6 Chapter 1 The Set of Real Numbers Section 1.1 Fractions 1. Basic Definitions The study of algebra involves many of the operations and procedures used in arithmetic. Therefore, we begin this text by reviewing the basic operations of addition, subtraction, multiplication, and division on fractions and mixed numbers. We begin with the numbers used for counting: the natural numbers: and the whole numbers: 1, 2, 3, 4, . . . Whole numbers are used to count the number of whole units in a quantity.A fraction is used to express part of a whole unit. If a child gains the child has gained two whole pounds plus a portion of a pound.To express the additional half pound mathematically, we may use the fraction, A Fraction and Its Parts Fractions are numbers of the form ab where a b and b does not equal zero. In the fraction the numerator is a, and the denominator is b. The denominator of a fraction indicates how many equal parts divide the whole. The numerator indicates how many parts are being represented.For instance, suppose Jack wants to plant carrots in of a rectangular garden. He can divide the garden into five equal parts and use two of the parts for carrots (Figure 1-1). 25 ab , ab , 12 . 212 lb, 0, 1, 2, 3, . . . 5 equal parts 2 parts Figure 1-1 2 5 The shaded region represents of the garden. Proper Fractions, Improper Fractions, and Mixed Numbers 1. If the numerator of a fraction is less than the denominator, the fraction is a proper fraction.A proper fraction represents a quantity that is less than a whole unit. 2. If the numerator of a fraction is greater than or equal to the denominator, then the fraction is an improper fraction. An improper fraction represents a quantity greater than or equal to a whole unit. 3. A mixed number is a whole number added to a proper fraction. Concepts 1. Basic Definitions 2. Prime Factorization 3. Simplifying Fractions to Lowest Terms 4. Multiplying Fractions 5. Dividing Fractions 6. Adding and Subtracting Fractions 7. Operations on Mixed Numbers
miller_beginning_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above