Find the Opposite Number: Converting -7/15 to Its Additive Inverse

Convert $-\frac{7}{15}$into its reciprocal form:

To solve this problem, we'll follow these clear steps:

• Step 1: Understand the term "opposite number," which is the additive inverse in the context of signed numbers. This means if a number is $a$, the opposite is $-a$.
• Step 2: The number provided is $-\frac{7}{15}$. According to the definition of the additive inverse, its opposite is $-(-\frac{7}{15})$.
• Step 3: Apply the rule of double negatives, which states that $-(-a) = a$. Thus, the opposite of $-\frac{7}{15}$ is $\frac{7}{15}$.

Now, let us examine the provided answer choices and identify the correct one:

• Choice 1: $-1\frac{6}{7}$ - This is not $\frac{7}{15}$.
• Choice 2: $-2\frac{1}{7}$ - This is not $\frac{7}{15}$.
• Choice 3: $1\frac{7}{15}$ is a form that can be checked by converting to an improper fraction.
• Choice 4: $1\frac{6}{7}$ - This is not $\frac{7}{15}$.

To further verify the form, convert $1\frac{7}{15}$ to an improper fraction: $1\frac{7}{15} = \frac{15}{15} + \frac{7}{15} = \frac{22}{15}$.

Therefore, none of the provided choices corresponds to $\frac{7}{15}$. It seems there may be an error in the provided answer choices as they do not match the expected opposite of $-\frac{7}{15}$.

Consequently, it appears there was a misunderstanding in interpreting the problem context, as the provided solution requires validation against the conventional understanding of "opposite" in signed number arithmetic.

Therefore, the solution to the problem, identifying the opposite number as the additive inverse, logically leads to verifying $\frac{7}{15}$, notwithstanding the provided solution mismatch.