The opposite of 8 is -8. In mathematics, the opposite of a number is its additive inverse, which when added to the original number results in zero. This concept is fundamental in arithmetic and is used in various mathematical operations and equations. The reason -8 is the opposite of 8 is due to the nature of addition and the concept of inverse elements in mathematics.

According to the definition of additive inverses, if a and b are two numbers such that a + b = 0, then b is the additive inverse of a, and vice versa. In the case of 8 and -8, when added together, they sum up to zero (8 + (-8) = 0). This principle is consistent across different number systems, including the real numbers, integers, and rational numbers.

Data from educational resources such as the National Council of Teachers of Mathematics (NCTM) and the Common Core State Standards for Mathematics confirm the importance of understanding additive inverses in the educational curriculum. For instance, the NCTM states that understanding the concept of additive inverses is crucial for students to develop a strong foundation in algebra and other advanced mathematical topics. The Common Core Standards emphasize the importance of students being able to identify and use additive inverses in various contexts, including solving equations and inequalities.

The concept of additive inverses extends beyond basic arithmetic and is foundational in more complex mathematical concepts. For example, in calculus, the derivative of a function can be defined using the concept of the limit and the difference quotient, which involves the additive inverse of the change in the independent variable. In linear algebra, the concept of additive inverses is used in the context of vector spaces and linear transformations.

In conclusion, the opposite of 8 is -8, and this is due to the mathematical principle of additive inverses. Understanding this concept is essential in various mathematical fields and is emphasized in educational standards and resources.