Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Unit 1:
Department
Unit Pricing and Currency
Exchange.
Goals:
In the workplace and your daily life, you will need to make decisions
about what to buy and how to pay the best price for it. In this unit you
will use some familiar mathematical concepts such as:
Fractions
Percentages
Rate
Ratio
in some new contexts.
You will apply these mathematical ideas to
Learn how to determine the best buy for a purchase, considering
quality and quantity as well as the unit price
Investigate sales promotions and compare their effects
Calculate percentage increase/decrease
Convert Canadian dollars into a foreign currency and foreign
currencies into Canadian dollars.
Key Terms: You will be able to define and use the following terms:
S.Duffy

Buying rate

Rate

Exchange rate

Ratio

Markup

Selling price

Promotion

Unit price

Proportion

Unit rate
Page 1
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Unit 1.1
Department
Proportional Reasoning.
 In this outcome you will learn to apply your knowledge of ratios in
new areas.
 Ratio: is a comparison between two numbers with the
same units.
 Since the units are the same you can omit them during
your calculations, but remember to include them in
your solution.
 A ratio can be written in several different ways
1. Canucks win 3 out of 4 games
or 3:4 or 3 to 4
2. Two out of three teenagers saw The Phantom
Menace
or 2:3 or 2 to 3
 The quantities in a ratio are called the terms.
S.Duffy
Page 2
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
 When working with ratios simplify them first
Department
20:50 can be simplified to 2:5 by ÷ each term by 10
÷ 10
20 : 50
÷ 10
2:5
 The two ratios 20:50 and 2:5 are called equivalent
ratios.
 Proportion is a fractional statement of equality
between two ratios or rates.
 The fractional equation
=
is referred to as a
proportion
Example 1:
Steven’s soccer team played 16 games and won 12 of them. Express
the number of games won to the number of games played as a ratio in
its simplest form in three ways.
S.Duffy
Page 3
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 2:
Department
Sam is looking for posters to cover the walls of his room. He finds one
poster that is 50cm by 50cm. He finds another one that is 21cm by
67cm.
a) Find the area of each of the posters.
(Hint: A = lxw)
b) Compare the area of the first poster to the area of the second
poster by estimating your answer first.
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 3:
Mark wants to mix a new shade of paint. He needs 3 parts blue to 1
Department
part green.
a) How many parts are there altogether?
b) If mark mixes 10 portions of green paint how many portions of blue
will he need?
c) How many portions of green paint will mark use if he mixes in 12
portions of blue paint?
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 4:
Department
A faller at a logging station needs to refuel his chainsaw.
The ratio of gasoline to oil that is needed is 40 parts gasoline to 1 part
oil. The chainsaw’s fuel tank holds 8 litres of gasoline, how many litres
of oil should be added to obtain the correct ratio?
Example 5:
Brian a builder has found that he can arrange the work cubicles of his
employees best if the ratio between the length and the width of a
room is 3:2.
If a room is 6m long, how wide should the room be?
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Page 6
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
 Rate: is a comparison between two numbers with different
units.
Department
 Here are some examples of rates
o The number of words you can type per minute.
o The number of hamburgers a concession stand sells in
one day.
o The price of lumber per linear foot.
o The price of stone per kilogram.
 A rate can be expressed using the same notation as ratio.
 Since the units are different in each term they must be
used.
Example 6:
A salmon in the fishmongers is on sale at $1.89 for 100grams.
Write this rate in three different ways.
Example 7:
Terry wants to buy 250 grams of this salmon, how much will it cost
her?
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Page 7
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 8:
A local plumbing store sells 100 copper- plated pipe straps for $4.97.
Department
You have estimated that you need 75 straps, how much will they cost
you?
Complete notebook assignment
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page 21 # 1-8
Page 8
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Department
Puzzle it out !!!!
What is a Magic 3x3 Square? _____________________________________________________
_____________________________________________________
_____________________________________________________
Can you assemble the numbers 1 to 9 in the square using each number
only once, so that the sum of the rows, the columns, and the diagonals
adds up to 15.
1
2
3
4
5
6
7
8
9
5
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Page 9
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Department
Magic Proportions !
C
