1. Basic
Mathematics
Basic
Chap. 1, 2, 3
PowerPoint Presentation
Prepared by
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
C Quinn, Seneca College.

2. Basic
Learning Objectives
Mathematics
After completing this chapter, you will be able to:
LO 1.
LO 2.
Perform arithmetic operations in their proper order
Convert fractions to their percent and decimal
equivalents
LO 3.
Maintain the proper number of digits in calculations
LO 4.
Solve for any one of percent rate, portion, or
base, given the other two quantities
also…
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3. Basic
Mathematics
LO 1.
rithmetic
perations
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4. Basic
Mathematics
( )
Brackets
Exponents
22
or 2 x 2
Division
or /
Multiplication 4(2 - 5) or 4 x (2 - 5)
or 4*(2 - 5)
Addition
+
Subtraction
–
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5. Basic
Mathematics
How do we evaluate (solve) the following
problem?
72
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(3 x 22) – 6

6. Basic
Mathematics
72
B
E
D
M
A
S
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(3 x 22) - 6
72
=
=
=
=
(3 x 22) - 6
72
(3 x 2 x 2) - 6
72
12
72
12
6
=
0
6
-6
-6

7. Basic
Mathematics
LO 2.
Converting
Decimals to Percents
Percents to Decimals
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8. Basic
Converting
Mathematics
Decimal
.75
Move decimal
point two places
to Right
for %
75%
Decimal
Move decimal
point two places
to Left for
decimal
.35
35%
5.0
500%
2.5
250%
1.745
174.50%
.124
12.4%
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9. Basic
Mathematics
Converting
Fractions to Percents
Percents to Fractions
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10. Basic
Converting
Mathematics
Fraction
Percents
Top / Bottom
* 100
1
10
5
13
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10%
38.4615%
Percents
Fraction
15
100
384
1000
Percent /100
15%
38.4%

11. Basic
Mathematics
Converting
Decimals to
Decimal Fractions
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12. Basic
Converting
Mathematics
Decimals to Decimal Fractions
Fractions
Decimal
Step
Write Digits
1
Step
Divide by 1
2
…with
appropriate
number of zeros
…and drop the
decimal point
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.24
.24
24
100
.345
.2
100
.345
345
10 0 0
1000
.2
2
10
10

13. Basic
Mathematics
LO 3.
Decimals
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14. Basic
Decimals
Mathematics
Decimal
Percent
.384615
Fraction
5
13
38.4615%
Rounding
1
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2
.38
3
.385
5
Decimal
Places
.4
If next digit is
5 or more,
then raise
current one to 38.5
next highest
38.46
digit.
.38462
38.462
Example

15. Basic
Example
Mathematics
A bag contains 46 M & M’s of various colours.
The 46 candies are distributed as follows:
18 Yellow 10 Red 7 Orange 5 Green 6 Brown.
Show the distribution in
(a) fractions, (b) decimals, and (c) as a percent.
Calculation
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16. Basic
Mathematics
Colour
No.
Yellow
18
Red
10
Orange
Green
Brown
7
5
6
46
Fraction
18
46
10
46
7
46
5
46
6
46
46/46 = 1
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Decimal
Percent
(hundredth) (hundredth)
.39
39.13%
.22
21.74%
.15
15.22%
.11
10.87%
.13
13.04%
1.00 = 1
100 % = 1

17. Basic
Mathematics
LO 4.
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18. Basic
Mathematics
The formula to use in percent calculations is:
Formula
…using the
„Triangle‟
will help us
remember the above
formula!
P
R B
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Portion = Rate * Base
Question is asking for…
P=
“…is ” or “…are ”
This indicates the Portion
that has to be found!
R=
B =
“%” indicates the Rate
“…of ” indicates the Base
which is 100% or 1

19. Basic
Mathematics
The formula to use in percent calculations is:
Formula
Portion = Rate * Base
Using this tool!
P
R B
P = R*B
P/R=B
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Where variables are
BESIDE EACH OTHER this
means to MULTIPLY!
Where a variable is ABOVE
ANOTHER this means to
DIVIDE!

20. Basic
Mathematics
The formula to use in percent calculations is:
Formula
Portion = Rate * Base
Using this tool! If you want to find P
P
R B
R
If you want to find B
If you want to find
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then
R*B
then
P/B
then
P/R

21. Basic
Mathematics
Solving for Portion
Sales of McDonalds drive-thru customers are 60% of
total sales. Total McDonald sales are $1,600,000.
What are the drive-thru sales?
What do you have to find?
P
Formula Portion = Rate * Base
R B
P = 60% * $1600000 or
P =
P =
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.60 * $1600000
$960,000

22. Basic
Mathematics
Solving for Rate
Cash Sales of McDonalds customers amount to
$1,200,000. Total McDonald sales are $1,600,000.
What percent of customers pay cash?
What do you have to find?
P
Formula Rate = Portion /Base
R B
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R = $1,200,000/$1,600,000
R = 12/16 = .75 = 75%

23. Basic
Mathematics
Solving for Base
60% of total sales are from drive-thru customers .
Sales of drive-thru customers are $960,000.
What are McDonald‟s total Sales?
$960,000 is 60% of what total sales?
What do you have to find?
P
Formula
R B
B = $960,000/ 60%
B =
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Base = Portion /Rate
$1,600,000

