4 cars could be pinstriped with one roll of vinyl, with
enough left over for 813
of another car.
e.g., 30 78 ÷ 1
2 = 30 7
8 x 2
= 60 +148
= 6168 , or 61
34
It will take 61 34 min.
1150002C03.indd 71 4/15/10 2:31:48 PM
Brian is a gas fi tter. Gas pipe costs $7.69 per yard. How much will it cost to construct a pipe from the gas supply at the front of this house to the hose hookup for the barbecue in the backyard?
1 How many metres of pipe will Brian need for the job? m + m + m = m
Brian will need m of pipe.
2 How many yards of pipe will Brian need?
1 m =̇ 1.09 yd m × 1.09 yd/m =∙ yd
3 How much will the pipe cost? yd × $7.69/yd =∙
ExampleA welder cuts a piece of steel 1.92 m long into four equal pieces.What is the length of each piece in inches?
Solution1.92 m ÷ = m or cm
48 cm ÷ cm/in. =∙ in.
Each piece of steel is about in. long.
Solving Problems with Decimals3 . 2try theseCalculate. Estimate to make sure your answer is reasonable.i) 155.75 + 29.35 iii) 23.5 × 0.5
Practice A truck driver is driving from Winnipeg to Vancouver. The total 1. distance is about 1870 km. He drives 965.5 km on the fi rst day and 423.6 km on the second day. How far does he have left to drive on the third day?
David is sewing drapes for a client and needs 6.5 m of fabric. 2. One metre of fabric costs $2.99. How much does 6.5 m cost?
Kari is an automotive engineer. Her team designed 3. a tractor-trailer engine that can go 4.27 km on 1 L of fuel. About how many litres of fuel would the engine need for a 675 km trip?
A box of fl oor tiles costs $15.85. If the total bill 4. before tax is $190.20, how many boxes of tiles were purchased?
a)5. About how many miles are equal to 1600 km?
About how many kilometres are equal to 1600 miles?b)
Every year, monarch butterfl ies migrate about 3200 km from c) Canada to Mexico. About how many miles do they migrate?
e.g., 1600 1.61 =· 994, so 1600 km is about 994 mi.
e.g., $190.20 $15.85 = 12
12 boxes of tiles were purchased.
e.g., 1600 x 1.61 =· 2576, so 1600 mi is about 2576 km.
e.g., 1600 km is about 994 mi, and 3200 km is twice as far.
They migrate about 1988 miles.
1150002C03.indd 73 4/15/10 2:31:50 PM
An offi cial marathon is 26 miles. Every day, Karen runs along a path that is 6.2 km long. How many times would Karen have to run the full path length to run the marathon length?
1 What is the marathon length to the nearest tenth of a kilometre?
1 mi =∙ 1.61 km
26 mi × km/mi =∙ km, or about km
2 How many times would Karen have to run the full path length to run the marathon length?
km ÷ km =
Karen would have to run the path length about times.
Example 1Alex works at an airline counter using the guidelines on the sign when checking bags. Which bags are under the airline size limit?
Deciding Which System to Use3 . 3try theseComplete. Use the charts inside the back cover.i) 1 in. is about cm iii) 1 mi is about km
Change the 157 cm size limit to 61.8 in. and then just add
the inch measurements.
32˝
30˝ 20˝
14˝54˝ 137.16 cm
156.21 cm
160.66 cm
15 ˝12 61 ˝12
13 ˝14 63 ˝1
4
89.53
3514
e.g., 158 – 89.53 = 68.47 cm, or about 68.5 cm
e.g., I used centimetres because the airline size was given
in centimetres, not inches.
54 137.16
26 11 17 54
3514
1150002C03.indd 75 4/15/10 2:31:51 PM
A contractor is ordering conduit. 2. Abco charges $50 for 20 ft and Zedco charges $50 for 6.5 m of the same kind of conduit.
Which conduit is the better a) buy?
Did you compare the two lengths in metres or feet? Why?b)
Justine is a travel agent. She is helping a client plan a ski trip. 3. A Canadian ski resort has 108 cm of snow and an American resort has 60 in. of snow. Which resort has more snow?
A machinist cuts metal to very precise lengths. Why do you 4. think machinists usually use metric measurements instead of imperial ones?
When there’s more than one unit, choose the one that will make it easier to solve the problem.
e.g., 5 x 72 cm is close to 5 x 70 cm = 350 cm or 3.5 m
3.5 m is close to 3.6 m, so my answer makes sense.
e.g., 30 ft x 0.31 m/ft =· 9.3 m
2.8 m x 2 = 5.6 m 9.3 m – 5.6 m = 3.7 m
There will be 3.7 m of tubing left on the roll.
e.g., I changed feet to metres because I knew 30 x 0.31 m
equals about 9.3 m, which is easy to work with, but
2 x 2.8 x 3.27 ft/m would have more decimal places.
34
2189
38
e.g., 18 34 in. 3 = 6 1
4 in.
The distance from one centre to the next is 6 14 in.
628 +3
18
172 x 4
12 x 4 + 12 x 14
34
1150002C03.indd 77 4/15/10 2:31:52 PM
Grayson is a charity event planner. Each star on his map is the location or “pitch” of a performer at a street fair. How many kilometres would someone have to walk around the perimeter of the fair to see all the pitches and return to where they started?
