CHAPTER 5 Summary 289 Important Facts and Concepts Examples and Discussion Section 5.1 Fundamental Theorem of Arithmetic Every composite number can be expressed as a unique product of prime numbers. Examples 2–3, pages 276–217 Sections 5.1–5.5 Sets of Numbers Natural or counting numbers: { }… 1, 2, 3, 4, Whole numbers: … {0, 1, 2, 3, 4, } Integers: { } … − − − … , 3, 2, 1, 0, 1, 2, 3, Rational numbers: Numbers of the form pq/ , where p and q are integers, ≠ q 0. Every rational number when expressed as a decimal number will be either a terminating or repeating decimal number. Irrational number: A real number that cannot be written as the ratio of two integers (not a rational number) Real numbers: The union of the rational numbers and the irrational numbers Discussion pages 213, 224, 235, 250, and 259 Section 5.2 Order of Operations 1. First, perform all operations within parentheses or other grouping symbols. 2. Next, evaluate all exponents. 3. Next, perform all multiplications and divisions from left to right. 4. Finally, perform all additions and subtractions from left to right. Discussion pages 231–232, Examples 11–12, page 232 Section 5.3 Fundamental Law of Rational Numbers a b a b c c ac bc b c 0, 0 = ⋅ = ≠ ≠ Discussion page 243, Examples 14–16, pages 243–245 Section 5.4 Rules of Radicals Product rule for radicals: ⋅ = ⋅ ≥ ≥ a b a b a b , 0, 0 Quotient rule for radicals: = ≥ > a b a b a b , 0, 0 Discussion pages 251 and 253, Examples 1–6, pages 252–254 Section 5.5 Properties of Real Numbers Commutative property of addition: + = + a b b a Commutative property of multiplication: ⋅ = ⋅ a b b a Associative property of addition: + + = + + a b c a b c ( ) ( ) Associative property of multiplication: ⋅ ⋅ = ⋅ ⋅ a b c a b c ( ) ( ) Distributive property: ⋅ + = + a b c ab ac ( ) Discussion pages 259–263, Examples 1– 4, pages 260–262 Summary CHAPTER 5
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