CHAPTER 4 Summary 207 Problem Solving In Exercises 29 and 30, we show lattice multiplications. (a) Determine the numbers being multiplied. (b) Determine the product. 29. 8 1 1 1 0 0 0 2 2 3 8 2 a) 253 46 × b) 11,638 30. 8 2 3 1 0 4 2 0 4 1 4 1 1 1 2 2 5 0 a) 475 263 × b) 124,925 In Exercises 31 and 32, we solve a multiplication problem using Napier’s rods. (a) Determine the numbers being multiplied. Each empty box contains a single digit. (b) Determine the product. 31. 1 2 3 2 0 8 INDEX a) 4 382 × b) 1528 32. 4 2 5 6 3 5 INDEX a) 7 685 × b) 4795 Challenge Problems/Group Activities In Exercises 33 and 34, use the method of duplation and mediation to perform the multiplication. See Section 4.1 for Egyptian and Roman numerals. Write the answer in the numeration system in which the exercise is given. 33. ( |||) ( ||) > >> ⋅ * 34. (XXVI) (LXVII) ⋅ MDCCXLII In Exercises 35 and 36, (a) use lattice multiplication to perform the multiplication. (Hint: Be sure not to list any number greater than or equal to the base within the box.) Write the answer in the base in which the exercise is given. (b) Multiply the numbers as explained in Section 4.4. If you do not obtain the results obtained in part (a), explain why. 35. 21 21 3 3 × 12113 36. 24 234 5 5 × 123315 Research Activities 37. John Napier In addition to Napier’s rods, John Napier is credited with making other important contributions to mathematics. Write a report on John Napier and his contributions to mathematics. 38. Duplation and Mediation Write a paper explaining why the duplation and mediation method works. *See Instructor Answer Appendix Summary CHAPTER 4 Important Facts and Concepts Examples/Discussion Section 4.1 Additive Numeration Systems Egyptian Hieroglyphics Roman Numerals Multiplicative Numeration Systems Traditional Chinese Numerals Ciphered Numeration Systems Ionic Greek Numerals Discussion page 173, Examples 1–2, page 173 Discussion page 174, Examples 3– 6, pages 174–175 Discussion pages 176–177, Examples 7–8, pages 176–177 Discussion page 178, Examples 9–10, page 178
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