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Chapter 1
Review of Arithmetic
Contemporary Business Mathematics with
Canadian Applications Eighth Edition S. A. Hummelbrunner/K. Suzanne CoombsPowerPoint: D. Johnston
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ObjectivesAfter completing chapter one, the student will
be able to:• Use order of operations.
• Determine equivalent fractions.
• Convert fractions to decimals.
• Convert percents to common fractions and decimals.
•
(continued)
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Objectives(continued)
• Change decimals and fractions to percents.
• Compute arithmetic and weighted averages.
• Calculate gross earnings.
• Solve problems involving GST, sales taxes, and property taxes.
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Basic Order of Operations
First Operations within bracket done first in proper order
Second Exponentiation
Third Multiplication and Division from left to right
Fourth Addition and Subtraction
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BEDMASA rule for basic order of operations
• B Brackets
• E Exponents
• D Division
• M Multiplication
• A Addition
• S Subtraction
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Examples Using BEDMAS
8 – 3 x 2 = 2 Multiplication done first
20 5 + 3 x 4 = 16 Division and Multiplication done before addition
(14 + 4) 2 – 5 = 4 Operations in brackets done first followed by division and then subtraction
144 32 = 16 Exponentiation done first followed by division
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Common Fractions
Terms are 4 and 5
4 5
Numerator Denominator
Proper fraction
3 7
Numerator less than Denominator
Improper fraction
7 3
Numerator greater than Denominator
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Equivalent FractionsChange terms without changing value
3 = 3 x 2 = 6 8 8 x 2 16
Multiply numeratorand denominator bythe same number.
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Equivalent Fractions in Lower Terms
25 = 25 25 = 1 75 75 25 3
Numerator and denominator are divisible by the same number
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Convert Common Fraction to Decimal Form
• Divide the numerator by the denominator
• 12/5 = 2.4
• 1/8 = 0.125
• 1/6 = 0.1666666….
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Convert a Mixed Number to Decimal Form
• A mixed number consists of a whole number and fraction
• 5 1/8 = 5.125
• 4 2/3 = 4.66666666…
• 8 3/4 = 8.75
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RoundingIf the first digit in the group of digits to be dropped is 5 or greater, the last digit retained is increased by 1.
6.885 rounded to two places after the decimal point is 6.89
If the first digit in the group of digits to be dropped is less than 5, the last digit retained is not changed.
6.8543 rounded to two decimal places is 6.85.
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Complex FractionsFractions may appear in the numerator or
denominator or both.
Fraction Solution
400(1 + .06 x 90/365) 400(1.01479454) = 405.92
950 1 + .05 x 292 365
950 / 1.04 = 913.46
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Using a Calculator to Evaluate a Complex Fraction
The 1 or x –1 function key can be used to xevaluate the following complex fraction:
1755
1 - 0.21 x 210 365
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Percent Means Hundredths
% means dividing by 100
17 % = 17/100
0.8% = .8/100 = 8/1000
1/8% = .125/100
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Changing Percents to Decimals
Drop percent symbol and move decimal pointtwo places to the left.
55 % = 0.55
215 % = 2.15
0.75% = .0075
3/8 % = .375% = .00375
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Changing Decimals to Percents
Move the decimal point two places to the rightand add the % symbol.
0.00525 = .525%
0.38 = 38%
2.55 = 255%
1 3/8 = 1.375 = 137.5%
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Changing Fractions to Percents
First convert the fraction to a decimal. Then convert the decimal to a percent. 7/8 = .875 = 87.5%
1/3 = .333333 = 33.3333%
4/7 = 0.5714 = 5.71%
1 ¼ = 1.25 = 125%
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Arithmetic Averages
1) Add the values in a set of numbers to find the sum of the data values.
2) Divide the sum of the data values by the number of values in the set. (continued)
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Arithmetic Averages(continued)
A student obtains the following scores on five mid-term exams: 78%, 80%, 50%, 65%, 72%
The average score on the five equally weighted mid-terms is: 0.78 + 0.80 + 0.50 + 0.65 + 0.72 = 0.69=69% 5
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Weighted Average
• Use a weighting factor to indicate the number of items in a group or the relative importance of data items.
(continued)
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Weighted Average Grade A=4, B= 3, C=2, D=1
Credit
Courses Grade Hours
Accounting B 3 Mathematics C 4 English A 3 Elective A 2 Total = 12 Weighted Average
(3x3+2x4+4x3+4x2) 12
= 3.08
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Commissions
• Straight - Percent on net sales for a given time period
• Graduated - Increase in percent paid for higher sales levels for a given time period
• Salary Plus Commission - Guarantees minimum income for a given time period
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Straight Commission
Monthly Sales $25,000
Monthly commissionrate
6%
Monthly commission $25,000 x .06 = $1500
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Graduated CommissionRate $50,000 monthly sales
5% First $10,000 6% Next $10,000 9% Above $20,000
.05 x 10,000 500
.06 x 10,000 600
.09 x (50,000-20,000) 2700 Commission 500+600+2700 =
3800
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Wages
• Compensation paid to hourly rated employees
• Gross Earnings = Gross Pay for regular workweek + Overtime Pay
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Calculating Gross Pay
• Regular workweek - 40 hours
• Overtime hourly rate - 1.5 x regular hourly rate
• Example
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Calculating Gross Earnings
Regular Workweek 40 hours
Regular hourly rate $16.50 / hour
Overtime rate 1.5 x regular rate/hour
Total Weekly Hours 52 hours worked
Regular Pay 40 x $16.50 = 660
Overtime Pay (52-40) x $16.50 x 1.5
Gross Earnings $660 + 297 = $957
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Overtime Premium
The overtime premium on the excess iscalculated separately.
52 X $16.50 = 858
12 x 0.5 x $16.50 = 99 (Excess)
Gross Pay = $858 + 99 = $957
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Goods and Services Tax
• The Goods and Services Tax (GST) is a federal tax charged on almost all goods and services.
• Purchase a VCR for $109.
• The GST = $109 x 7% = 109 x .07 = $7.63
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Provincial Sales Tax
• Provinces levy a sales tax as well (PST).
• Ontario has an 8% sales tax.
• Purchase a VCR for $109 in Ontario .
• GST = $109 x .06 = $6.54
• PST = $109 x .08 = $8.72
• Total Sales Tax = GST + PST = $15.26.
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Property Tax• Municipal tax charged on the assessed
value of real estate.
• Based on a mill rate.
• Mill rate is the amount of tax levied per $1000 of assessed value of property.
• Property tax = Mill rate x .001 x Assessed Value of Property
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Calculating Property Tax
Tax Levy Mill RateGeneral 2.50Garbage collection 1.10Schools 11.50Capital Development 1.05
Assessed Value $110,000 Property Tax16.15 mills x .001 x $110,000 = $1776.50