Section 1.6 Multiplication and Division of Real Numbers 67 Dividing Real Numbers Example 4 Divide the real numbers. a. b. Solution: a. 15 25 Different signs. Quotient is negative. b. Different signs. Quotient is negative. Multiply by the reciprocal of which is . Divide out common factors. Multiply the fractions. 3 14 3 1 14 2 1 6 7 1 93 Skill Practice Divide. 15. 16. Multiplication can be used to check any division problem. If then (provided that ). For example: 142122 8 Check: ✔ 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: ✔ 2. The quotient of any nonzero number and 0 is undefined. For example: 60 Finding the quotient is equivalent to asking, “What number times zero will equal 6?”That is, . 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 the 00 form is equivalent to asking, “What number times zero will equal 0?” That is, 1021?2 0 . Any real number will satisfy this requirement; however, expressions involving are usually discussed in advanced mathematics courses. 00 ? 1021?2 6 6 0 ? 0 6 0 because 6 0 0 8 4 2 b 0 ab c, bc a 3 4 a 9 16 12 1182 b 79 9 7 7 9 3 14 9 7 3 5 15 25 3 14 9 7 15 25 TIP: If the numerator and denominator of a fraction have opposite signs, then the quotient will be negative. Therefore, a fraction has the same value whether the negative sign is written in the numerator, in the denominator, or in front of the fraction. 3 5 Answers 15. 16. 4 3 2 3 3 5 3 5
miller_beginning_intermediate_algebra_4e_ch1_3
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