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**Extra info for Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes**

**Example text**

107 8= 992 -:- IlO: take 8, leave 112; 112 - 16 = 968 -:- 110 = 8 and 8H over. 88 - 16 = 726 -:- 110 = Gand 66 over. 66· - 12 = 549 -:- 110 = 4 and 109 over. lU9 - 8 = 99 96 72 54 lUI When dividing by 73, divide actually by 70, and adjust by subtracting 3 times each quotient. Example 3,' 73 ) 6 2 3 8 24 2 0 and 24 over. 39 5 30(j 14 8 5 4 Answer: 85420: remainder 24. DIVISION 61 Explanation: 63 -24 45 -15 26 -12 86 = = = = 39 30 14 2. Practice will cnable thesc sums to be worked almost as fast as figures can be writtcn.

Similarly 325 X 375 = 121875. Other fractions are amenable to the same method if they add up to 1; thus: 4~ X 4~ = 20i;. (4 X 5 and ~ X 3A X 3tI =: 121~1' (3 X 4 and /1 X fd The practical value of this knowledge to teachers taking blackboard work in multiplication of fractions is very great. 2 (j). It can now be seen that if the last two figures of any two factors add up to 100, the same method can be used. n SIMPLE MULTIPLICATION 33 Thus: 291 X 209 = 60819. ) 396 X 304 = 120384. ) Revise the general method given in section 2 (e) and you will then be able to work the following at sight: 246 X 254 = 62484.

775 X 725 23. 31 X 31 24. 6* X 6f 25. 4, X 4, 26 81 X 8, 27. 91 X 91 28. lli X 111 29. 51 X 51 30. 7ft. X 7M EXERCISE 2 (0) 1. 27 X 23 2. 34 X 36 3. 41 X 49 4. 53 X 57 5. 82 X 88 6. 47 X 43 7. 84 X 86 8. 76 X 74 9. 117 X 113 SIMPtE MULTIPLICAtION 37 10. 67 X 47 11. 36 X 76 12. 25 X 85 13. 33 X 73 14. 49 X 69 15. 28 X 88 16. 97 X 17 17. 52 X 52 18. 56 X 56 19. 493 X 407 20. 821 X 879 21. 631 X 669 22. 748 X 752 23. 985 X 915 24. 991 X 909 25. 327 X 687 26. 413 X 593 27. 374 X 634 28. 826 X 186 29.