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9.3 The Rational Numbers Rational numbers – A. Inverses (Opposites) Recall: Additive Inverse—is the opposite of a number. Example 1. 3 1. 4 B. Find the additive inverse of each of the following. 2. − 5 .1 −9 3. Absolute Value Recall: Absolute Value—is the distance form 0 to a number on the number line. Example 2. −1 1. 8 Find the absolute value of each of the following. 1 −3 2. 3. − 8 .2 4 C. Addition and Subtraction of Rational Numbers: Example 3. Find each value. 1. 1 4 − 1.4 + (−6.1) − 2. 7 5 − 8 6 D. Multiplication of Rational Numbers Example 4. Find each value. 1. − 2.2(3.2) E. Reciprocals of a Number 2. 3 4 ⋅− 7 5 Reciprocals: Example 5. 4 1. 5 Find the reciprocals of the following. 2. − 7 9 F. Division of Rational Numbers Find each value. Example 6. 3 4 1. ÷− 5 7 3. − 3.6 1.2 G. Classifying Real Numbers 1 − 6 3 ÷ − 7 5 4. − 3.1 − 12.4 Whole #’s 0, 1, 2, 3, 4,…. Rational #’s 3 1 , 0, 2, − 3, , , 4 , − 4 , ...... 2 4 3 − Real #’s 2. Natural #’s 1, 2, 3, …. Integer #’s ... − 3, − 2, − 1, 0,1, 2, 3,.... Irrational #’s π , 2 ,− 2 , 3 ,− 3 ,.... Two types of Real Numbers 1. Rational Numbers—any numbers that can be written as a , b ≠ 0 and will terminate or b repeat when written as a decimal. 2. a , b ≠ 0 and will never b terminate or repeat when written as a decimal. Irrational Numbers—any numbers that cannot be written as Example 7. Classify each number by making a check mark in the appropriate row. − 2 7 3.4 8 Natural number Whole number Integer Rational number Irrational number Real number 9.3(page 525-526) GW: HW: Read: # 2 – 58 even. # 1 – 59 odd. Section 9.4 81 −2 3 4 2 ____ 0. 36 0