Skip to main content
Mathematics LibreTexts

2.S: Summary

  • Page ID
    23749
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Key Concepts Summary

    2.1: Order of Operations (Proceed in an Orderly Manner)

    • A review of key mathematical operator symbols
    • Rules for order of operations are known as BEDMAS

    2.2: Fractions, Decimals, and Rounding (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
    • Procedures for proper rounding
    • The rounding rules that are used throughout this textbook

    2.3: Percentages (How Does It All Relate?)

    • Converting decimal numbers to percentages
    • Working with percentages in the form of rates, portions, and bases

    2.4: 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?

    2.5: 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

    2.6: Natural Logarithms (How Can I Get That Variable Out of the Exponent?)

    • A review of the logarithm concept
    • The rules and properties of natural logarithms

    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.

    natural logarithm

    A logarithm with a base value of the mathematical constant \(e\).

    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.

    The Formulas You Need to Know

    Symbols Used

    \(\% \) = percentage

    \(\boldsymbol{dec}\) = any number in decimal format

    \(\ln \)= natural logarithm

    Rate = the relationship between the portion and base

    Portion = the part of the whole

    Base = the whole quantity

    Formulas Introduced

    Formula 2.1 Percentage Conversion: \(\% = \boldsymbol{dec} × 100\)

    Formula 2.2 Rate, Portion, Base: \(\text {Rate} =\dfrac{\text { Portion }}{\text { Base }}\)

    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

    \(x^2\) is used for exponents that are squares. \(2^2\) is keyed in as \(2 x^2\).

    \(y^x\) is used for exponents that are not squares. \(2^3\) is keyed in as \(2 y^x 3 =\).

    \(\pm \) is used to change the sign of a number. To use, key in the number first and then press the \(\pm \) key.

    Memory

    STO Store

    RCL Recall

    0–9 Memory cell numbers (10 in total)

    To store a number on the display, press STO # (where # is a memory cell number).

    To recall a number in the memory, press RCL # (where # is the memory cell where the number is stored).

    Natural Logarithms

    clipboard_e682731302b60e9ed40c173ce4bb6e785.png

    The natural logarithm function, LN, is located in the left-most column of your calculator. To use this function, input the power and then press the LN button. The solution displayed is the exponent. To calculate the power, input the exponent and then press 2nd ex (called the anti-log).

    Recognized Mathematical Symbols

    The common mathematical symbols that Excel recognizes are +, −, * (multiplication), / (division), ^ (exponents), and round brackets.

    Contributors and Attributions


    This page titled 2.S: Summary is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jean-Paul Olivier via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.