Copyright © 2008 Pearson Education Canada 1-1 Chapter 1 Review of Arithmetic Contemporary Business Mathematics with Canadian Applications Eighth Edition.

Copyright © 2008 Pearson Education Canada 1-1

Chapter 1

Review of Arithmetic

Contemporary Business Mathematics with

Canadian Applications Eighth Edition S. A. Hummelbrunner/K. Suzanne CoombsPowerPoint: D. Johnston


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)


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.


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


BEDMASA rule for basic order of operations

• B Brackets

• E Exponents

• D Division

• M Multiplication

• A Addition

• S Subtraction


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


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


Equivalent FractionsChange terms without changing value

3 = 3 x 2 = 6 8 8 x 2 16

Multiply numeratorand denominator bythe same number.


Equivalent Fractions in Lower Terms

25 = 25 25 = 1 75 75 25 3

Numerator and denominator are divisible by the same number


Convert Common Fraction to Decimal Form

• Divide the numerator by the denominator

• 12/5 = 2.4

• 1/8 = 0.125

• 1/6 = 0.1666666….


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


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.


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


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


Using the Calculator Function 1/x


Percent Means Hundredths

% means dividing by 100

17 % = 17/100

0.8% = .8/100 = 8/1000

1/8% = .125/100


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


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%


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%


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)


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


Weighted Average

• Use a weighting factor to indicate the number of items in a group or the relative importance of data items.

(continued)


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


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


Straight Commission

Monthly Sales $25,000

Monthly commissionrate

6%

Monthly commission $25,000 x .06 = $1500


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


Wages

• Compensation paid to hourly rated employees

• Gross Earnings = Gross Pay for regular workweek + Overtime Pay


Calculating Gross Pay

• Regular workweek - 40 hours

• Overtime hourly rate - 1.5 x regular hourly rate

• Example


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


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


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


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.


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


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


Summary

• Common business applications such as payroll, commissions, and taxes involve the use of basic arithmetical operations, fractions, percents, and decimals.

• Averages are useful in analyzing data.

Copyright © 2008 Pearson Education Canada 1-1 Chapter 1 Review of Arithmetic Contemporary Business Mathematics with Canadian Applications Eighth Edition.

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