Question

Let a = −8 and b = 3. Again, find q and r per the division algorithm.

a,b must be integers
b > 0
r is non negative and less than b

a) q = -3, r = 1
b) q = -2, r = 1
c) q = -3, r = 2
d) q = -2, r = 2

Answer 1

When dividing −8 by 3 using the division algorithm, the quotient (q) is −3 and the remainder (r) is 1. Therefore, the correct answer is option a) q = -3, r = 1.

Step-by-step explanation:

The student's question involves using the division algorithm to find the quotient (q) and the remainder (r) when dividing one integer by another. Specifically, with a = −8 and b = 3, we want to find values of q and r such that:

a = bq + r, where r must be a non-negative integer and less than b.

In this case, we can see that 3q will need to be just less than −8 for r to be a small positive number. We can find the correct q and r by performing the division:

−8 divided by 3 is −3 with a remainder of 1.

Therefore, the correct answer is:

• q = −3
• r = 1

The pair (q, r) that match these criteria is answer option a) q = -3, r = 1.