Can you assemble the numbers 0 to 8 in the square using each number
Conly once so that the columns add up in the ratio 1:2:3
0
1
2
3
4
5
6
7
8
22
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Page 10
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Unit 1.2
Department
Unit Price.
Ma
 In this outcome you will learn to compare the cost of items to
determine the best buy using the unit price.
 Unit Price: is the cost of one unit, or a rate expressed as a
fraction where the denominator is 1.
 Unit Rate: is the rate or cost for one item or unit.
 Comparing unit prices can save you money; however it’s not
the only factor to consider when buying in bulk. You may
prefer to consider quality over quantity.
Example 1:
Rosa buys supplies for her office in Langley where she works as a clerk.
She wants to buy pens. The supplier sells a box of 12 pens for $6.25.
Calculate the unit price of 1 pens.
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Page 11
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 2:
Department
Claire picks fresh strawberries at the farm.
If she fills a pint basket (0.5506 Litres) it will cost her $1.50.
If she fills a 4 Litre pail it will cost her $9.00.
Which size of container will give her a better buy?
Complete notebook assignment
S.Duffy
page 26-27 # 1-6
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Unit 1.3
Department
Setting a Price.
 In this outcome you will learn that the price at which goods and
services are sold depend on whether you are a consumer or
working in a business.
 Prices rise and fall due to consumer demand and supply:
 If demand rises suppliers are able to charge more.
 If demand falls or if there is a large supply of a product,
prices may fall.
 Prices also rise and fall according to the cost of materials
and labour that go into the creation of a product or service.
 Markup: is the difference between the amount a dealer sells
a product for and the amount he or she paid for it. It is
added to the cost so that a profit can be made.
 When a business owner buys items for resale he or she buys
them at a wholesale price. This price is then marked up and
the item sold at a higher retail price.
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Page 13
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
 This markup is usually a percent of the wholesale price.
Department
 Percent: means out of 100
 When setting prices for goods and services psychological
factors also have an impact on buyers.
 Why do retailers advertise items at $39.95 instead of
$40.00?______________________________________
____________________________________________
 Remember Taxes also need to be added to arrive at a final
price.
 All Canadians pay 5% Federal Goods and Service tax (GST)
 Most provinces also charge Provincial Sales Tax (PST) which
varies from province to province.
 The 5 highlighted provinces in the table below charge a
Harmonized Sales Tax (HST). This sales tax replaces GST
and PST.
 The northern territories do not charge a provincial tax.
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Department
Province
PST %
GST %
HST %
Alberta
0
5
5
British Columbia
7
5
12
Manitoba
7
5
New Brunswick
8
5
13
Newfoundland
and Labrador
8
5
13
Nova Scotia
10
5
15
Ontario
8
5
13
Prince Edward
Island
10.5
5
15.5
Quebec
7.5
5
12.5
Saskatchewan
5
5
10
Use this table to solve problems including taxes.
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Page 15
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 1:
Arlene purchases fabric at a wholesale price for her custom sewing
Department
business. She pays $46.00 / m. She charges a markup of 20% on the
fabric. What will Arlene charge her clients per metre?
Example 2:
A furniture store in in Saskatoon is selling a bedroom suite for
$1599.00. What will the total cost be including taxes?
Complete notebook assignment
S.Duffy
page 32-33 # 1-7
Page 16
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Department
Unit 1.4
On Sale.
 In this outcome you will learn about the different types of sales
promotions which offer better deals and ultimately attract
buyers.
 When you go shopping, you often see something is on sale for a
discounted price usually represented by percentages.
eg. 20% or 50% off.
o This may be because:
 The clothes could be out of season or out of fashion.
 The store could have ordered more than they could
sell.
 A Promotion: is an activity that increases awareness of a product
or attracts customers.
 Businesses may use other promotions to attract buyers:
o Coupons usually give you an amount off the retail price
usually used to promote a new product or line.
o In store card point systems allow customers to participate
in rewards programs and encourages them to remain loyal to
their store.
o BOGO promotions:
 Buy one get one free
 Buy two get one half price
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Page 17
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 1:
Jonas needs to buy a new winter jacket. He saw one he liked three
Department
