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Arithmetic operations are the building blocks of mathematics. They include addition, subtraction, multiplication, and division, and they allow us to perform calculations with numbers. When it comes to adding positive and negative numbers, we use these operations to find the sum, which is the result of addition.

For instance, if we have two numbers, one positive and one negative, like in the exercise example of adding 18 and -2, we are performing an arithmetic operation. The sign of the number determines how we treat it in the operation: positive numbers are straightforward additions, whereas negative numbers can be thought of as removing or subtracting that value.

Integer addition involves combining whole numbers, which can either be positive, negative, or zero. The rules of integer addition are straightforward when dealing with two positive numbers or two negative numbers: simply add their absolute values together. However, when the integers have different signs, like in the exercise where we add 18 and -2, we are looking at a different process.

In such cases, we subtract the smaller absolute value from the larger one. So, we turn the problem into subtracting 2 from 18, as the absolute value of -2 is 2. Then we take into account the sign of the number with the greater absolute value, which in this exercise is positive. Hence the sum of 18 and -2 is 16, indicating that the positive number has a greater impact on the result.

The absolute value of a number is the distance of that number from zero, regardless of its direction on the number line. It's always a non-negative number. Absolute value is denoted by two vertical bars surrounding the number; for example, the absolute value of -2 is written as \( |{-2}| \).

To understand integer addition involving both positive and negative numbers, recognizing the concept of absolute value is crucial. This is because when these numbers are added, you essentially compare their distances from zero. The number with the larger absolute value dictates the direction of the result. So, when adding 18 and -2, the absolute value of 18 is 18, and the absolute value of -2 is 2. Since 18 is larger, the final answer retains the sign of 18, which is positive, resulting in 16.