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Integer operations are an essential aspect of arithmetic, and understanding them helps in solving a variety of mathematical problems. Integers include all positive and negative whole numbers, along with zero. They do not have fractional or decimal parts. These numbers support various operations, such as addition, subtraction, multiplication, and division.

When dealing with integer operations, it's crucial to follow the rules for each type of operation, ensuring you correctly calculate the outcome. For instance, when adding two integers, if both integers are positive, the result is positive. If both are negative, the outcome is negative. However, if one is positive and the other is negative, the result will take the sign of the larger absolute value. This basic understanding lays the groundwork for more complicated expressions involving integers.

Evaluating an expression means calculating its value. When you evaluate an arithmetic expression, you replace variables with numbers and perform the operations in specific steps. This process requires a solid understanding of mathematical operations and the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

In the given exercise, absolute value is a crucial component. It refers to the distance of a number from zero, without considering the direction on the number line. For instance, the absolute value of both 15 and -1 is 15 and 1, respectively, because distance is always positive. After replacing each absolute value in the expression, further operations like subtraction can take place. Careful step-by-step evaluation is vital for an accurate result.

Subtraction is one of the fundamental operations in arithmetic, and it involves taking away a number from another. In our evaluated expression, subtraction follows the calculation of absolute values: from the expression |15| - |-1|, we substitute and simplify it to 15 - 1.

A useful way to comprehend subtraction is to think of it as the addition of a negative. For example, calculating 15 - 1 is the same as adding 15 and -1 together. Understanding this can demystify seemingly complex expressions.

Furthermore, subtraction uses the concept of a number line, where moving left represents subtraction, and moving right signifies addition. By using this method, we can visualize how subtraction affects an expression and simplifies computations.