The Correct Answer and Explanation is:
The correct answer is -7.92.
In mathematics, the “opposite” of a number is its additive inverse. This concept is best visualized using a number line, where zero sits at the center. Positive numbers are located to the right of zero, and negative numbers are to the left. A number’s opposite is the value that is the exact same distance from zero but on the contrary side. The number 7.92 is a positive value, so it is located 7.92 units to the right of zero. To find its opposite, we must look for the number that is 7.92 units to the left of zero. This position on the number line corresponds to -7.92. Thus, 7.92 and -7.92 are opposites because they are equidistant from zero.
The more formal way to understand this is through the principle of the additive inverse. The additive inverse of a number is the value you must add to it to get a sum of zero. This is a fundamental property in arithmetic and algebra. For the given problem, we are looking for a number that, when added to 7.92, results in zero. We can set up a simple equation: 7.92 + x = 0. To solve for x, we would subtract 7.92 from both sides, revealing that x = -7.92. This calculation confirms that -7.92 is the additive inverse of 7.92.
The practical rule for finding the opposite of any number is to simply change its sign. If a number is positive, you make it negative. If a number is negative, you make it positive. The number in the question, 7.92, is positive. Therefore, to find its opposite, we just place a negative sign in front of it. The magnitude, or absolute value, of the number remains unchanged. The question asks for the answer to be written as a decimal, and -7.92 is the correct decimal representation of the opposite of 7.92.
