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Understanding negative numbers is crucial in mathematics and everyday life. Mathematically, a negative number is a real number that is less than zero. Symbolized with a '-' sign, it represents quantities such as loss, decrease, or below a reference level, like sea level for altitude. Conceiving negative numbers can be challenging, but with a fundamental idea, you can simplify complex problems.

In the exercise, we deal with both positive and negative numbers. Picture negative numbers as you would money you owe while positive numbers are money you have; adding negative numbers effectively subtracts from your total wealth. Remember that when a number has no sign, it's usually positive by default.

Arithmetic is the branch of mathematics that deals with numbers and the traditional operations among them: addition, subtraction, multiplication, and division. When adding negative numbers, we're using the arithmetic concept that adding a negative is the same as subtracting its positive counterpart.

For example, in the expression from the exercise, when we add \( -2 \) to 7, we actually subtract 2 from 7, making it simpler to calculate. These operations follow rules and properties that make them predictable and manageable. Being comfortable with these operations helps in progressing to more complex math levels.

Algebra is the branch of mathematics concerning the study of the rules of operations and relations. In basic algebra, we work with variables and constants to represent numbers and quantities in formulae and equations. Addition of negative numbers appears frequently in algebraic equations.

However, in the context of the given exercise, we used fundamental algebraic principles to simplify and solve an arithmetic problem. Understanding how to combine like terms and simplify expressions is integral in algebra. Indeed, when we simplified the expression \(7-2-8\), we were applying these basic principles. Mastering such operations lays the groundwork for more advanced algebraic concepts.