To convert the fraction \( \frac{15}{82} \) into a mixed number, we first check if the numerator (15) is larger than the denominator (82). Since 15 is less than 82, we can see that this fraction is less than 1, and therefore it cannot be expressed as a mixed number with a whole number part.
In this case, \( \frac{15}{82} \) is already in its simplest form. So, as a mixed number, it can be represented simply as:
\( 0 \frac{15}{82} \)
However, since mixed numbers typically represent numbers greater than or equal to 1, the answer in simplest terms remains as \( \frac{15}{82} \).
If you are looking to express it in a different way, it stays as an improper fraction \( \frac{15}{82} \), since it does not transform into a traditional mixed number.