Section 1.2 Fractions Review 15 1b. Write 120 as a product of any two of its factors. Rewrite 12 as 2 · 6 and 10 as 2 · 5. Circle the prime factors 2, 2, and 5. Rewrite 6 as 2 · 3. The prime factorization of 120 is 2 · 2 · 3 · 2 · 5 or 23 · 3 · 5. Student Check 1 Write the prime factorization of each number. a. 24 b. 128 Fractions In Section 1.1, we defined a rational number as a number that can be written as the quotient of two integers. A fraction is a quotient of two real numbers. ������������������������ A fraction is a number of the form a b , where a and b are real numbers with b ≠ 0. The number a is called the numerator and b is called the denominator. A fraction represents a division of a whole into parts. The denominator of a fraction represents the “total number of parts in the whole” while the numerator represents the “number of parts chosen.” For example, the fraction 3 4 represents 3 parts out of 4. We can visualize this as shown in Figure 1.1. It is important to note that a fraction may or may not be a rational number. For example, 3 4 This fraction is a rational number since it is a quotient of two integers. π 2 This fraction is not a rational number since π is not an integer. If the numerator of a fraction is less than the denominator, the fraction is called a proper fraction. Some examples are 1 2 and 4 15 . If the numerator is greater than the denominator, the fraction is called an improper fraction. Some examples are 5 17 and . An improper fraction can also be written as a mixed number. For instance, 3 2 5 3 = 1 2 3 and 17 2 = 8 1 2 �� ������������������������ ������������������ Write a fraction that represents each quantity. 2a. Prior to the 2010 gubernatorial elections, 23 Republicans, 1 Independent, and 26 Democrats held the office of governor in the United States. Write fractions that represent the portion of the U.S. governors who were Republican, Independent, and Democratic. Objective 2 ▶ Define and write fractions. �������������������� 120 12 10 2 6 2 5 2 3
hendricks_beginning_algebra_1e_ch1_3
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