In basic arithmetic with signed integers, a negative number plus a positive number equals what type of result when only their signs are known?

Introduction / Context:
When students first encounter arithmetic with positive and negative integers, they often try to apply oversimplified rules such as negative plus positive is always negative or always positive. In reality, the result of adding a negative number and a positive number depends on the relative sizes of their absolute values. This question checks whether you understand that signs alone are not enough to determine the final sign of the sum.

Given Data / Assumptions:
- One addend is a negative integer.
- The other addend is a positive integer.
- No information is given about their exact numerical values or magnitudes.
- We are asked what the result will be based only on this sign information.

Concept / Approach:
The general form of such a sum is -a + b, where a and b are positive real numbers or integers. The sign of the result is decided by comparing a and b. If the negative number has greater magnitude, the result is negative. If the positive number has greater magnitude, the result is positive. If the magnitudes are equal, the result is zero. Without knowing specific values, we cannot fix a single outcome.

Step-by-Step Solution:
Step 1: Represent the negative number as -a and the positive number as b, where a > 0 and b > 0. Step 2: Consider the sum S = -a + b. Step 3: If a > b, then the negative part dominates and S = -(a - b), which is negative. Step 4: If a < b, then the positive part dominates and S = b - a, which is positive. Step 5: If a = b, then S = -a + a = 0, so the sum is exactly zero. Step 6: Since the problem does not specify the sizes of a and b, all three outcomes are possible.

Verification / Alternative Check:
You can verify this by simple examples:
- Example 1: -7 + 2 = -5, which is negative.
- Example 2: -3 + 10 = 7, which is positive.
- Example 3: -4 + 4 = 0, which is zero.
These cases show clearly that different numeric choices give different types of results, even though every sum is negative plus positive.

Why Other Options Are Wrong:
Option A (A negative number) is wrong because sometimes the positive number is larger in magnitude, giving a positive result instead of a negative one.
Option B (A positive number) is wrong for the same reason; sometimes the negative number dominates, making the sum negative.
Option C (Zero) is wrong because zero occurs only in the special case when the magnitudes are exactly equal, which is not guaranteed here.

Common Pitfalls:
A common mistake is to memorize a rule that a negative plus a positive is always positive or always negative. Another error is to focus only on the sign of one number and ignore magnitudes. Correct integer arithmetic always compares absolute values when combining opposite signs.

Final Answer:
Because the magnitudes of the negative and positive numbers are not specified and all three outcomes are possible, the result cannot be determined from the signs alone.