90 Chapter 1 The Set of Real Numbers Concept Connections Simplify. 0 4 18. 19. 2 0 20. 25 0 21. 0 18.22 Instructor Note: Memory Device: Zero under the line, division undefined. Skill Practice Simplify. 22. 3636 142 132 Answers 18. 0 19. Undefined 20. Undefined 21. 0 22. 33 Multiplication can be used to check any division problem. If then (provided that ). For example, 142122 8 Check: ✔ 8 4 2 b 0 This relationship between multiplication and division can be used to investigate division problems involving the number zero. 1. The quotient of 0 and any nonzero number is 0. For example: ✔ 0 6 0 because 6 0 0 2. The quotient of any nonzero number and 0 is undefined. For example, 60 6 0 ? Finding the quotient equal 6?” That is, 1021?2 is equivalent to asking, “What number times zero will 6 . No real number satisfies this condition. Therefore, we say that division by zero is undefined. 3. The quotient of 0 and 0 cannot be determined. Evaluating an expression of 00 the form is equivalent to asking, “What number times zero will equal 0?” That is, . Any real number will satisfy this requirement; however, expressions involving are usually discussed in advanced mathematics courses. 00 ? 1021?2 0 Division Involving Zero Let a represent a nonzero real number. Then, 0 a 0 1. 2. a 0 is undefined 4. Applying the Order of Operations Applying the Order of Operations Example 5 Simplify. Solution: 8 8 122 162 Perform division before addition. The quotient of and is positive or . Write as a fraction. 8 8 122 162 8 142 162 8 1 4 6 2 3 8 The common denominator is 3. 24 3 22 3 2 3 Add. 23 46 8 4 6 ab c, bc a Classroom Example: p. 94, Exercise 104
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