Problem 7 Suppose b is any integer. Ifb mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12 gives a remainder of 5, what is the remainder when 6b is divided by 12?

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Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division
of b by 12 gives a remainder of 5, what is the remainder when 6b is divided by 12?

Because b mod 12 = 5 there is an integer m such that b = 12m +_____ . Multiply both sides of this equation by 6 and then simplify the right-hand side to find values of q and r such that 6b = 12q + r with 0 ≤ r < 12. The result is q = _____ and r = ______

Now 0 ≤ r < 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 6b is divided by 12 is _____

Please show steps for q and r
Problem 7 Suppose b is any integer. Ifb mod 12 = 5, what is 6b mod 12? In other words, if division
of b by 12 gives a remainder of 5, what is the remainder when 6b is divided by 12?
Transcribed Image Text:Problem 7 Suppose b is any integer. Ifb mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12 gives a remainder of 5, what is the remainder when 6b is divided by 12?
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