6.S: Percents (Summary)
- Page ID
- 5031
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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 Terms
| commission | A percentage of total sales as determined by the rate of commission |
| discount | A percent off the original price, determined by the discount rate |
| mark-up | The amount added to the wholesale price, determined by the mark-up rate |
| percent | A ratio whose denominator is 100 |
| percent decrease | The percent the amount of decrease is of the original amount |
| percent increase | The percent the amount of increase is of the original amount |
| proportion | An equation of the form \(\dfrac{a}{b} = \dfrac{c}{d}\), where b ≠ 0, d ≠ 0.The proportion states two ratios or rates are equal. The proportion is read “ a is to b, as c is to d”. |
| sales tax | A percent of the purchase price |
| simple interest | If an amount of money, P, the principal, is invested for a period of t years at an annual interest rate r, the amount of interest, I, earned is I = Prt. Interest earned according to this formula is called simple interest. |
Key Concepts
6.1 - Understand Percent
- Convert a percent to a fraction.
- Write the percent as a ratio with the denominator 100.
- Simplify the fraction if possible.
- Convert a percent to a decimal.
- Write the percent as a ratio with the denominator 100.
- Convert the fraction to a decimal by dividing the numerator by the denominator.
- Convert a decimal to a percent.
- Write the decimal as a fraction.
- If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100.
- Write this ratio as a percent.
- Convert a fraction to a percent.
- Convert the fraction to a decimal.
- Convert the decimal to a percent.
6.2 - Solve General Applications of Percent
- Solve an application.
- Identify what you are asked to find and choose a variable to represent it.
- Write a sentence that gives the information to find it.
- Translate the sentence into an equation.
- Solve the equation using good algebra techniques.
- Write a complete sentence that answers the question.
- Check the answer in the problem and make sure it makes sense.
- Find percent increase.
- Find the amount of increase: increase = new amount − original amount
- Find the percent increase as a percent of the original amount.
- Find percent decrease.
- Find the amount of decrease. decrease = original amount − new amount
- Find the percent decrease as a percent of the original amount.
6.3 - Solve Sales Tax, Commission, and Discount Applications
- Sales Tax: The sales tax is a percent of the purchase price.
- sales tax = tax rate • purchase price
- total cost = purchase price + sales tax
- Commission: A commission is a percentage of total sales as determined by the rate of commission.
- commission = rate of commission • original price
- Discount: An amount of discount is a percent off the original price, determined by the discount rate.
- amount of discount = discount rate • original price
- sale price = original price – discount
- Mark-up: The mark-up is the amount added to the wholesale price, determined by the mark-up rate.
- amount of mark-up = mark-up rate wholesale price
- list price = wholesale price + mark up
6.4 - Solve Simple Interest Applications
- Simple interest
- If an amount of money, P, the principal, is invested for a period of t years at an annual interest rate r, the amount of interest, I, earned is I = Prt
- 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 \(\dfrac{a}{b} = \dfrac{c}{d}\), where b ≠ 0, d ≠ 0.The proportion states two ratios or rates are equal. The proportion is read “ a is to b, as c is to d”.
- Cross Products of a Proportion
- For any proportion of the form \(\dfrac{a}{b} = \dfrac{c}{d}\), where b ≠ 0, its cross products are equal: a • d = b • c.
- Percent Proportion
- The amount is to the base as the percent is to 100. \(\dfrac{amount}{base} = \dfrac{percent}{100}\)
Contributors and Attributions
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."