Rules for Multiplying and Adding in Modulo # Calculation

[MathewsMD]

Hi,

Are there any rules against multiplying or adding first when using modulo #?

The reason I ask is because I'm doing the dot product for two vectors:

[10, 9, 8, 7, 6, 5, 4, 3, 2, 1].[8, 0 ,3 ,7, 0, 9, 9, 0, 2, 6]

By doing this, I get:

80 + 0 + 24 + 49 + 0 + 45 + 36+ 0 + 4 + 6 = 0 (mod11) - it equals 244

Now, if I simplify first before adding:

3 + 0 + 2+ 5+ 0 + 1 + 3+ 4 + 6 = 2 (mod11)

I'm not exactly sure if my arithmetic is poor and I am completely missing a simple error, or if I am dismissing a fundamental concept, but I can't seem to find my problem. Is there any reason why I get 0 as one answer, and 2 as the other (in mod11)?

 

[WWGD]

244 =242+2 = 11(11)+2 = 2 Mod 11. Basically, addition mod11 is associative :

(a+b)Mod11 =aMod11+ bMod11.

 

[MathewsMD]

244 =242+2 = 11(11)+2 = 2 Mod 11. Basically, addition mod11 is associative :

(a+b)Mod11 =aMod11+ bMod11.

Thank you. So according to its associative property, it should not depend on when it is added/subtracted.

I just realized my solutions manual had an incorrect value. Thank you for the help and this question has been solved.

 

[WWGD]

No problem; glad it helped.

 

[HallsofIvy]

Hi,

Are there any rules against multiplying or adding first when using modulo #?

The reason I ask is because I'm doing the dot product for two vectors:

[10, 9, 8, 7, 6, 5, 4, 3, 2, 1].[8, 0 ,3 ,7, 0, 9, 9, 0, 2, 6]

By doing this, I get:

80 + 0 + 24 + 49 + 0 + 45 + 36+ 0 + 4 + 6 = 0 (mod11) - it equals 244

This is the error- the sum is indeed 244= 242+ 2= 11(22)+ 2 so this is 2 (mod 11), not 0.

Now, if I simplify first before adding:

3 + 0 + 2+ 5+ 0 + 1 + 3+ 4 + 6 = 2 (mod11)

I'm not exactly sure if my arithmetic is poor and I am completely missing a simple error, or if I am dismissing a fundamental concept, but I can't seem to find my problem. Is there any reason why I get 0 as one answer, and 2 as the other (in mod11)?