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By Gwilym M. Jenkins, Donald G. Watts

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40. What is the sign of the product of an even number of negative factors? 26 CHAPTER 1 • Review of Real Numbers OBJECTIVE B To add, subtract, multiply, and divide rational numbers 41. a. Describe the least common multiple of two numbers. b. Describe the greatest common factor of two numbers. ͩ ͪ For Exercises 43 to 70, simplify. 7 3 5 5 Ϫ Ϫ Ϫ 43. 44. 12 16 8 12 45. 5 14 Ϫ Ϫ 9 15 46. 1 1 5 ϩ Ϫ 2 7 8 49. 2 5 5 Ϫ ϩ 3 12 24 50. Ϫ 53. ͩ ͪͩ ͪ 54. 2 9 Ϫ 3 20 57. Ϫ 11 7 Ϭ 24 12 58. 14 7 Ϭ Ϫ 9 27 7 4 5 ϩ ϩ 10 5 6 48.

Add the numerators. Place the sum over the common denominator. ͩ ͪ 7 1 Ϫ Ϫ 15 6 7 1 ϩ 15 6 • Write subtraction as addition of the opposite. ෇ Ϫ7 2 1 5 Ϫ14 5 и ϩ и ෇ ϩ 15 2 6 5 30 30 • Write each fraction in terms of the common denominator, 30. ෇ Ϫ9 3 ෇Ϫ 30 10 • Add the numerators. Write the answer in simplest form. The product of two fractions is the product of the numerators over the product of the denominators. HOW TO • 11 Ϫ Multiply: Ϫ 8 5 и 12 15 5 8 5и8 40 и ෇Ϫ ෇Ϫ 12 15 12 и 15 180 ෇Ϫ 20 и 2 2 ෇Ϫ 20 и 9 9 • The signs are different.

Note that the natural numbers and the positive integers are the same set of numbers. The integer zero is neither a positive nor a negative integer. Still other numbers are necessary to solve the variety of application problems that exist. For instance, a landscape architect may need to purchase irrigation pipe that has a diameter of 5 8 in. The numbers that include fractions are called rational numbers. Rational numbers ෇ 2 3 9 2 The numbers , Ϫ , and 5 1 p Άq, where p and q are integers and q 0· are examples of rational numbers.

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