What is the rule for dividing two numbers with the same sign?

When dividing two numbers that share the same sign, the rule is that the quotient will always be positive. This occurs because when you divide two positive numbers, their ratio remains positive, as both values contribute positively to the result. Similarly, when dividing two negative numbers, this situation also results in a positive quotient, as the negatives cancel each other out.

For instance, if you take 10 divided by 2, the result is 5, and both numbers are positive. On the other hand, if you divide -10 by -2, the result is also 5, as the negatives negate each other, leading to a positive outcome. Thus, the fundamental principle underlying this rule is the concept that the division of like signs—whether both positive or both negative—results in a positive quotient.