1. Ratios
&
Proportions
Chapter 3
McGraw-Hill Ryerson©

2. Learning Objectives also… Set up and solve proportions
Ratios
Proportions 3
Learning Objectives
After completing this chapter, you will be able to:
LO 1.
Set up and manipulate ratios
LO 2. & 3.
Set up and solve proportions
Use proportions to allocate or prorate an amount on a proportionate basis
also…

3. Use quoted exchange rates to convert between currencies
Learning Objectives
LO 4.
Use quoted exchange rates to convert between currencies
Relate currency exchange rate movement to currency appreciation or depreciation
LO 5.

4. Expressing a Ratio in Equivalent Forms
Ratios
Proportions 3
LO 1.
Mcgraw-Hill Ryerson©

5. Expressing a Ratio in Equivalent Forms Q
LO 1. Q
Colleen, Heather and Mark’s partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respectively.
What is the ratio of Colleen’s to Heather’s to Marks’s partnership interest?

6. Expressed In colon notation format
Expressing
a Ratio in
Equivalent Forms
Colleen, Heather and Mark’s partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respectively.
Colleen
Heather
Mark
Expressed In colon notation format
7800 :
5200 :
6500
Equivalent ratio (each term divided by 100) : : 78 52 65
Equivalent ratio with lowest terms
Divide 52 into each one
: :

7. Expressing a Ratio in Equivalent Forms Q
The ratio of the sales of Product X to the sales of Product Y is 4:3. The sales of product X in the next month are forecast to be $1800.
What will be the sales of product Y if the sales of the two products maintain the same ratio?

8. Divide both sides of the equation by 4
Expressing
a Ratio in
Equivalent Forms
The ratio of the sales of Product X to the sales of Product Y is 4:3. The sales of product X in the next month are forecast to be $1800.
Since X : Y = 4 : 3,
then $1800 : Y = 4 : 3
$1800 4 =
Cross - multiply Y 3
Divide both sides of the equation by 4
4Y = 1800 * 3
Y = 1800 * 3
= $1350 4

9. Expressing a Ratio in Equivalent Forms Q
A 560 bed hospital operates with registered nurses and other support staff The hospital is about to open a new 86-bed wing.
Assuming comparable staffing levels, how many more nurses and support staff will need to be hired?

10. S Expressing a Ratio in Equivalent Forms
A 560 bed hospital operates with registered nurses and 185 other support staff The hospital is about to open a new 86-bed wing.
560 : 232 : 185 = 86 : RN : SS S
R N
560 86
560 86
Hire or RN’s =
Hire or SS =
185
232 RN SS
560RN = 232*86
560SS = 185*86
560RN = 19952
560SS = 15910
RN = / 560
SS = / 560

11. Expressing a Ratio in Equivalent Forms Q
LO 2. & 3. Q
A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2:1.
If you are looking to make litres of punch for a party, how much of each ingredient is needed?

12. * 3 * 2 * 1 Expressing a Ratio in Equivalent Forms 3+2+1 = 6
A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2:1.
F J
G A V
Total Shares
3+2+1 = 6
333 ml per share
2 litres / = 333 ml per share
* 3
* 2
* 1
= 1 litre
= 667 mls
= 333 mls

13. If you have 1.14 litres of vodka, how much punch can you make?
Expressing
a Ratio in
Equivalent Forms Q
A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2:1.
If you have 1.14 litres of vodka, how much punch can you make?
3+2+1 = 6
Total Shares 1
1.14 =
Cross - multiply 6
Punch
Punch = 6 * 1.14 litres
= 6.84 litres

14. Expressing a Ratio in Equivalent Forms Q
You check the liquor cabinet and determine that someone has been drinking the vodka You have less than half a bottle, about 500 ml.
How much fruit juice and ginger ale do you use if you want to make more punch using the following new punch recipe? Fruit juice: ginger ale: vodka = 3 : 2 : 1.5

15. Expressing a Ratio in Equivalent Forms
How much fruit juice and ginger ale do you use if you want to make more punch using the following new punch recipe?: Fruit juice: ginger ale: vodka = 3 : 2 : 1.5
500 ml
F J
G A 3
F J 2
G A = =
Cross - multiply
Cross - multiply
1.5
0.5
1.5
0.5
Fruit Juice = 3 * 0.5 /1.5
Ginger Ale = 2 * 0.5 /1.5
= 1 litre
= .667 litre = 667 ml.

