Intermediate Algebra

Chapter 1 Foundations
10 Topics
Introduction
1.1 Use the Language of Algebra
1.2 Integers
1.3 Fractions
1.4 Decimals
1.5 Properties of Real Numbers
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 2 Solving Linear Equations
12 Topics
Introduction
2.1 Use a General Strategy to Solve Linear Equations
2.2 Use a Problem Solving Strategy
2.3 Solve a Formula for a Specific Variable
2.4 Solve Mixture and Uniform Motion Applications
2.5 Solve Linear Inequalities
2.6 Solve Compound Inequalities
2.7 Solve Absolute Value Inequalities
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 3 Graphs and Functions
11 Topics
Introduction
3.1 Graph Linear Equations in Two Variables
3.2 Slope of a Line
3.3 Find the Equation of a Line
3.4 Graph Linear Inequalities in Two Variables
3.5 Relations and Functions
3.6 Graphs of Functions
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 4 Systems of Linear Equations
12 Topics
Introduction
4.1 Solve Systems of Linear Equations with Two Variables
4.2 Solve Applications with Systems of Equations
4.3 Solve Mixture Applications with Systems of Equations
4.4 Solve Systems of Equations with Three Variables
4.5 Solve Systems of Equations Using Matrices
4.6 Solve Systems of Equations Using Determinants
4.7 Graphing Systems of Linear Inequalities
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 5 Polynomials and Polynomial Functions
9 Topics
Introduction
5.1 Add and Subtract Polynomials
5.2 Properties of Exponents and Scientific Notation
5.3 Multiply Polynomials
5.4 Dividing Polynomials
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 6 Factoring
10 Topics
Introduction to Factoring
6.1 Greatest Common Factor and Factor by Grouping
6.2 Factor Trinomials
6.3 Factor Special Products
6.4 General Strategy for Factoring Polynomials
6.5 Polynomial Equations
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 7 Rational Expressions and Functions
11 Topics
Introduction
7.1 Multiply and Divide Rational Expressions
7.2 Add and Subtract Rational Expressions
7.3 Simplify Complex Rational Expressions
7.4 Solve Rational Equations
7.5 Solve Applications with Rational Equations
7.6 Solve Rational Inequalities
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 8 Roots and Radicals
13 Topics
Introduction
8.1 Simplify Expressions with Roots
8.2 Simplify Radical Expressions
8.3 Simplify Rational Exponents
8.4 Add, Subtract, and Multiply Radical Expressions
8.5 Divide Radical Expressions
8.6 Solve Radical Equations
8.7 Use Radicals in Functions
8.8 Use the Complex Number System
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 9 Quadratic Equations and Functions
13 Topics
Introduction
9.1 Solve Quadratic Equations Using the Square Root Property
9.2 Solve Quadratic Equations by Completing the Square
9.3 Solve Quadratic Equations Using the Quadratic Formula
9.4 Solve Equations in Quadratic Form
9.5 Solve Applications of Quadratic Equations
9.6 Graph Quadratic Functions Using Properties
9.7 Graph Quadratic Functions Using Transformations
9.8 Solve Quadratic Inequalities
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 10 Exponential and Logarithmic Functions
10 Topics
Introduction
10.1 Finding Composite and Inverse Functions
10.2 Evaluate and Graph Exponential Functions
10.3 Evaluate and Graph Logarithmic Functions
10.4 Use the Properties of Logarithms
10.5 Solve Exponential and Logarithmic Equations
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 11 Conics
10 Topics
Introduction
11.1 Distance and Midpoint Formulas; Circles
11.2 Parabolas
11.3 Ellipses
11.4 Hyperbolas
11.5 Solve Systems of Nonlinear Equations
Key Terms
Key Concepts
Review Exercises
Practice Test
Chapter 12 Sequences, Series and Binomial Theorem
9 Topics
Introduction
12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences and Series
12.4 Binomial Theorem
Key Terms
Key Concepts
Review Exercises
Practice Test
Answer key
12 Topics
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Index
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1.3 Fractions

Intermediate Algebra Chapter 1 Foundations 1.3 Fractions

Learning Objectives

By the end of this section, you will be able to:

  • Simplify fractions
  • Multiply and divide fractions
  • Add and subtract fractions
  • Use the order of operations to simplify fractions
  • Evaluate variable expressions with fractions

BE PREPARED 1.3
A more thorough introduction to the topics covered in this section can be found in the Elementary Algebra 2e chapter, Foundations.

Simplify Fractions

A fraction is a way to represent parts of a whole. The fraction 2/3 represents two of three equal parts. See Figure 1.5. In the fraction 2/3, the 2 is called the numerator and the 3 is called the denominator. The line is called the fraction bar.

Figure shows a circle divided in three equal parts. 2 of these are shaded.
Simplify Fractions
A fraction is a way to represent parts of a whole. The fraction 23
2
3 represents two of three equal parts. See Figure 1.5. In the fraction 2/3, the 2 is called the numerator and the 3 is called the denominator. The line is called the fraction bar.

FRACTION
A fraction is written ab,ab, where b≠0b≠0 and
a is the numerator and b 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.

Fractions that have the same value are equivalent fractions. The Equivalent Fractions

Property allows us to find equivalent fractions and also simplify fractions.

Example 1.29 Solution

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