unit 1 ch 1 3 mathes
TRANSCRIPT
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Basic
Mathematics
Basic
Mathematics
Chap. 1, 2, 3Chap. 1, 2, 3
Basic
PowerPoint Presentation Prepared by
C Quinn, Seneca College.
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Basic
Mathematics
Basic
Mathematics
After completing this chapter, you will be able to:
Perform arithmetic operations in their proper order
Convert fractions to their percent and decimal equivalents
Maintain the proper number of digits in calculations
Solve for any one of percent rate, portion, or
base, given the other two quantities
also…
Learning ObjectivesLearning Objectives
LO 1. LO 1.
LO 2. LO 2.
LO 3. LO 3.
LO 4. LO 4.
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Basic
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Basic
Mathematics
rithmetic
perations
LO 1. LO 1.
Basic
Mathematics
Basic
Mathematics
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Basic
Mathematics
Basic
Mathematics Brackets
Exponents
Division
Multiplication
Addition
Subtraction
( )( )
22
4(2 - 5) or 4 x (2 - 5)
+ –
or 2 x 2
or /
or 4*(2 - 5)
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Basic
Mathematics
Basic
Mathematics How do we evaluate (solve) the following
problem?Known as an‘Expression’!
72 (3 x 22) – 6
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Basic
Mathematics
72 (3 x 22) - 6
= 0= 0
72 (3 x 2 x 2) - 6=72 12 - 6=72 12 - 6=
6 - 6=
72 (3 x 22) - 6
72 (3 x 22) - 6
BED M
A
S
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Basic
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Basic
Mathematics
Decimals to Percents
Percents to Decimals
Converting LO 2. LO 2.
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Mathematics
Basic
Mathematics
Decimal
.75
Move decimal point two places to Right
for %75%
5.0 500%
Move decimal point two places
to Left for
decimal
35%.35
2.5 250%
Converting
Decimal
1.745 174.50% .124 12.4%
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Basic
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Basic
Mathematics
Fractions to Percents
Percents to Fractions
Converting
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Basic
Mathematics
Basic
MathematicsConverting
10% 110
Fraction Top / Bottom
* 100
513 38.4615%
Percents
15% 15100
Percent /100Fraction
3841000
Percents
38.4%
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Basic
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Basic
Mathematics
Decimal Fractions
ConvertingDecimals to
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Basic
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…with appropriate number of zeros…and drop the decimal point
…with appropriate number of zeros…and drop the decimal point
Converting
Write Digits .24
Decimal
Decimals to Decimal Fractions
Step 1Step 1
Step 2Step 2 Divide by 1
Fractions
.241 0 0
241 0 0
.345 .34510 0 0
3451 0 0 0
.2 .21 0
21 0
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Basic
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Basic
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Decimals
LO 3. LO 3.
Basic
Mathematics
Basic
Mathematics
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Mathematics
Basic
Mathematics
513 .384615
DecimalFraction
38.4615%
Percent
Rounding
Decimals
1
2
3
.4
.38
.385
5 .38462
38.538.46
38.462
If next digit is 5 or more,
then raise current one to next highest digit.
If next digit is 5 or more,
then raise current one to next highest digit.Decimal
Places
Decimal Places
Example
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Basic
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Basic
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.
ExampleExample
Show the distribution in (a) fractions, (b) decimals, and (c)
as a percent.
Show the distribution in (a) fractions, (b) decimals, and (c)
as a percent.
Calculation
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No.No.ColourColour
Yellow
Red
Orange
Green
Brown
18
10
7
5
6
46
18
46
Fraction Decimal (hundredth)
Percent (hundredth)
.39 39.13%
.22 21.74%
.15 15.22%
.11 10.87%
.13 13.04%
1046 746 546
46 6
46/46 = 1 1.00 = 1 100 % = 1
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Basic
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LO 4. LO 4.
Basic
Mathematics
Basic
Mathematics
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Basic
Mathematics
This indicates the Portion that has to be found!
This indicates the Portion that has to be found!
…using the ‘Triangle’ will help us
remember the above
formula!
Portion = Rate * BaseFormula Formula
The formula to use in percent calculations is:
PR B
P = “…is ” or “…are ”
R = “%” indicates the Rate“%” indicates the Rate
B = “…of ” indicates the Base which is 100% or 1
“…of ” indicates the Base which is 100% or 1
Question is asking for… Question is asking for…
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Basic
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Where variables are BESIDE EACH OTHER this
means to MULTIPLY!
Where a variable is ABOVE ANOTHER this means to
DIVIDE!
PR B
Using this tool!Using this tool!
P/R=BP/R=B
P = R*BP = R*B
Portion = Rate * BaseFormula Formula
The formula to use in percent calculations is:
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Basic
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Portion = Rate * BaseFormula Formula
The formula to use in percent calculations is:
If you want to find P then R*B
If you want to find R
then P/R
then P/B
If you want to find B
PR B
Using this tool!Using this tool!
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Basic
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Basic
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PR B
Sales of McDonalds drive-thru customers are 60% of total sales. Total McDonald sales are $1,600,000.
