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Elementary Algebra

Key Terms

Elementary AlgebraKey Terms
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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Chapter Review
      1. Key Terms
      2. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope–Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solve Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Quadratic Trinomials with Leading Coefficient 1
    4. 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Chapter Review
      1. Key Terms
      2. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 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
  13. Index

Key Terms

absolute value
The absolute value of a number is its distance from 0 on the number line. The absolute value of a number nn is written as |n||n|.
additive identity
The additive identity is the number 0; adding 0 to any number does not change its value.
additive inverse
The opposite of a number is its additive inverse. A number and it additive inverse add to 0.
coefficient
The coefficient of a term is the constant that multiplies the variable in a term.
complex fraction
A complex fraction is a fraction in which the numerator or the denominator contains a fraction.
composite number
A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.
constant
A constant is a number whose value always stays the same.
counting numbers
The counting numbers are the numbers 1, 2, 3, …
decimal
A decimal is another way of writing a fraction whose denominator is a power of ten.
denominator
The denominator is the value on the bottom part of the fraction that indicates the number of equal parts into which the whole has been divided.
divisible by a number
If a number mm is a multiple of nn, then mm is divisible by nn. (If 6 is a multiple of 3, then 6 is divisible by 3.)
equality symbol
The symbol “==” is called the equal sign. We read a=ba=b as “aa is equal to bb.”
equation
An equation is two expressions connected by an equal sign.
equivalent decimals
Two decimals are equivalent if they convert to equivalent fractions.
equivalent fractions
Equivalent fractions are fractions that have the same value.
evaluate an expression
To evaluate an expression means to find the value of the expression when the variable is replaced by a given number.
expression
An expression is a number, a variable, or a combination of numbers and variables using operation symbols.
factors
If a·b=ma·b=m, then aandbaandb are factors of mm. Since 3 · 4 = 12, then 3 and 4 are factors of 12.
fraction
A fraction is written abab, where b≠0b≠0 aa is the numerator and bb is the denominator. A fraction represents parts of a whole. The denominator bb is the number of equal parts the whole has been divided into, and the numerator aa indicates how many parts are included.
integers
The whole numbers and their opposites are called the integers: ...−3, −2, −1, 0, 1, 2, 3...
irrational number
An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
least common denominator
The least common denominator (LCD) of two fractions is the Least common multiple (LCM) of their denominators.
least common multiple
The least common multiple of two numbers is the smallest number that is a multiple of both numbers.
like terms
Terms that are either constants or have the same variables raised to the same powers are called like terms.
multiple of a number
A number is a multiple of n if it is the product of a counting number and n.
multiplicative identity
The multiplicative identity is the number 1; multiplying 1 by any number does not change the value of the number.
multiplicative inverse
The reciprocal of a number is its multiplicative inverse. A number and its multiplicative inverse multiply to one.
number line
A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.
numerator
The numerator is the value on the top part of the fraction that indicates how many parts of the whole are included.
opposite
The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero: −a−a means the opposite of the number. The notation −a−a is read “the opposite of aa.”
origin
The origin is the point labeled 0 on a number line.
percent
A percent is a ratio whose denominator is 100.
prime factorization
The prime factorization of a number is the product of prime numbers that equals the number.
prime number
A prime number is a counting number greater than 1, whose only factors are 1 and itself.
radical sign
A radical sign is the symbol mm that denotes the positive square root.
rational number
A rational number is a number of the form pqpq, where p and q are integers and q≠0q≠0. A rational number can be written as the ratio of two integers. Its decimal form stops or repeats.
real number
A real number is a number that is either rational or irrational.
reciprocal
The reciprocal of abab is baba. A number and its reciprocal multiply to one: ab·ba=1ab·ba=1.
repeating decimal
A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.
simplified fraction
A fraction is considered simplified if there are no common factors in its numerator and denominator.
simplify an expression
To simplify an expression, do all operations in the expression.
square and square root
If n2=mn2=m, then mm is the square of nn and nn is a square root of mm.
term
A term is a constant or the product of a constant and one or more variables.
variable
A variable is a letter that represents a number whose value may change.
whole numbers
The whole numbers are the numbers 0, 1, 2, 3, ....
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