By Mark Dugopolski
The Dugopolski sequence in developmental arithmetic has helped hundreds of thousands of scholars achieve their developmental math classes. user-friendly & Intermediate Algebra, 4e is a part of the most recent choices within the winning Dugopolski sequence in arithmetic. In his books, scholars and college will locate brief, distinctive factors of phrases and ideas written in transparent, comprehensible language that's mathematically exact. Dugopolski additionally incorporates a double cross-referencing approach among the examples and workout units, so irrespective of the place the scholars commence, they're going to see the relationship among the 2. eventually, the writer unearths it vital not to merely supply caliber but additionally a large choice and volume of workouts and purposes.
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Additional info for Elementary and Intermediate Algebra, 4th Edition
2 4 59. 09 Ϳ 60. 00987 Ϳ Έ Έ Έ Έ Select the smaller number in each given pair of numbers. 61. Ϫ16, 9 5 9 63. Ϫᎏᎏ, Ϫᎏᎏ 2 4 62. Ϫ12, Ϫ7 5 6 64. ᎏᎏ, ᎏᎏ 8 7 Miscellaneous Write the interval notation for the interval of real numbers shown in each graph. 91. 2 3 4 5 6 7 8 9 92. Ϫ6 Ϫ4 Ϫ2 0 2 4 6 93. Ϫ40 Ϫ30 Ϫ20 Ϫ10 0 10 Ϫ50 Ϫ40 Ϫ30 Ϫ20 Ϫ10 0 94. 2 d) Explain how to find a rational number between any two given rational numbers. 95. 0 10 20 30 40 50 20 30 13 Fractions 96. Ϫ10 0 10 104. Discussion Suppose that a is a negative real number.
31 ϭ ᎏᎏ 36 Add. d) To perform addition with the mixed number 2 1ᎏᎏ, first convert it into an 1 1 6 1 7 improper fraction: 2 ᎏ3ᎏ ϭ 2 ϩ ᎏ3ᎏ ϭ ᎏ3ᎏ ϩ ᎏ3ᎏ ϭ ᎏ3ᎏ. 2 U Calculator Close-Up V Fractions 21 1 5 7 5 1 2ᎏᎏ ϩ ᎏᎏ ϭ ᎏᎏ ϩ ᎏᎏ Write 2ᎏᎏ as an improper fraction. 3 3 9 3 9 7и3 5 ϭ ᎏᎏ ϩ ᎏᎏ The LCD is 9. 3и3 9 21 5 ϭ ᎏᎏ ϩ ᎏᎏ Simplify. 9 9 26 ϭ ᎏᎏ Add. 9 You can check these results with a graphing calculator. Note how a graphing calculator handles mixed numbers. 1 5 3 5 8 Note that ᎏ3ᎏ ϩ ᎏ9ᎏ ϭ ᎏ9ᎏ ϩ ᎏ9ᎏ ϭ ᎏ9ᎏ.
If we multiply the absolute values of Ϫ2 and 5, we get 10. 99. The absolute value of any negative number is greater than 0. 100. The absolute value of any positive number is less than 0. 105. Discussion 101. The absolute value of Ϫ9 is larger than the absolute value of 6. 102. The absolute value of 12 is larger than the absolute value of Ϫ11. Determine whether each number listed in the following table is a member of each set listed on the side of the table. For example, 1ᎏᎏ is a real number and a rational 2 number.