Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 8b is divided by 12? Fill in the blanks to show...

Extracted text: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 8b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. . Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q and r such that Because b mod 12 = 7, there is an integer m such that b = 12m + 7 8b = 12g + r with 0 < 12.="" the="" result="" is="" q="7m" +="" 2="" and="" r="4" now="" 0=""><>< 12,="" and="" q="" is="" an="" integer="" because="" products="" and="" sums="" of="" integers="" are="" integers="" so="" the="" uniqueness="" part="" of="" the="" quotient="" remainder="" theorem="" guarantees="" that="" the="" remainder="" obtained="" when="" 8b="" is="" divided="" by="" 12="" is="">