Question

Statistics negative numbers and subtraction in a modular arithmetic system

Answer 1

(a)

`\begin{gathered} let\text{ the unknown be x} \\ -7=x(mod\text{ 6\rparen} \\ multiples\text{ of 6 are 6, 12, 18,...} \\ Thus,\text{ } \\ -7(mod\text{ 6\rparen}=-7+12(mod\text{ 6\rparen} \\ =5\text{ mod 6} \\ The\text{ answer = 5} \end{gathered}`

(b)

`\begin{gathered} 24-25=x(mod\text{ 9\rparen} \\ =-1(mod9)_ \\ Multiples\text{ of 9 are 9, 18, 27, 36,etc} \\ Thus,\text{ } \\ -1(mod\text{ 9\rparen= -1 + 9 \lparen mod 9\rparen} \\ =9=8\text{ \lparen mod 9\rparen} \\ The\text{ answer is 8} \end{gathered}`