Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Prealgebra 2e

Key Concepts

Prealgebra 2eKey Concepts
Search for key terms or text.

Key Concepts

6.1 Understand Percent

  • Convert a percent to a fraction.
    1. Step 1. Write the percent as a ratio with the denominator 100.
    2. Step 2. Simplify the fraction if possible.
  • Convert a percent to a decimal.
    1. Step 1. Write the percent as a ratio with the denominator 100.
    2. Step 2. Convert the fraction to a decimal by dividing the numerator by the denominator.
  • Convert a decimal to a percent.
    1. Step 1. Write the decimal as a fraction.
    2. Step 2. If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100.
    3. Step 3. Write this ratio as a percent.
  • Convert a fraction to a percent.
    1. Step 1. Convert the fraction to a decimal.
    2. Step 2. Convert the decimal to a percent.

6.2 Solve General Applications of Percent

  • Solve an application.
    1. Step 1. Identify what you are asked to find and choose a variable to represent it.
    2. Step 2. Write a sentence that gives the information to find it.
    3. Step 3. Translate the sentence into an equation.
    4. Step 4. Solve the equation using good algebra techniques.
    5. Step 5. Write a complete sentence that answers the question.
    6. Step 6. Check the answer in the problem and make sure it makes sense.
  • Find percent increase.
    1. Step 1. Find the amount of increase:
      increase=new amount−original amountincrease=new amount−original amount
    2. Step 2. Find the percent increase as a percent of the original amount.
  • Find percent decrease.
    1. Step 1. Find the amount of decrease.
       decrease=original amount−new amountdecrease=original amount−new amount
    2. Step 2. 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 pricesales tax=tax rate⋅purchase price
    • total cost=purchase price+sales taxtotal 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 pricecommission=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 priceamount of discount=discount rate⋅original price
    • sale price=original price –discountsale 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 priceamount of mark-up=mark-up rate wholesale price
    • list price=wholesale price+mark uplist price=wholesale price+mark up

6.4 Solve Simple Interest Applications

  • Simple interest
    • If an amount of money, PP, the principal, is invested for a period of tt years at an annual interest rate rr, the amount of interest, II, earned is I=PrtI=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 ab=cdab=cd, where b≠0b≠0, d≠0d≠0.The proportion states two ratios or rates are equal. The proportion is read “aa is to bb, as cc is to dd”.
  • Cross Products of a Proportion
    • For any proportion of the form ab=cdab=cd, where b≠0b≠0, its cross products are equal: a⋅d=b⋅ca⋅d=b⋅c.
  • Percent Proportion
    • The amount is to the base as the percent is to 100. amountbase=percent100amountbase=percent100
PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction
Citation information

© Feb 17, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.