What do you have to find?What do you have to find?
Portion = Rate * Base Formula Formula
P = 60% * $1600000 or
P = .60 * $1600000
P = $960,000
Solving for Portion
What are the drive-thru sales?
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PR B
What do you have to find?What do you have to find?
Rate = Portion /Base Formula Formula
R = $1,200,000/$1,600,000
Cash Sales of McDonalds customers amount to
$1,200,000. Total McDonald sales are $1,600,000.
R = 12/16 = .75 = 75%12/16 = .75 = 75%
Solving for Rate
What percent of customers pay cash?
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What do you have to find?What do you have to find?
60% of total sales are from drive-thru customers .
Sales of drive-thru customers are $960,000.
Solving for Base
What are McDonald’s total Sales?
PR B B = $960,000/
B = $1,600,000$1,600,000
Base = Portion /Rate Formula Formula
60%
$960,000 is 60% of what total sales? $960,000 is 60% of what total sales?
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Basic
Mathematics
Basic
Mathematics
You buy a new stereo in Ontario and pay a total of $649. This includes 6% GST and 8% PST .
Solving for Base
What do you have to find?What do you have to find?
$649 is 114% of the sticker price.
6% GST + 8% PST
Calculate
Find (a) the sticker price of the stereo before taxes, and (b) the amount of each tax.
The problem can be restated as:
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Basic
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Basic
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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.
Solving for Base
$6491.14
$649 is 114% (or 1.14) of the sticker price.Statement:
= $569.30(A)(A) (B)(B) $569.30 * 6% GST
$569.30 * 8% PST
= $45.54= $45.54
= $34.16= $34.16$34.16 GST$45.54 PST
$34.16 GST$45.54 PST
$569.30 +
= $649
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Basic
Mathematics
If McDonald’s sales increase from $1,600,000 to $2,400,000, what is the percent change?
% change = Difference Base
Base Method Base Method
$1,600,000
Initial(Base)Value $ 1,600,000Final Value 2,400,000
Difference $ 800,000
% change =$ 800,000
= .5 or 50% Increase
Solving for Rate of Percent Change
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Basic
Mathematics
Consumer Price Index – CPIConsumer 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”)
=CPI *100Price of CPI basket on the selected datePrice of CPI basket on the base date
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Basic
Mathematics
Basic
Mathematics Consumer Price Index – CPIConsumer 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?
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 Formula
=CPI *100Price of CPI basket on the selected datePrice of CPI basket on the base date
= 25 98023450 *100
= 110.79= 110.79…Also
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Basic
Mathematics
Basic
Mathematics Consumer Price Index – CPIConsumer 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?
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.
Amounts with the same purchasing power will be in the same ratio as the CPIs on the respective dates.
2004 $$2003 $$ = 2004 CPI
2003 CPI
2004 $$ $1000 = 124.8
122.5
$10002004 $$ = 124.8*122.5
= $1018.78$1018.78
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Basic
Mathematics
Basic
Mathematics The Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base year.
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?
=Percent inflation 2004 CPI - 2003 CPI2003 CPI *100%
124.8 - 122.5122.5 *100%=
= 1.88%= 1.88%
…Also
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Basic
Mathematics
Basic
Mathematics The Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base year.
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 2003 Salary
2004 CPI 2003 CPI
=
2004 Salary $50 000
124.8 122.5
=
2004 Salary * $50 000124.8 122.5
=
= $50938.77= $50938.77
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Basic
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Basic
Mathematics
Exponents Rule of
= 32*4
34 34
Base 3Exponent 4 3i.e. 3*3*3*3
Power = 81= 81
32 *33 32 *33
= 32 + 3
= 3 5
= 243= 243
(1 + i)20 (1 + i)20 (1 + i)8 (32)4(32)4
=(1+ i)20-8
= (1+ i)t= 3 8
= 6561= 6561
MoreMore
Algebra
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Exponents Rule of
X4
3x6y3 2
x2z3
Simplify inside the brackets first
Simplify inside the brackets first
= 3x4y3 2
z3
Square each termSquare each term
= 32x4*2y3* 2 Z3*2
SimplifySimplify
z69x8y6 =
3x6y3 2
x2z3
Algebra
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Use Calculator
Exponents Rule of
…to (a) evaluate (1.62)5
…to (b) evaluate (1.62)-5
1.6211.1611.16
1.62 5
0.0896 0.0896
5
Algebra
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Basic
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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.
SA Wage
= (20.50 +15.00 + 29.00) / 3= $64.50 / 3
= $21.50 = $21.50
= Wages per hour / # different wages
What is the Simple Average of the 3 hourly wages?
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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.
[Wage 1* #D + Wage 2*#C + Wage 3*#M]
[(20.50(46) +15.00(14) + 29.00(10)]
[$943 + 210 + 290] / 70
Calculate the Weighted Average hourly rate earned by the 3 categories of employees.
$1443.00 / 70
WA Wage = Total # of Employees
(46+14+10)WA Wage =
WA Wage =
WA Wage = = $20.61 = $20.61
= 70= 70