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a4-3-08

# a4-3-08 - Section 36 1 Working in Z10(a 3 3 = 6(b 6 6 = 2(c...

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Section 36 1. Working in Z 10 (a) 3 + 3 = 6 (b) 6 + 6 = 2 (c) 7 + 3 = 0 (d) 9 + 8 = 7 (e) 12 + 4 =? Technically, according to the de°nition of Z n on page 310, the number 12 is not in Z 10 , so this addition is not de°ned. Personally, in the context of Z 10 , I think of 12 as being equal to 2 which is in Z 10 . So 12 + 4 = 6 . (f) 3 ° 3 = 9 (g) 4 ° 4 = 6 (h) 7 ° 3 = 1 (i) 5 ° 2 = 0 (j) 6 ° 6 = 6 (k) 4 ° 6 = 4 (l) 4 ° 1 = 4 (m) 12 ° 5 = 0 , or 12 ° 5 is not de°ned (see part ( e ) ) (n) 5 ± 8 = 7 . I±m sure that ± 3 is not an acceptable answer for this textbook because he does not consider ± 3 to be in Z 10 . Lots of other people would not accept ± 3 , and I don±t either. What is the point of this problem if ± 3 is an acceptable answer? One could have just as well have answered 21 to part ( h ) . (o) 8 ± 5 = 3 (p) 8 = 7 = 4 because 4 ° 7 = 28 = 8 (q) 5 = 9 = 5 because 5 ° 9 = 45 = 5 2. Solve for x (a) 3 x = 4 in Z 11 . The answer is x = 5 . (b) 4 x ± 8 = 9 in Z 11 becomes 4 x = 17 = 6 , and the answer is x = 7 . 1

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(c) 3 x + 8 = 1 in Z 10 becomes 3 x = ± 7 = 3 , and the answer is clearly x = 1 .
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a4-3-08 - Section 36 1 Working in Z10(a 3 3 = 6(b 6 6 = 2(c...

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