16. Percent
Change %

17. Percent % Change Q If $1000 grows to $2500, find the percent change
Initial Value
Final Value %
(/100)
Difference or Change $
1000
100 1
2500
250
2.5
1500
150
1.5
If $1000…………= 100% or 1
What does $2500 = ? =
100% x
2500
Cross - multiply
1000
X = 2500*100% / 1000 = %
…Also

18. This method is referred to as
Percent
Change % Q
If $1000 grows to $2500, find the percent change
We can use the following alternative method to calculate the percent change!
Review
Chapter 1
Initial(Base)Value
Final Value
Difference
$ 1000
This method is referred to as
the Base Method
2500
$ 1500
$1500
% change =
$1000
% change = Difference
Base
= or 150% increase

19. Percent
Change % Q
If 15kg. of fruit shrinks to 3 kg. in the drying process, find the percent change.
Initial Value
Final Value %
(/100)
Difference or Change
Kg. 15
100 1 3 20 .2 12 80 .8
If 15kg.…………= 100% or 1
What does 3kg. = ? =
100% x 15 3
Cross - multiply
X = 3*100% / 15 = 20%

20. Converting Percent Differences to Proportions
Change %
Converting Percent Differences to Proportions
Two companies, Markham Tire and Unionville Tire, normally offer the same tire prices. Markham Tire has now marked-down the price of its Bridgestone Blizzard tires by 20%.
What percentage more will you pay if you buy your new tires from Unionville Tire?
Be Aware

21. Percent % Change Example A: Example B: Example C: AND... Be Aware = =
…when interpreting certain comparisons!
“A is 40% of B”
Example A: A B = 40
100
Means
… A = 40 when B = 100 and
“A is 40% greater than B” or
“A is 140% of B”
Example B:
Mean
… A = = 140 when B = 100
and A B =
140
100
“A is 40% less than B” or
“A is 60% of B”
Example C:
… A = when B = 100 and A B = 60
100
Means
AND...

22. Percent Change % Limits
Be Aware
If A and B both represent positive quantities, it is NOT POSSIBLE that “A is 140% Less than B”
Limits
The limit is “A is 100% less than B”
…which makes A = 0
Back to the tire question

23. Percent Change % = = = 1.25 or 125% …both MT & UT = 100%
Two companies, Markham Tire and Unionville Tire, normally offer the same tire prices. Markham Tire has now marked-down the price of its Bridgestone Blizzard tires by 20%.
What percentage more will you pay if you buy your new tires from Unionville Tire?
MT = 100 – 20 = 80 MT UT = 80
100
To find the ‘price size’ of UT compared with MT, we invert the proportion… UT MT =
100 80
= 1.25 or 125%
UT charges 125% of MT’s price(25% more than MT)

24. C
urrency
Europe
North
& South
America
Asia
Africa
Australia E
xchange

25. C urrency E xchange Points
LO 4.
As we just saw, every area in the world uses some form of currency
The currency of one country may not be
able to be converted into that of another on a one-for-one basis.
…some are recognized as having more value than others.
Points
In order to place each currency on an ‘equivalent basis’, it is necessary to ‘exchange currency’ at the prevailing rate in the marketplace.

