Chapter 1 Review Exercises 87 40. The property of multiplication states that the grouping of the things being multiplied doesn’t change the result. a(bc) = . 41. is the identity element of multiplication. 42. The property of multiplication states that multiplying a number by doesn’t change its value. a · = a. 43. The property of multiplication states that multiplying a number and its is one. a · = 1. 44. The property enables us to multiply a number by a sum or difference. a(b + c) = . 45. When a(n) number is distributed to a sum, the signs of each of the terms . SECTION 1.8 Algebraic Expressions 46. A(n) is a number or a product of a number and a variable raised to powers. The in an algebraic expression are separated by addition or subtraction. 47. A(n) is a term that contains a variable. 48. A(n) is a term that does not contain a variable. 49. The of a variable term is the number multiplied by the variable. 50. Terms that have the same variables with the same powers are terms. Terms that do not have the same variables or same powers are terms. 51. To combine like terms, add their and keep the the same. 52. To simplify algebraic expressions, clear any and then combine . CHAPTER 1 / REVIEW EXERCISES SECTION 1.1 Classify each number as a natural number, whole number, integer, rational number, irrational number, and/or real number. If the number is an irrational number, approximate its value to the nearest hundredth. (See Objective 1.) 1. 5 1 3 2. 7.19 3. 10π 4. 151 Give an example of a real number that satisfies each condition. (See Objective 1.) 5. An integer that is not a whole number. 6. An irrational number that is between 2 and 3. 7. A rational number that is between 3 2 and 2. 8. An integer that is not a natural number. Graph each number on a real number line. (See Objective 2.) 9. e-2.33, 2 1 4 , 5 f 10. e-π, 17, 20 3 f Compare the values of each pair of numbers. Use a <, >, or = symbol to make the statement true. (See Objectives 3 and 5.) 11. 22 7 π 12. 149 -u-7u Find the opposite of each real number. (See Objective 4.) 13. 1.1212 14. 5.2 15. -3 1 5 16. 7 9 Simplify each absolute value expression. (See Objective 5.) 17. u-5.8u 18. -u1.9u 19. -P- 6 13 P 20. -P 5 4 P SECTION 1.2 Write the prime factorization of each number. (See Objective 1.) 21. 90 22. 560 23. 945 24. 200 Simplify each fraction to lowest terms. (See Objective 3.) 25. 30 45 26. 168 288 27. 336 378 28. 126 360 Perform the indicated operation. Express answers in lowest terms, when applicable. (See Objectives 4 and 5.) 29. 7 12 + 11 28 30. 1 2 - 3 10 31. 3 1 5 · 1 1 4 32. 2 1 7 ÷ 6 3 7 33. 7 12 · 9 14 34. 6 1 5 - 7 3 5 SECTION 1.3 Use the order of operations to simplify each expression. (See Objectives 1 and 2.) 35. 4(-11) - 9(-2) 36. 2.15(-1)2 + (-3.16)(0) 37. -5 - (-5)-6 + (-2) 38. - 3 14 (-12) + 10 7 39. 12 + (-4) -21 + (-9) 40. -1.5(-4)2 + 3.2(2) + 6.5 41. (-1 · 6)2 - 5 · 12 ÷ 6 - (-3.6) 42. (-6)2 - (-15) ÷ 5 · 3 - 7 43. u-8(-12) + 2(-13)u 44. 1(14-10)2 + (-18 + 15)2
hendricks_beginning_algebra_1e_ch1_3
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