Chapter 2 Summary
Formula & Symbol Hub Summary
For this chapter you used the following:
Symbols Used
- [latex]\sum[/latex] = Summation
- [latex]\%C[/latex] = Percent change
- [latex]\text{GAvg}[/latex] = Geometric average
- [latex]n[/latex] = Number of pieces of data
- [latex]\text{SAvg}[/latex] = Simple average
- [latex]w[/latex] = Weight factor for a piece of data
- [latex]\text{WAvg}[/latex] = Weighted average
- [latex]x[/latex] = A piece of data
Formulas Used
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Formula 2.4a – Simple Average
[latex]\begin{align*}\text{SAvg}=\frac{\sum x}{n}\end{align*}[/latex]
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Formula 2.4b – Weighted Average
[latex]\begin{align*}\text{WAvg}=\frac{\sum wx}{\sum w}\end{align*}[/latex]
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Formula 2.4c – Geometric Average
[latex]\begin{align*}\text{GAvg}=\left(\left[\left(1 +\%C_1\right)\times\left(1+\%C_2\right)\times\text{ . . . }\times\left(1+\%C_n\right)\right]^{\frac{1}{n}}-1\right)\times 100\end{align*}[/latex]
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Formula 3.1b – Rate (see Section 3.1)
[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex]
Key Concepts Summary
Section 2.1: Rounding of Whole Numbers and Decimals
- Procedures for proper rounding
- The rounding rules that are used throughout this textbook
Section 2.2: Fractions and Decimals (Just One Slice of Pie, Please)
- The language and types of fractions
- Working with equivalent fractions by either solving for an unknown or increasing/reducing the fraction
- Converting any fraction to a decimal format
Section 2.3: Order of Operations (Proceed in an Orderly Manner)
- A review of key mathematical operator symbols
- Rules for order of operations are known as BEDMAS
Section 2.4: Averages (What Is Typical?)
- The calculation of simple averages when everything is equal
- The calculation of weighted averages when not everything is equal
- The calculation of geometric averages when everything is multiplied together
Section 2.5: Algebraic Expressions (The Pieces of the Puzzle)
- Learning about the language of algebra
- The rules for manipulating exponents
- The rules of algebra for addition and subtraction
- The rules of algebra for multiplication
- The rules of algebra for division
- What is substitution and how it is performed?
Section 2.6: Linear Equations: Manipulating and Solving (Solving the Puzzle)
- A review of key concepts about equations
- The procedures required to solve one linear equation for one unknown variable
- The procedures required to solve two linear equations for two unknown variables
The Language of Business Mathematics
algebraic equation An equation that takes two algebraic expressions and makes them equal to each other.
algebraic expression Indicates the relationship between and mathematical operations that must be conducted on a series of numbers or variables.
base The entire amount or quantity of concern.
BEDMAS An order of operations acronym standing for Brackets, Exponents, Division, Multiplication, Addition, and Subtraction.
common logarithm A logarithm with a base value of 10.
complex fraction A fraction that has fractions within fractions, combining elements of compound, proper, and/or improper fractions together.
compound fraction A fraction that combines an integer with either a proper or improper fraction.
denominator Any term by which some other term is divided; commonly the number on the bottom of a fraction.
divisor line The line that separates the numerator and the denominator in a fraction.
equivalent fractions Two or more fractions of any type that have the same numerical value upon completion of the division.
exponent A mathematical shorthand notation that indicates how many times a quantity is multiplied by itself
factor Components of terms that are separated from by multiplication or division signs.
fraction A part of a whole.
improper fraction A fraction in which the numerator is larger than the denominator.
left side of the equation The part of an equation that is to the left of the equal sign.
like terms Terms that have the same literal coefficient.
linear equation An algebraic expression in which the variable has an exponent of 1; when plotted, it will form a straight line.
literal coefficient A factor that is a variable.
logarithm The exponent to which a base must be raised to produce a particular power.
monomial An algebraic expression with only one term.
nomial The number of terms that appear in an algebraic expression.
nonlinear equation An algebraic expression in which the variable has an exponent other than 1; when plotted, it will not form a straight line.
numerator Any term into which some other term is being divided; commonly the number on the top in a fraction.
numerical coefficient A factor that is numerical.
percentage A part of a whole expressed in hundredths.
polynomial An algebraic expression with two or more terms.
portion Represents part of a whole or base.
proper fraction A fraction in which the numerator is smaller than the denominator.
rate Expresses a relationship between a portion and a base.
right side of the equation The part of an equation that is to the right of the equal sign.
root The value of the unknown variable that will make a linear equation true.
substitution Replacing the literal coefficients of an algebraic expression with their numerical values.
term In any algebraic expression, the components that are separated by addition and subtraction.
triangle technique A memorization technique that displays simple multiplication formulae in the form of a triangle. Anything on the same line is multiplied, and items above or below each other are divided to arrive at various solutions.
Technology
Calculator Formatting Instructions
|
Buttons Pushed |
Calculator Display |
What It Means |
|
2nd Format |
DEC=2.00 |
You have opened the Format window to its first setting. DEC tells your calculator how to round the calculations. In business math, it is important to be accurate. Therefore, we will set the calculator to what is called a floating display, which means your calculator will carry all of the decimals and display as many as possible on the screen. |
|
9 Enter |
DEC=9. |
The floating decimal setting is now in place. Let us proceed. |
|
↓ |
DEG |
This setting has nothing to do with business math and is just left alone. If it does not read DEG, press 2nd Set to toggle it. |
|
↓ |
US 12-31-1990 |
Dates can be entered into the calculator. North Americans and Europeans use slightly different formats for dates. Your display is indicating North American format and is acceptable for our purposes. If it does not read US, press 2nd Set to toggle it. |
|
↓ |
US 1,000 |
In North America it is common to separate numbers into blocks of 3 using a comma. Europeans do it slightly differently. This setting is acceptable for our purposes. If your display does not read US, press 2nd Set to toggle it. |
|
↓ |
Chn |
There are two ways that calculators can solve equations. This is known as the Chain method, which means that your calculator will simply resolve equations as you punch it in without regard for the rules of BEDMAS. This is not acceptable and needs to be changed. |
|
2nd Set |
AOS |
AOS stands for Algebraic Operating System. This means that the calculator is now programmed to use BEDMAS in solving equations. |
|
2nd Quit |
0. |
Back to regular calculator usage. |
Exponents and Signs
[latex]x^2[/latex] is used for exponents that are squares. [latex]2^2[/latex] is keyed in as [latex]2\;x^2[/latex].
[latex]y^x[/latex] is used for exponents that are not squares. [latex]2^3[/latex] is keyed in as [latex]2\;y^x\;3\;=[/latex].
[latex]\pm[/latex] is used to change the sign of a number. To use, key in the number first and then press the [latex]\pm[/latex] key.
Memory
[latex]\text{STO}=[/latex] Store
[latex]\text{RCL}=[/latex] Recall
[latex]0\text{-}9=[/latex] Memory cell numbers ([latex]10[/latex] in total)
To store a number on the display, press [latex]\text{STO}[/latex] # (where # is a memory cell number).
To recall a number in the memory, press [latex]\text{RCL}[/latex] # (where # is the memory cell where the number is stored).
Attribution
“Chapter 2 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.
