98 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Further recall that for and is undefined. Therefore, and is undefined. Example: and is undefined. 2. Proper and Improper Fractions If the numerator is less than the denominator in a fraction, then the fraction is called a proper fraction. Furthermore, a proper fraction represents a number less than 1 whole unit. The following are proper fractions. 6 7 1 3 5 0 0 5 0 a 0 0 a 0 a 0, 0 a 0 a 0 An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. For example: and An improper fraction represents a quantity greater than 1 whole unit or equal to 1 whole unit. 7 7 4 3 numerator equal to denominator 7 7 4 3 numerator greater than denominator 1 unit 1 unit 1 unit Categorizing Fractions Example 4 Identify each fraction as proper or improper. 5 12 12 5 a. b. c. 12 12 Solution: a. Improper fraction (numerator is greater than denominator) 12 5 5 12 b. Proper fraction (numerator is less than denominator) 12 12 c. Improper fraction (numerator is equal to denominator) Concept Connections Division can be checked by multiplication. For example: means that 2 3 6. Use this fact to explain: 6. 7. is undefined. 6 0 0 3 0 Answers 6. 03 means 0 3 0 7. is undefined because there is no 60 0 number that when multiplied by 0 equals 6. 8. Improper 9. Proper 10. Improper 63 2 Skill Practice Identify each fraction as proper or improper. 8. 9. 10. 9 7 7 9 10 10 1 unit 1 unit
miller_basic_college_math_3e_ch1_3
To see the actual publication please follow the link above