Question

which expression best represents the opposite of the opposite of $8\frac{1}{4}$?

Explanation:

Step1: Define the opposite of a number

The opposite of a number \( a \) is \( -a \). So, the opposite of \( 8\frac{1}{4} \) is \( -8\frac{1}{4} \).

Step2: Find the opposite of the result from Step1

Now, we need the opposite of \( -8\frac{1}{4} \). Using the definition of the opposite, the opposite of \( -8\frac{1}{4} \) is \( -(-8\frac{1}{4}) \). By the property of negatives, \( -(-x)=x \) for any real number \( x \), so \( -(-8\frac{1}{4}) = 8\frac{1}{4} \). This means the expression for the opposite of the opposite of \( 8\frac{1}{4} \) is \( -(-8\frac{1}{4}) \), which simplifies back to \( 8\frac{1}{4} \).

Answer:

The expression that best represents the opposite of the opposite of \( 8\frac{1}{4} \) is \( -(-8\frac{1}{4}) \) (which is equal to \( 8\frac{1}{4} \)). If we consider the general form, for a number \( n \), the opposite of the opposite of \( n \) is \( -(-n) \), so substituting \( n = 8\frac{1}{4} \), we get \( -(-8\frac{1}{4}) \).