Question

Let a = 8 and b = 3. Find the quotient q and the remainder r per the division algorithm.

A) Quotient (q) = 2, Remainder (r) = 2
B) Quotient (q) = 2, Remainder (r) = 1
C) Quotient (q) = 3, Remainder (r) = 2
D) Quotient (q) = 3, Remainder (r) = 1

Answer 1

The division of 8 by 3 results in a quotient of 2 and a remainder of 2 by the division algorithm, which fits option A.

Step-by-step explanation:

The division algorithm states that for two integers a and b, where b is not zero, there exist unique integers q (the quotient) and r (the remainder) such that a = bq + r, and 0 ≤ r < b.

Given that a = 8 and b = 3, we can calculate the quotient and the remainder by dividing 8 by 3. The division of 8 by 3 gives a quotient of 2 (since 3 goes into 8 twice, making 6) and a remainder of 2 (since 8 minus 6 leaves 2).

Therefore, the correct answer is Quotient (q) = 2, Remainder (r) = 2. This corresponds to option A.