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Prealgebra 2e

Key Concepts

Prealgebra 2eKey Concepts
Table of contents
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

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
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