Chapter 3 Summary
Formula & Symbol Hub Summary
For this chapter you used the following:
Symbols Used
- [latex]\sum=[/latex] summation symbol, which means you add everything up
- [latex]\%C=[/latex] percent change
- [latex]\text{AV}=[/latex] assessed value of a property
- [latex]\text{Current Currency}=[/latex] currency you are converting from
- [latex]\text{Desired Currency}=[/latex] currency you are converting to
- [latex]\text{Exchange Rate}=[/latex] per-unit conversion rate for current currency
- [latex]\text{GE}=[/latex] gross earnings
- [latex]n=[/latex] a count of something, whether a total number of periods or a total quantity
- [latex]\text{Property Tax}=[/latex] property tax amount
- [latex]\text{PTR}=[/latex] property tax rate, usually set on a per [latex]\$100[/latex] (tax rate) or per [latex]\$1,000[/latex] (mill rate) basis
- [latex]\text{Remit}=[/latex] tax remittance
- [latex]RoC=[/latex] = rate of change per time period
- [latex]S=[/latex] selling price
- [latex]S_tax=[/latex] selling price including taxes
- [latex]\text{Tax Collected}=[/latex] total tax collected through sales
- [latex]\text{Tax Paid}=[/latex] total tax paid through purchases
- [latex]V_\textrm{f}=[/latex] the value that a quantity has become; the number that is being compared
- [latex]V_\textrm{i}=[/latex] the value that a quantity used to be; the number to compare to
- [latex]x=[/latex] any individual piece of data
Formulas Used
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Formula 3.1a – Percentage
[latex]\%=\text{dec}\times 100[/latex]
Used to convert a decimal number into a percentage.
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Formula 3.1b – Rate, Portion, Base
[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex]
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Formula 3.2a – Percent Change
[latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex]
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Formula 3.2b – Rate of Change Over Time
[latex]\begin{align*}RoC=\left(\left(\frac{V_\textrm{f}}{V_\textrm{i}}\right)^{\frac{1}{n}}\right)\times 100\end{align*}[/latex]
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Formula 3.3 – Salary & Hourly Gross Earnings
[latex]\small\text{GE}=\text{Regular Earnings}+\text{Overtime Earnings}+\text{Holiday Earnings}+\text{Stat Holidays Worked Earnings}[/latex]
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Formula 3.4a- Selling Price Including Tax
[latex]S_\textrm{tax}=S+\left(S\times\text{Rate}\right)[/latex]
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Formula 3.4b – GST/HST Remittance
[latex]\text{Remit}=\text{Tax Collected}-\text{Tax Paid}[/latex]
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Formula 3.5 – Property Taxes
[latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex]
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Formula 3.7 – Currency Exchange
[latex]\text{Desired Currency}=\text{Exchange Rate}\times\text{Current Currency}[/latex]
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Formula 4.3a – Selling Price of a Product (see Section 4.3)
[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex]
Key Concepts Summary
Section 3.1: Percentages (How Does It All Relate?)
- Converting decimal numbers to percentages
- Working with percentages in the form of rates, portions, and bases
Section 3.2: Percent Change (Are We Up or Down?)
- Measuring the percent change in a quantity from one value to another
- Measuring the constant rate of change over time in a quantity
Section 3.3 Payroll
- Calculating salary and hourly gross earnings
- Discussion of employment contract characteristics for salary and hourly earners
- Calculating commission gross earnings
- Calculating piecework gross earnings
Section 3.4: Sales Tax
- The three sales taxes, current rates, and how to calculate prices including taxes
- How businesses complete GST/HST remittances
Section 3.5: Property Taxes
- How municipalities levy mill rates and tax rates against real estate owners
Section 3.6: Ratios, Proportions, and Prorating (It Is Only Fair)
- The characteristics of a ratio
- How to simplify and reduce a ratio to its lowest terms
- How to simplify a ratio by reducing its smallest term to a value of one
- How to equate two ratios into the form of a proportion
- How to use proportions to prorate
Section 3.7: Exchange Rates and Currency Exchange
- Converting currencies through exchange rates
- The rise and decline of exchange rates: currency appreciation and depreciation
The Language of Business Mathematics
assessed value The portion of the market value of a property that is subject to municipal taxes.
average A single number that represents the middle of a data set.
buy rate The rate at which a foreign currency is bought; it will always be lower than the mid-rate in terms of money per unit of foreign currency.
commission An amount or a fee paid to an employee for performing or completing some form of transaction.
currency appreciation When one currency strengthens relative to another currency, resulting in an ability to purchase more of that other currency than it could previously.
currency depreciation When one currency weakens relative to another currency, resulting in an ability to purchase less of that other currency than it could previously.
graduated commission A form of compensation where an employee is offered increasing rates of commission for higher levels of performance.
gross earnings The amount of money earned before any deductions are removed from a paycheque.
