Contemporary Business Mathematics With Canadian Applications Ninth Edition S. A....

Copyright © 2012 Pearson Canada Inc. 1-1

Chapter 1

Review of Arithmetic

Contemporary Business Mathematics with Canadian Applications Ninth Edition S. A. Hummelbrunner/K. Suzanne CoombsPowerPoint: D. Johnston, Revised by P. Au


ObjectivesAfter completing chapter one, the student will

be able to:• Simplify arithmetic expressions using the

basic order of operations.• Determine equivalent fractions and convert

fractions to decimals.• Convert percents to common fractions and to

decimals, and change decimals and fractions to percents.

(continued)


Objectives(continued)

• Through problem solving, compute simple arithmetic and weighted averages.

• Determine gross earnings for employees remunerated by the payment of salaries, hourly wages, or commissions.

• Through problem solving, compute GST, HST, PST, sales taxes, and property taxes.

Basic Order of Operations

1. Perform all operations inside a bracket first (operations inside the bracket must be performed in the proper order)

2. Perform all exponents 3. Perform multiplication and division in the

order as they appear from the left to right.4. Perform addition and subtraction in order

as they appear from left to right.Copyright © 2012 Pearson Canada Inc. 1-4


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

Multiply numerator

and denominator by the same number.


Equivalent Fractions in Lower Terms

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


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


Using a Calculator to Evaluate a Complex Fraction

The 1 or x –1 function key can be used to x evaluate the following complex fraction:


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:


Weighted Average

• Use a weighting factor to indicate the number of items in a group or the relative importance of data items.– Multiply each item by the numbers involved or

by a weighting factor representing its importance.

(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

Payroll ApplicationsSalaries

• Compensation of employees by salary is usually on a monthly or a yearly basis.– Monthly salaried personnel get paid either monthly

or semi-monthly– Personnel on a yearly salary basis may get paid

monthly, semi-monthly, every two weeks, weekly, or according to special schedules such as those used by some boards of education to pay their teachers.

• If salary is paid weekly or every two weeks, the year is assumed to consist of exactly 52 weeks



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 are calculated by multiplying the number of hours worked by the hourly rate of pay plus any overtime pay

Gross Earnings = Gross Pay for regular workweek +

Overtime Pay


Calculating Gross Pay

• Regular workweek - 40 hours• Overtime is most often paid at time-and-a-half

the regular hourly rate for any hours exceeding an established number of regular hours per week or per day

Overtime hourly rate = 1.5 x regular hourly rate


Calculating Gross EarningsRegular 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

Application Taxes

• A tax is a fee charged on sales, services, property, or income by a government to pay for services provided by the government. As consumers, we encounter the;– provincial sales tax (PST),– goods and services tax (GST), – or the harmonized sales tax (HST).



Application Taxes

• The Goods and Services Tax (GST) is a federal tax charged on almost all goods and services.

• PST and GST are blended to form the Harmonized Sales Tax or HST in some provinces. For British Columbia and Ontario, the HST came into effect on July 1, 2010. British Columbia 12% HST– Newfoundland 13% HST– New Brunswick 13% HST– Nova Scotia 15% HST– Ontario 13% HST

• Purchase a VCR for $109.• The HST (On) = $109 x 13% = 109 x 0.13 = $14.17


Provincial Sales Tax

• Some Provinces such as Manitoba levy a PST (7%) and GST (5%)– Alberta does not levy a PST– Quebec levies a GST + QST

• Purchase a VCR for $109 in Manitoba• GST = $109 x .07 = $7.63• PST = $109 x .05 = $5.45• Total Sales Tax = GST + PST = $13.08.


Property Tax• Municipal tax charged on the assessed value of real

estate.• Based on the assessed value of real estate, both

residential and commercial. • Some education taxes are also calculated using this

method. The property tax is determined by applying a percent to the assessed value of the property.

• In some municipalities, the assessed value is divided by 1000, and then the percent is applied.

Calculating Property Tax



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.

Contemporary Business Mathematics With Canadian Applications Ninth Edition S. A....

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