In mathematics, the expression "a divides b" is used to describe a specific relationship between two numbers. It means that a is a divisor (or factor) of b, which implies that b can be evenly divided by a without leaving any remainder.

Formally, we say that "a divides b" if there exists an integer c such that:

b = a * c

In this equation, "b" is the dividend, "a" is the divisor, and "c" is the quotient. If the quotient "c" is an integer (meaning there's no fractional part), then a is said to divide b.

For example:

1. 4 divides 12 because 12 = 4 * 3 (where a = 4, b = 12, and c = 3).
2. 7 divides 42 because 42 = 7 * 6 (where a = 7, b = 42, and c = 6).
3. 2 divides -10 because -10 = 2 * (-5) (where a = 2, b = -10, and c = -5).

On the other hand, if "a" does not divide "b," then "b" is not divisible by "a," and there will be a remainder when you attempt to divide "b" by "a."