96 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Section 2.1 Introduction to Fractions and Mixed Numbers 1. Definition of a Fraction In Chapter 1, we studied operations on whole numbers. In this chapter, we work with numbers that represent part of a whole. When a whole unit is divided into equal parts, we call the parts fractions of a whole. For example, the pizza in Figure 2-1 is divided into 5 equal parts. One-fifth of the pizza has been eaten, and fourfifths 12 of 45 the pizza remains. 115 2 1 has been eaten 5 4 remains 5 Figure 2-1 A fraction is written in the form , where a and b are whole numbers and In the fraction , the “top” number, 5, is called the numerator. The “bottom” number, 8, is called the denominator. numerator denominator 5 8 58 b 0. ab Identifying the Numerator and Denominator of a Fraction Example 1 For each fraction, identify the numerator and denominator. 1 8 3 5 a. b. c. 8 1 Solution: a. The numerator is 3.The denominator is 5. 3 5 1 8 b. The numerator is 1.The denominator is 8. 8 1 c. The numerator is 8.The denominator is 1. The denominator of a fraction denotes the number of equal pieces into which a whole unit is divided.The numerator denotes the number of pieces being considered. Concepts 1. Definition of a Fraction 2. Proper and Improper Fractions 3. Mixed Numbers 4. Fractions and the Number Line Skill Practice Identify the numerator and denominator. 1. 2. 3. 6 1 0 5 4 11 Avoiding Mistakes The fraction can also be written as a⁄b. However, we discourage the use of the “slanted” fraction bar. In later applications of algebra, the slanted fraction bar can cause confusion. ab Answers 1. Numerator: 4, denominator: 11 2. Numerator: 0, denominator: 5 3. Numerator: 6, denominator: 1
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