Understanding the Sum of Two Integers
When we talk about the sum of two integers, we need to consider the various possibilities based on the nature of the integers involved. Here’s a breakdown of the scenarios:
1. Positive Integers
- If both integers are positive (e.g., 3 and 5), their sum will always be positive.
- Example: 3 + 5 = 8
2. Negative Integers
- If both integers are negative (e.g., -3 and -5), their sum will always be negative.
- Example: -3 + (-5) = -8
3. Mixed Integers
- If one integer is positive and the other is negative (e.g., 5 and -3), the sum can be positive, negative, or zero, depending on their absolute values.
- Example:
- If |5| > |3|, then 5 + (-3) = 2 (Positive)
- If |5| < |3|,="" then="" -3="" +="" 5="2" (positive)="" />
- If |5| = |3|, then 5 + (-5) = 0 (Zero)
4. Zero as an Integer
- Including zero in the sum does not change the value of the other integer.
- Example: 0 + 5 = 5 (Positive)
- Example: 0 + (-5) = -5 (Negative)
Conclusion
The sum of two integers can never be strictly defined as positive, negative, or zero; it depends on the integers themselves. Therefore, the answer to the question is that the sum of two integers can be positive, negative, or zero based on the integers' values. Understanding these scenarios helps in grasping how integers interact in addition.