weeks ago for $249.95. It is now in the sale and discounted by 20%.
How much will the jacket cost if Jonas lives in Nunavut where there is
no PST
Example 2:
A fisher sells fresh salmon, live crabs and prawns at the dock in
Steveston, BC on Saturdays and Sundays. As the weekend winds down
he needs to sell off his stock or it will spoil. He has a sale !
He offers 20% off all his regular prices.
Salmon is regularly $18.50/kg and prawns are $34.50/kg.
At a 20% discount what is the price of
a) 3kg of salmon?
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b) 500g of prawns?
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
 Percedntage Increase/Decrease is calculated using the following
Department
formulas.
o Percentage Increase =
x 100 %
o Percentage Decrease =
x 100 %
o Profit: an increase in value.
o Loss: a decrease in value.
Example 3:
Sarah bought a house in 2009 for $200,000. She was thinking of
selling in 2010 and her Real Estate Agent valued her property at
$250,000. If Sarah was to sell her house this year what would be her
percentage profit?
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Page 19
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 4:
Peter bought a car 3 years ago for $25,000. He sold it this year for
Department
$12,000. What was Peter’s percentage loss?
Complete notebook assignment
S.Duffy
page 37-38 # 1-6
Page 20
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Unit 1.5
Department
Currency Exchange
Rates.
 In this outcome you will become familiar with the different
currencies used in different countries around the world and
perform calculations to exchange money into different
currencies.
 Currency: is the system of money a country uses.
 Currency is exchanged in:
o Banks
o Currency exchange companies
o Travel agencies
 Not all currencies are available at every exchange and you may
have to order it in advance so you need to plan ahead.
 Since banks and currency agencies charge a fee called
commission usually around 1-3% it is best to shop around to get
the best deal.
 Exchange Rate : is the price of one country’s currency in terms
of another nation’s currency.
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Page 21
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
 The exchange rate between two countries like Canada and Japan
is used to calculate how many dollars you need to convert to yen.Department
 The exchange rate fluctuates from day to day and from one
currency exchange agency to another.
 The Exchanges set a selling rate and a buying rate for currency
and these rates are different from one another.
 Selling Rate: the rate at which a currency agency sells money to
its customers.
o If you plan to go to Italy and need to obtain euros from
your bank you will pay the selling rate as the bank is selling
the euros to you.
 Buying Rate: the rate at which a currency agency buys money
from customers.
o If you have euros left over when you return to Canada
you will receive the buying rate to change them back into
Canadian dollars as the bank is buying them from you.
 When travelling in a foreign country it is often helpful to
estimate what something costs in your own currency to help you
compare prices.
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Page 22
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Use the table of exchange rates on page 45 to answer the following
questions.
Department
Example 1:
Maria is planning a trip to Denmark. The unit of Danish currency is the
krone. The plural of krone is kroner.
She has $500.00 CAD spending money. How many kroner will she
receive?
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Example 2:
Department
After purchasing her Kroner Maria finds out she is unable to travel due
to an unforeseen accident. She needs to sell her kroner back to the
bank.
a) How many $CAD will she receive?
b) How much money will she lose?
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Complete notebook assignment
page 47-48 # 1-6
Complete Unit 1 Review
page 50-51 # 1-10
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Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
Department
Reflect on your learning
Now that you have completed this unit check  the box that applies
to you
RED
AMBER
GREEN
I understand all the key terms.
I can apply ratios and rates
in new contexts.
I can calculate unit price.
I can determine the best buy.
I can calculate sales discounts
and promotions using %.
I can calculate % increase
and % decrease.
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Page 25
Mathematics
Apprenticeship and workplace Math 10
St.John Brebeuf
I can exchange both foreign
Department
currency into $ and $ into
foreign currency.
I have completed all
homework assignments.
I have completed my
Project “Party Planner”
I have attended lunchtime
tutorials for extra help.
I am ready to sit my
unit 1 test.
Target:
In my Unit Test I hope to achieve
Student’s Signature ____________________
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%
Date__________
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