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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4.5 Add and Subtract Fractions with Different Denominators

PreAlgebra 2e 4 Fractions 4.5 Add and Subtract Fractions with Different Denominators

Learning Objectives

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

  • Find the least common denominator (LCD)
  • Convert fractions to equivalent fractions with the LCD
  • Add and subtract fractions with different denominators
  • Identify and use fraction operations
  • Use the order of operations to simplify complex fractions
  • Evaluate variable expressions with fractions

In the previous section, we explained how to add and subtract fractions with a common denominator. But how can we add and subtract fractions with unlike denominators?

Let’s think about coins again. Can you add one quarter and one dime? You could say there are two coins, but that’s not very useful. To find the total value of one quarter plus one dime, you change them to the same kind of unit—cents. One quarter equals 25 cents and one dime equals 10 cents, so the sum is 35 cents. See Figure 4.7.

A quarter and a dime are shown. Below them, it reads 25 cents plus 10 cents. Below that, it reads 35 cents.

Figure 4.7 Together, a quarter and a dime are worth 35 cents, or 35100 of a dollar.

Identify and Use Fraction Operations

By now in this chapter, you have practiced multiplying, dividing, adding, and subtracting fractions. The following table summarizes these four fraction operations. Remember: You need a common denominator to add or subtract fractions, but not to multiply or divide fractions

Use the Order of Operations to Simplify Complex Fractions

In Multiply and Divide Mixed Numbers and Complex Fractions, we saw that a complex fraction is a fraction in which the numerator or denominator contains a fraction. We simplified complex fractions by rewriting them as division problems. For example,

Now we will look at complex fractions in which the numerator or denominator can be simplified. To follow the order of operations, we simplify the numerator and denominator separately first. Then we divide the numerator by the denominator.

Evaluate Variable Expressions with Fractions

We have evaluated expressions before, but now we can also evaluate expressions with fractions. Remember, to evaluate an expression, we substitute the value of the variable into the expression and then simplify.

Section 4.5 Exercises

Practice Makes Perfect

Find the Least Common Denominator (LCD)

In the following exercises, find the least common denominator (LCD) for each set of fractions.

Writing Exercises

434. 

Explain why it is necessary to have a common denominator to add or subtract fractions.435. 

Explain how to find the LCD of two fractions.

Self Check

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

.

ⓑ After looking at the checklist, do you think you are well prepared for the next section? Why or why not?

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