PreAlgebra 2e

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

PreAlgebra 2e 4 Fractions 4.7 Solve Equations with Fractions

Learning Objectives

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

  • Determine whether a fraction is a solution of an equation
  • Solve equations with fractions using the Addition, Subtraction, and Division Properties of Equality
  • Solve equations using the Multiplication Property of Equality
  • Translate sentences to equations and solve

Determine Whether a Fraction is a Solution of an Equation

As we saw in Solve Equations with the Subtraction and Addition Properties of Equality and Solve Equations Using Integers; The Division Property of Equality, a solution of an equation is a value that makes a true statement when substituted for the variable in the equation. In those sections, we found whole number and integer solutions to equations. Now that we have worked with fractions, we are ready to find fraction solutions to equations.

The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number, an integer, or a fraction.

Solve Equations with Fractions using the Addition, Subtraction, and Division Properties of Equality

In Solve Equations with the Subtraction and Addition Properties of Equality and Solve Equations Using Integers; The Division Property of Equality, we solved equations using the Addition, Subtraction, and Division Properties of Equality. We will use these same properties to solve equations with fractions.

Solve Equations with Fractions Using the Multiplication Property of Equality

Consider the equation equation x 4=3. We want to know what number divided by 4 gives 3. So to “undo” the division, we will need to multiply by 4. The Multiplication Property of Equality will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.

Section 4.7 Exercises

Practice Makes Perfect

Determine Whether a Fraction is a Solution of an Equation

In the following exercises, determine whether each number is a solution of the given equation.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

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ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

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