Proper Fractions: Improper Fractions: Mixed Numbers: 1 8 8 8 238 3 5 7 5 115 2. Prime Factorization To perform operations on fractions it is important to understand the concept of a factor. For example, when the numbers 2 and 6 are multiplied, the result (called the product) is 12. 2 6 12 factors product The numbers 2 and 6 are said to be factors of 12. (In this context, we refer only to natural number factors.) The number 12 is said to be factored when it is written as the product of two or more natural numbers. For example, 12 can be factored in several ways: 12 1 12 12 2 6 12 3 4 12 2 2 3 A natural number greater than 1 that has only two factors, 1 and itself, is called a prime number.The first several prime numbers are 2, 3, 5, 7, 11, and 13. A natural number greater than 1 that is not prime is called a composite number. That is, a composite number has factors other than itself and 1. The first several composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, and 16. Writing a Natural Number as a Product of Prime Factors Example 1 Write each number as a product of prime factors. a. 12 b. 30 Solution: a. Divide 12 by prime numbers Or use a factor tree until the result is also a prime number. 12 2 6 2 3 2212 226 3 12 2 2 3 30 2 3 5 2230 b. 30 2 15 3 5 3215 5 Skill Practice Write the number as a product of prime factors. 1. 40 2. 72 Section 1.1 Fractions 7 Avoiding Mistakes The number 1 is neither prime nor composite. Answers 1. 2 2 2 5 2. 2 2 2 3 3
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