6.7.2: Key Concepts
- Page ID
- 118944
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Key Concepts
6.1 Understand Percent
- Convert a percent to a fraction.
- Step 1. Write the percent as a ratio with the denominator 100.
- Step 2. Simplify the fraction if possible.
- Convert a percent to a decimal.
- Step 1. Write the percent as a ratio with the denominator 100.
- Step 2. Convert the fraction to a decimal by dividing the numerator by the denominator.
- Convert a decimal to a percent.
- Step 1. Write the decimal as a fraction.
- Step 2. If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100.
- Step 3. Write this ratio as a percent.
- Convert a fraction to a percent.
- Step 1. Convert the fraction to a decimal.
- Step 2. Convert the decimal to a percent.
6.2 Solve General Applications of Percent
- Solve an application.
- Step 1. Identify what you are asked to find and choose a variable to represent it.
- Step 2. Write a sentence that gives the information to find it.
- Step 3. Translate the sentence into an equation.
- Step 4. Solve the equation using good algebra techniques.
- Step 5. Write a complete sentence that answers the question.
- Step 6. Check the answer in the problem and make sure it makes sense.
- Find percent increase.
- Step 1. Find the amount of increase:
- Step 2. Find the percent increase as a percent of the original amount.
- Step 1. Find the amount of increase:
- Find percent decrease.
- Step 1. Find the amount of decrease.
- Step 2. Find the percent decrease as a percent of the original amount.
- Step 1. Find the amount of decrease.
6.3 Solve Sales Tax, Commission, and Discount Applications
- Sales Tax The sales tax is a percent of the purchase price.
- Commission A commission is a percentage of total sales as determined by the rate of commission.
- Discount An amount of discount is a percent off the original price, determined by the discount rate.
- Mark-up The mark-up is the amount added to the wholesale price, determined by the mark-up rate.
6.4 Solve Simple Interest Applications
- Simple interest
- If an amount of money, , the principal, is invested for a period of years at an annual interest rate , the amount of interest, , earned is
- Interest earned according to this formula is called simple interest.
6.5 Solve Proportions and their Applications
- Proportion
- A proportion is an equation of the form , where , .The proportion states two ratios or rates are equal. The proportion is read “ is to , as is to ”.
- Cross Products of a Proportion
- For any proportion of the form , where , its cross products are equal: .
- Percent Proportion
- The amount is to the base as the percent is to 100.