24. Basic
Mathematics
Solving for Base
You buy a new stereo in Ontario and pay a total of
$649. This includes 6% GST and 8% PST .
Find (a) the sticker price of the stereo before taxes,
and (b) the amount of each tax.
What do you have to find?
The problem can be restated as: $649 is 114% of the sticker price.
6% GST + 8% PST
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Calculate

25. Basic
Mathematics
Solving for Base
You buy a new stereo in Ontario and pay a total of
$649. This includes 6% GST and 8% PST. Find (a) the
sticker price of the stereo before taxes, and (b) the
amount of each tax.
Statement:
(A)
$649
1.14
$649 is 114% (or 1.14) of the sticker price.
=
$569.30
(B) $569.30 * 6% GST
= $34.16
$569.30
= $649
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+
$34.16 GST
$45.54 PST
$569.30 * 8% PST
= $45.54

26. Basic
Mathematics
Solving for Rate of Percent Change
If McDonald’s sales increase from $1,600,000 to
$2,400,000, what is the percent change?
$ 1,600,000
2,400,000
Difference
Base Method
Initial(Base)Value
Final Value
$ 800,000
% change = Difference % change =$ 800,000
$1,600,000
Base
= .5 or 50% Increase
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27. Basic
Mathematics
Consumer Price Index – CPI
Used to compare prices of goods and services
purchased by a typical Canadian family.
Statistics Canada tracks the prices of about
600 consumer goods and services
(the CPI “basket”)
Price of CPI basket on the selected date *100
CPI = Price of CPI basket on the base date
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28. Basic
Mathematics
Consumer Price Index – CPI
The price of goods and services included in the
Consumer Price Index cost $23 450 on the base date.
Six years later, the same basket cost $25 980. What
was the CPI on the latter date?
Formula
Price of CPI basket on the selected date *100
CPI = Price of CPI basket on the base date
= 25 980
23450 *100
= 110.79
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…Also

29. Basic
Mathematics
Consumer Price Index – CPI
The Consumer Price Index was
122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base year.
What amount in Aug. 2004 had the same
purchasing power as $1000 in Aug. 2003?
Amounts with the
same purchasing
power will be in
the same ratio as
the CPIs on the
respective dates.
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
2004 $$
2003 $$
=
2004 CPI
2003 CPI
2004 $$
$1000
=
124.8
122.5
2004 $$
124.8*$1000
= 122.5
= $1018.78

30. Basic
Mathematics
The Consumer Price Index was
122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base year.
What was the overall percent inflation from
Aug.2003 to Aug.2004?
=
2004 CPI - 2003 CPI 100%
*
2003 CPI
=
Percent inflation
124.8 - 122.5 100%
122.5 *
= 1.88%
…Also
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31. Basic
Mathematics
The Consumer Price Index was
122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base year.
If you earned $50 000 in 2003, how much would you
have to earn in 2004 to keep up with inflation?
2004 Salary = 2004 CPI
2003 Salary
2003 CPI
2004 Salary = 124.8
$50 000
122.5
2004 Salary = 124.8 * $50 000
122.5
= $50938.77
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32. Basic
Algebra
Mathematics
Exponents
Rule of
34
Base
32 *33
3
= 32 + 3
5
=3
Exponent
3
4
i.e. 3*3*3*3
Power = 81
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= 243
(1 + i)20
(1 + i)8
=(1+
= (1+
(32)4
i)20-8
= 32*4
t
= 38
i)
= 6561
More

33. Basic
Algebra
Mathematics
Exponents
Rule of
3x6y3
x 2 z3
Square each term
Simplify inside
the brackets first
X4
3x6y3 2 3x4y3
2 z3 =
x
z3
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2
2
=
2x4*2y3* 2
3
3*2
Z
Simplify
=
8y6
9x
z
6

34. Basic
Algebra
Mathematics
Exponents
Rule of
…to (a) evaluate (1.62)5
Use
Calculator
1.62
5
11.16
…to (b) evaluate (1.62)-5
1.62
5
0.0896
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35. Basic
Mathematics
Ontario Transport has 46 drivers each earning
$20.50 per hour, 14 clerical staff members each
earning $15.00 per hour, and 10 mechanics each
earning $29.00 per hour.
What is the Simple Average of the 3 hourly wages?
SA Wage = Wages per hour / # different wages
= (20.50 +15.00 + 29.00) / 3
= $64.50 / 3
= $21.50
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36. Basic
Mathematics
Ontario Transport has 46 drivers each earning
$20.50 per hour, 14 clerical staff members each
earning $15.00 per hour, and 10 mechanics each
earning $29.00 per hour.
Calculate the Weighted Average hourly rate earned
by the 3 categories of employees.
WA Wage = [Wage 1* #D + Wage 2*#C + Wage 3*#M]
Total # of Employees
[(20.50(46) +15.00(14) + 29.00(10)]
WA Wage =
(46+14+10)
= 70
WA Wage = [$943 + 210 + 290] / 70
WA Wage = $1443.00 / 70
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= $20.61