Intermediate Algebra, 3rd Edition by Julie Miller, Molly O'Neill, Nancy Hyde

By Julie Miller, Molly O'Neill, Nancy Hyde

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3 a. Check: 1721Ϫ62 ϭ Ϫ42 ✓ 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. Ϫ96 Ϫ144 Write the mixed number as an improper fraction, and multiply by the reciprocal of the second number. 1 31 5 ϭ aϪ b 10 2 2 ϭϪ d. 31 Ϫ31 31 ϭ ϭ 4 4 Ϫ4 31 4 Different signs. The quotient is negative. Ϫ8 8 ϭ Ϫ7 7 Same signs. The quotient is positive.

0 Ϫ8 Ϫ 3 0 Ϫ 1Ϫ8 Ϫ 32 91. 25 Ϫ 2 3 17 Ϫ 32 2 Ϭ 44 ϩ 218 Ϫ 2 92. 229 Ϫ 22 ϩ 38 Ϫ 316 Ϫ 22 4 Ϭ 4 ؒ 5 93. 0 110 Ϫ 72 Ϫ 23 0 94. 16 Ϭ 8 ؒ 3 1 2 6Ϫ4 2 5ϩ2 2 b ϩa b 95. a b ϩ a 2 5 10 29 Operations on Real Numbers 0 Ϫ12 Ϫ 17 Ϫ 32 2 2 0 96. a 62 Ϫ 8 Ϭ 2 2 8 Ϫ 1Ϫ22 2 23 b Ϭ a b 23 ϩ 1 32 For Exercises 97–98, find the average of the set of data values by adding the values and dividing by the number of values. 97. Find the average low temperature for a week in January in St. John’s, Newfoundland. Round to the nearest tenth of a degree.

1 2 ______ 4 9 8. 2 3. Interval Notation The set {x 0 x Ն 3} represents all real numbers greater than or equal to 3. This set can be illustrated graphically on the number line. Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 By convention, a closed circle ● or a square bracket [ is used to indicate that an “endpoint” (x ϭ 3) is included in the set. The set {x 0 x Ͼ 3} represents all real numbers strictly greater than 3. This set can be illustrated graphically on the number line. Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 4 5 By convention, an open circle ᭺ or a parenthesis ( is used to indicate that an “endpoint” (x ϭ 3) is not included in the set.

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