GST The goods and services tax is a Canadian federal sales tax on most products purchased by businesses and consumers alike.
hidden term In prorating, this is the sum of all the other terms on the same side of the proportion and represents a total.
holiday earnings Earnings paid to an employee on a statutory holiday for which no work is performed.
hourly wage A variable compensation based on the time an employee has worked.
HST The harmonized sales tax is a tax that combines the GST and PST into a single tax.
market value A snapshot of the estimated selling price of a property at some specified point in time.
mid-rate An exchange rate that does not involve or provide for any charges for currency conversion.
mill rate A tax per $1,000 of assessed value to determine property taxes.
percent change An expression in percent form of how much any quantity changes from a starting period to an ending period.
piecework A form of compensation where an employee is paid on a per-unit basis.
property taxes Annual taxes paid by the owners of real estate to local levying authorities to pay for services such as roads, water, sewers, public schools, policing, fire departments, and other community services.
PST The provincial sales tax is a consumer sales tax administered by Canadian provinces and territories.
proportion A statement of equality between two ratios.
prorating The process of taking a total quantity and allocating or distributing it proportionally.
public holiday A provincially recognized day for which employees may or may not get a day of rest and may or may not receive pay depending on provincial employment standards.
overtime Work time in excess of an employee’s regular workday or regular workweek.
overtime or premium earnings Earnings determined by an employee’s overtime rate of pay and that occur when regular hours are exceeded.
rate of change over time A measure of the percent change in a variable per time period.
ratio A fixed relationship between two or more quantities, amounts, or sizes of a similar nature where all terms are nonzero.
regular earnings Earnings determined by an employee’s regular rate of pay.
salary A fixed compensation paid to a person on a regular basis for services rendered.
salary plus commission A form of compensation in which gross earnings combine a basic salary together with commissions on transactions.
sales tax A percent fee levied by a government on the supply of products.
sell rate The rate at which a foreign currency is sold. It is always higher than the mid-rate in terms of money per unit of foreign currency.
simple average An average where each piece of data shares the same level of importance and frequency but does not represent percent changes or numbers that are intended to be multiplied with each other.
statutory holiday A legislated day of rest with pay.
statutory holiday worked earnings Earnings paid to an employee on a statutory holiday at a premium rate for working on the statutory holiday.
straight commission A form of compensation where the employee’s entire earnings are based on dollar transactions and calculated strictly as a percentage of the total transactions.
terms of the ratio The numbers appearing in a ratio.
tax policy A municipality-based percentage of the market value of a property that is used to convert the market value into an assessed value.
tax rate A tax per $100 of assessed value to determine property taxes.
tax remittance The fulfillment of a tax obligation.
weighted average An average where not all pieces of data share the same level of importance or they do not occur with the same frequency; the data cannot represent percent changes or numbers that are intended to be multiplied with each other.
Technology
Calculator
Percent Change
[latex]\text{2nd}\;\Delta\%[/latex] (located above the [latex]5[/latex] key) to access and enter three of the following. Press [latex]\text{CPT}[/latex] on the unknown to compute. It is recommended to clear a previous question from memory by then pressing [latex]\text{2nd CLR Work}[/latex].
[latex]\text{OLD}=[/latex] The old or original quantity; the number to compare to
[latex]\text{NEW}=[/latex] The new or current quantity; the number wanting to be compared
[latex]\%\text{CH}=[/latex] The percent change; in percent format
[latex]\text{#PD}=[/latex] Number of consecutive periods for the change. By default, it is set to [latex]1[/latex]. However, if you want to increase a number by the same percentage (a constant rate of change) consecutively, enter the number of times the change occurs. For example, if increasing a number by [latex]10\%[/latex] three times in a row, set this variable to [latex]3[/latex].
Attribution
“Chapter 2, 3, 4 & 7 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.