1 What is the perimeter of the map?
P = 2 (length + width)
= 2( cm + cm)
= 2( cm)
= cm
2 How many metres does each centimetre on the map represent?
3 What is the outside perimeter of the street fair in metres?
cm × m/cm = m
4 How many kilometres would someone have to walk around the outside perimeter to see all the pitches?
1000 m = 1 km
m = km
Someone would have to walk km to see them all.
Solving Perimeter Problems3 . 4try theseExpress each measurement in the unit given.i) 2.5 m = cm iii) 6 yd = ft
Example 1Jamilla installs underground wire for invisible fences for pets. The wire is sold by the foot. How many feet of wire will she need for the perimeter of this lot?
SolutionHow long is the side of the lot with no length A. label?
What are the other measures equal to in feet?B. 1 yd = 3 ft
16 yd × 3 ft/yd = ft
20 yd × 3 ft/yd = ft
What is the perimeter of the lot in feet?C.
How many feet of wire will Jamilla need to outline the lot? D. Jamilla will need ft of wire.
Example 2Jeff designs jewellery. He has 61
2 in. of gold wire for a triangular
pendant. If he makes the base 134 in. and uses all the gold wire to
go around the pendant, how long will the other two sides be?
SolutionWhat is the combined length of the two equal sides?A.
Practice Alex is building a hexagonal deck with six equal sides. She 1. plans to put a railing around the entire deck. She thinks the perimeter is about 10 m. Is her estimate reasonable?
A real estate agent is helping a Winnipeg family buy a house 2. in Seattle. The family wonders if they can use a wallpaper border they bought for their old kitchen in the new kitchen. The floor plans of both kitchens are rectangular.
What is the perimeter of each kitchen in metres?a) Winnipeg kitchen:
5.0 m long and 2.7 m wide
P = 2 (length + width)
Seattle kitchen:
20 ft long and 10 ft wide
How much extra border will they need for the new kitchen?b)
A rectangular city pool is 40 ft wide. 3. Its perimeter is 230 ft.
e.g., The areas increase as the length and width get closer
to the same value.
1150002C03.indd 81 4/15/10 2:31:55 PM
Simon works for the city water department. He is ordering the liner for a new overfl ow tunnel at the pumping station. If the radius of the tunnel is 12 ft, what should the circumference of the tunnel liner be?
1 What is the diameter of the tunnel?
Diameter = radius × 2
= ft × 2
= ft
2 What is the circumference of the tunnel?
Circumference = π × diameter
= π × ft
=∙ ft
The circumference of the tunnel liner should be about ft.
Solving circumference Problems3 . 5i) Construct a circle using a compass.
What compass setting did you use?ii) Draw a line across the circle through the centre.
How long is the line? iii) How does the line length compare to the compass setting
you used to draw the circle? iv) Cut a string to match the centre line. About how many
string lengths fi t around the outside of the circle?
try theseYou will need• a compass• string• scissors
AW100-17-650271-8
Figure Number
Company
Technical
Pass 1st Pass
C03-F20-AW10.eps
Approved
Not Approved
12 ft
tunnel linerradius
a straight line from the centre of a circle to any point on the circumference
circumference
the perimeter of a circleCircumference = π × d, where d is the diameter(π is about 3.14)
diameter
a straight line through the centre of a circle that joins two points on the circumferenceDiameter = radius × 2
Example 1The stone centre of the Majorville Medicine Wheel hasa circumference of 28 m. The outer wheel has a circumference of 85 m. About how long are the spokes?
SolutionWhat equation can give you the diameter of A. the outer wheel if you know its circumference?
Circumference = π × diameter
Diameter = ÷
What is the diameter of the outer wheel?B. m ÷ =∙ m
What is the diameter of the stone centre?C. m ÷ =∙ m
About how long are the spokes?D. Length of 2 spokes + centre diameter = wheel diameter
Length of 2 spokes + m = m
Length of 2 spokes = m
Length of 1 spoke = m
Each spoke is about m long.
PracticeShane is building a curb around a circular fountain. The 1. diameter of the fountain is 3.8 m. What is its circumference?
Lila sells tires. A customer told her the circumference of the 2. wheel rim on his tires, but Lila needs the diameter to get the tire size. If the circumference is 47 in., what is the diameter?
AW100-17-650271-8
Figure Number
Company
Technical
Pass 2nd Pass
C03-F21-AW10.eps
Approved
Not Approved
W E
N
S
Pi Some calculators have a special key for π. If your calculator doesn’t have this key, you can use 3.14 as an estimate for π.
Nathan can cut 3 pieces 8 14 in. long from a 25 in. pipe.
e.g., 42.3 L x $1.09/L = $46.11
The gas costs $46.11.
e.g., 0.75 km +0.75 km = 1.5 km
e.g., 1 km =· 0.62 mi so 1.5 km =· 0.93 mi
1 mi = 1760 yd, so 7185 yd 1760 yd/mi = 4.08 mi
4.08 mi +0.93 mi = 5.01 mi Adam walked about 5 miles.
e.g., miles; I didn’t use yards because I would have had to
work with larger numbers in the solution. But I could have
changed 4.08 miles to kilometres and used those instead.
1238 +7
68 8
2316 – 2
1416
3 +324
354
24
For example:
1150002C03.indd 86 4/15/10 2:31:59 PM
The triangle highlighted in this bridge design 5. has equal sides. If the perimeter is 17.85 m, how long is each side?
Kiana is making a display for a trade show. 6. She plans to put a decorative border around the display board that is 60 in. tall and 52 in. wide. Borders come in packages of 35 feet. About how much border will be left over from one package?
A cylinder-shaped grain bin has a circular base with 7. a diameter of 44 ft.
