Introduction:

When adding a negative integer and a positive integer, the result can be a positive integer. In mathematics, integers are whole numbers that can be positive, negative, or zero. Adding two integers involves combining their values to find the sum. Understanding the rules of addition can help explain how the sum of a negative and positive integer can be positive.

Explanation:

1. Positive integers:
Positive integers are numbers greater than zero. They are denoted by the symbol "+". Examples of positive integers include 1, 2, 3, and so on.

2. Negative integers:
Negative integers are numbers less than zero. They are denoted by the symbol "-". Examples of negative integers include -1, -2, -3, and so on.

3. Addition of negative and positive integers:
When adding a negative integer and a positive integer, the sum depends on the magnitude or absolute value of the numbers being added.

4. Examples:
Let's consider a few examples to understand the concept better:

Example 1:
-3 + 5 = 2

In this case, we are adding a negative integer (-3) with a positive integer (5). The sum of -3 and 5 is 2, which is a positive integer.

Example 2:
-10 + 8 = -2

Here, we have a negative integer (-10) and a positive integer (8). The sum of -10 and 8 is -2, which is a negative integer.

5. Explanation:
The sign of the sum depends on the relative magnitudes of the integers being added. If the positive integer has a greater absolute value than the negative integer, the sum will be positive. Conversely, if the negative integer has a greater absolute value, the sum will be negative.

When the positive integer has a greater absolute value, it cancels out some of the negative value, resulting in a positive sum. However, if the negative integer has a greater absolute value, the sum will be negative since the negative value dominates.

Conclusion:
In summary, when adding a negative integer and a positive integer, the sum can be a positive integer if the positive integer has a greater absolute value than the negative integer. The sign of the sum depends on the relative magnitudes of the integers being added. Understanding the concept of absolute value and the rules of addition can help in determining the sign of the sum.

negative