SOLUTION: MAT 145: Topics In Contemporary Math More Modular Arithmetic Find each of the following. 7) (48 - 15) mod 10 8) (24 - 31) mod 5 9) (62

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Question 1192796: MAT 145: Topics In Contemporary Math

More Modular Arithmetic
Find each of the following.
7) (48 - 15) mod 10
8) (24 - 31) mod 5
9) (62 - 85) mod 12
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064) (Show Source):
You can put this solution on YOUR website!

I suppose you want (X - Y) mod R in the form A + RN where 0 ≤ A < R, and where N is any integer. (48 - 15) mod 10
48 - 15 = 38, it's greater than 10, subtract 10, get 28. Still greater than 10. Subtract 10, get 18. Still greater than 10, subtract 10, get 8. Answer: 8 + 10N ------------------------------------------------------------- (24 - 31) mod 5
24 - 31 = -7, it's negative, so add 5, get -2. Still negative, add 5, get 3 Answer: 3 + 5N ------------------------------------------------------------- (62 - 85) mod 12 62 - 85 = -23, it's negative. so add 12, get -12. Still negative, add 12 again, get 1. Answer: 1 + 12N Edwin

Answer by greenestamps(13215) (Show Source):
You can put this solution on YOUR website!

The other tutor works these problems of finding (A-B) mod C by first performing the indicated subtractions and then finding the mod C equivalents of the results by adding or subtracting multiples of C until the result is 0 < n < C.

While that is a valid method, in most cases the work is easier if you use the features of modular arithmetic.

7) (48-15) mod 10 = (48) mod 10 - (15) mod 10 = 8-5 = 3

8) (24-31) mod 5 = (24) mod 5 - (31) mod 5= 4-1 = 3

9) (62-85) mod 12 = (62) mod 12 - (85) mod 12 = 2-1 = 1

SOLUTION: MAT 145: Topics In Contemporary Math More Modular Arithmetic Find each of the following. 7) (48 - 15) mod 10 8) (24 - 31) mod 5 9) (62 - 85) mod 12