What are the rules for the multiplying and dividing integers?

Answer 1

Positive x positive = positive

Negative x negative = negative

Positive x negative / negative x positive = negative. It is the same with dividing.
N = negative

P = Positive

N x P = N

P x N = N

N x N = P

P x P = p

This is also same for division

Answer 2

The product or quotient of two numbers that have the same sign is positive. The product or quotient of two numbers with different signs is negative.