26. Some major ‘marketplaces’ for prevailing currency rates
Frankfurt

28. Table 3.1 Foreign Exchange Rates (noon, Toronto, April 11, 2001)

29. Table 3.2 Currency Cross rates (noon, Toronto, April 11, 2001)
US$
Euro DM F S
Canadian $ = C Y

30. y C urrency E xchange Q = ¥39,910 ¥ y ¥ * C$500 C$ Y ¥79.82 =
Using the exchange rates given, calculate the number of yen that C$500 could purchase.
Canadian $ C$
If a C$.…………… =
What does C$ = ? Y =
¥79.82 y =
Cross - multiply
C$500
C$1 =
¥39,910
Purchase y
¥79.82
* C$500 =
C$1.00
Note

31. C urrency E xchange C C$ 1 Y … instead of this,
we could use the following exchange rate to find the number of Canadian$’s that each yen will buy!
Canadian $ C$
US$
Euro DM Y = C C$
1 Y
= =
Calculation

32. y C urrency E xchange Q = ¥39,910 ¥ y ¥ * C$500 ¥1 ¥1 Cross - multiply
Using the exchange rates given, calculate the number of yen that C$500 could purchase.
If C$ … =
What does C$ = ? ¥1 y
C$500 ¥1
Cross - multiply = C$ =
¥39,910
Purchase y C$ ¥1
* C$500 =

33. C urrency E xchange Q = C = = Y = C$100.22
Using the exchange rates given, calculate the number of Canadian$ that could buy. Y = Q
Canadian $ C$
US$
Euro DM Y = C C$
If a ……………… …. = C$
What does = ? C$
C$X
¥1.00 =
Cross - multiply
¥8000 =
Purchase
C$100.22 C$ =
* ¥8000
¥1.00

34. C urrency E xchange Q Step Step
How much will it cost in Canadian dollars to purchase US$500 of currency at a bank that charges % commission on the transaction? Assume C$ = US$1.00
Step
Calculate the cost of US$ in Can$
Step
Calculate the commission cost in Can$

35. C urrency E xchange Step * 1.5% = Step C$1.5628 C$ ? C$781.40 US$1.00
How much will it cost in Canadian dollars to purchase US$500 of currency at a bank that charges 1.5% commission on the transaction? Assume C$ = US$1.00
C$ cost to Purchase US$500
Step
C$1.5628
C$ ?
C$781.40
US$1.00 =
C$793.12
US$500
Commission
Step
* 1.5% =
C$781.40
C$11.72

36. (1 US gallon = 3.785 litres) Assume C$1.5628 = US$1.00
xchange C
urrency Q
Gasoline sold for C$0.659 per litre in Vancouver and US$1.39 per gallon in Seattle. How much cheaper (based on the Vancouver price) was gas in Seattle?
(1 US gallon = litres) Assume C$ = US$1.00
Step
Calculate the cost in Canadian$ for the equivalent of 1 gallon of gas.
Step
Convert US$1.39 to C$.
Step
How much cheaper is the gas in Seattle?

37. C urrency E xchange Step Step Step * US$1.39 = C$0.322 cheaper
Gasoline sold for C$0.659 per litre in Vancouver and US$1.39 per gallon in Seattle. How much cheaper (based on the Vancouver price) was gas in Seattle? (1 US gallon = litres) Assume C$ = US$1.00
Step
3.785 litres  C$0.659 per litre = C$2.494
Step
C$X
C$1.5628 =
Cross - multiply
US$1.39
US$1.00
C$1.5628
C$X =
* US$1.39
= C$2.172
US$1.00
Step C$
= C$0.322 cheaper
C$2.172

38. If C$ drops 0.5%, we can buy .995(DM 1.4104)
xchange C
urrency
LO 5. Q
If the C$ weakens by 0.5% relative to the DM, what will be the new values for DM per C$1.00 and C$ per DM1.00?
Canadian $ C$
C$1.00 = DM1.4104
If the Canadian dollar weakens, that means that we can buy fewer DM with each dollar!
If C$ drops 0.5%, we can buy .995(DM )
or DM
C$1.00 = DM
Values
New 1
= C$0.7125
DM1 = DM

39. This completes Chapter 3
Mcgraw-Hill Ryerson©