96 CHAPTER R Review of Basic Concepts Concepts Examples The union of sets A and B, written A´B, is made up of all the elements belonging to set A or to set B (or to both). A∪B = 5x∣ x{A or x{B or x{both A and B6 Sets of Numbers Natural numbers 51, 2, 3, 4, c6 Whole numbers 50, 1, 2, 3, 4, c6 Integers 5c , -3, -2, -1, 0, 1, 2, 3, c6 Rational numbers E p q P p and q are integers and q≠0F Irrational numbers 5x x is real but not rational6 Real numbers 5x x corresponds to a point on a number line6 Let A = 51, 2, 3, 46 and B = 53, 4, 66. A´B = 51, 2, 3, 4, 66 5, 17, 142 0, 27, 96 -24, 0, 19 - 3 4 , -0.28, 0, 7, 9 16 , 0.666 -215, 0.101101110c , 22, p -46, 0.7, p, 219, 8 5 7 7 -5 0 615 0 30 = 3 and 0 -30 = 3 Evaluate each expression. -4 # 7 - 24 , 1-32 = -28 - 24 , 1-32 = -28 - 1-82 = -28 + 8 = -20 32 , 41-22 - 32 -2 - 1-72 - 10 , 5 = 32 , 41-22 - 9 -2 - 1-72 - 10 , 5 = 81-22 - 9 - 2 - 1-72 - 2 = -16 - 9 -2 + 7 - 2 = -25 5 - 2 = - 25 3 R.3 Real Number Operations and Properties Order a 7b if a is to the right of b on a number line. a 6b if a is to the left of b on a number line. Absolute Value 0 a0 = e a −a if a #0 if a *0 Order of Operations If grouping symbols such as parentheses, square brackets, absolute value bars, or fraction bars are present, begin as follows. Step 1 Work separately above and below each fraction bar. Step 2 Use the rules below within each set of parentheses or square brackets. Start with the innermost set and work outward. If no grouping symbols are present, follow these steps. Step 1 Simplify all powers and roots. Work from left to right. Step 2 Do any multiplications or divisions in order. Work from left to right. Step 3 Do any negations, additions, or subtractions in order. Work from left to right.
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