SOLUTION: MAT 145: Topics In Contemporary Math More Modular Arithmetic Find each of the following. 10) (5 * 11) mod 4 11) (31 * 14) mod 7 12) (15 * 4) mod 9

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Question 1192797: MAT 145: Topics In Contemporary Math

More Modular Arithmetic
Find each of the following.
10) (5 * 11) mod 4
11) (31 * 14) mod 7
12) (15 * 4) mod 9


Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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(10)  Multiply 5 by 11;  then take the remainder of division this product by 4.


(11)  Multiply 31 by 14;  then take the remainder of division this product by 7.


(12)  Multiply 15 by  4;  then take the remainder of division this product by 9.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You can work this kind of problem mod n by doing the indicated multiplications and evaluating the products mod n.

10) (5*11) mod 4 = (55) mod 4; 55/4 = 12 remainder 3 --> answer: 3
11) (31*14) mod 7 = (434) mod 7; 434/7 = 62 remainder 0 --> answer: 0
12) (15*4) mod 9 = (60) mod 9; 60/9 = 6 remainder 6 -- answer: 6

I suspect if this is a learning exercise in modular arithmetic that you were expected to use the features of modular arithmetic, as follows.

10) (5*11) mod 4 = (5) mod 4 * (11) mod 4 = 1*3=3
11) (31*14) mod 7 = (31) mod 7 * (14) mod 7 = 3*0 = 0
12) (15*4) mod 9 = (15) mod 9 + (4) mod 9 = (6*4) mod 9 = (24) mod 9 = 6

In these examples, working the problems this second way is a bit easier; in example 11 it makes the work very simple.