## New PDF release: A Binomial Congruence

By Mike Swarbrick Jones

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1 ʦ‫ގ‬ 3 b. 1 ʦ‫ޗ‬ 3 c. Ϫ5 ʦ ‫ޚ‬ d. Ϫ5 ʦ ‫ޑ‬ c. 1 ʦ‫ޚ‬ 3 d. 1 ʦ‫ޑ‬ 3 23. a. 25 ʦ ‫ގ‬ b. 25 ʦ ‫ޗ‬ 24. a. p ʦ ‫ޚ‬ b. p ʦ ‫ޑ‬ c. 25 ʦ ‫ޚ‬ d. 25 ʦ ‫ޑ‬ c. p ʦ ‫ވ‬ d. p ʦ ‫ޒ‬ . indd Page 14 5/30/12 5:22 AM user-f462 /208/MH01591/miL35635_disk1of1/0078035635/miL35635_pagefiles CA— 14 Chapter R Review of Prerequisites 25. 25 ʦ {x 0 x is an integer and a multiple of 5} 26. Ϫ7 ʦ {x 0 x is a natural number less than 10} 27. 8} 28. 45} 29. 22 ʦ {x 0 x is an even whole number} 30. Ϫ24 ʦ {x 0 x is an integer and a multiple of 4} 31.

2xy3 48. Ϫ 2 n 5 m 46. 4cd 5 ϩ d 6 47. 49. x 0 y ϩ z 0 50. m13 ϩ n Objective 3: Apply Properties of Real Numbers For Exercises 51–56, apply the commutative property of addition or multiplication. 51. 7 ϩ x 52. 9 ϩ z 54. Ϫ11 ϩ p 55. y ؒ 1 3 53. Ϫ3 ϩ w 56. indd Page 26 5/30/12 5:22 AM user-f462 /208/MH01591/miL35635_disk1of1/0078035635/miL35635_pagefiles CA— 26 Chapter R Review of Prerequisites For Exercises 57–60, apply the associative property of addition or multiplication. Then simplify if possible.

B. One estimate for the number of stars in the Milky Way is 230 billion. c. 2 g. indd Page 34 5/30/12 5:03 AM user-f462 /208/MH01591/miL35635_disk1of1/0078035635/miL35635_pagefiles CA— 34 Chapter R Review of Prerequisites Solution: a. 0000002 is between 0 and 1. Use a negative power of 10. 7 place positions First write 230 billion in standard form. b. 3 ϫ 1011 stars The number 230 billion is greater than 10. Use a positive power of 10. 11 place positions c. 2 ϫ 100 g The decimal point is moved zero units, so the exponent on 10 is 0.