compare your answers.

 

Try This

 

TT 11.

 

Use an SI (metric)–imperial conversion tool of your choice to do SC 14–SC 16 a second time.

 

Mastering Concepts

 

Try this question.

A carpenter wants to drill a hole through the centre of a board in wide. How far from each side should he drill?

 

Compare your answer.

 

Mathematics 10-3 Learn EveryWare © 2010 Alberta Education