When you divide a negative integer by a positive integer, the quotient is always negative.

This statement is true. When dividing integers, the signs of the numbers determine the sign of the quotient. Specifically:

1. Negative Integer: Any integer less than zero (e.g., -1, -2, -3, ...).
2. Positive Integer: Any integer greater than zero (e.g., 1, 2, 3, ...).
3. Rule of Signs: When dividing a negative number by a positive number, the result is always negative.

Examples:

• When we divide -6 by 3, $-6 \div 3 = -2$.
• When we divide -10 by 5, $-10 \div 5 = -2$.

The general form can be expressed as: $\text{If } a < 0 \text{ and } b > 0, \text{ then } \frac{a}{b} < 0.$

In summary, the quotient of a negative integer divided by a positive integer is always negative based on the basic rules of arithmetic regarding the division of signed numbers.