To express [tex]\( 105 / 12 \)[/tex] as an equivalent improper fraction, follow these steps:
1. Identify the numerator and the denominator of the fraction. In this case, the numerator is [tex]\( 105 \)[/tex] and the denominator is [tex]\( 12 \)[/tex].
2. Since the fraction is already given as [tex]\( 105 / 12 \)[/tex], this is indeed an improper fraction because the numerator (105) is greater than the denominator (12).
3. Verify that the simplest form of the fraction [tex]\( 105 / 12 \)[/tex] exactly matches the given numerator and denominator without further need for reduction.
The equivalent improper fraction is:
[tex]\[ \frac{105}{12} \][/tex]
None of the provided options in the question ([tex]\( 12/125, 125/12, 120/12, 10^{12}/5 \)[/tex]) match this fraction. Therefore, the correct answer is:
[tex]\[ \boxed{105/12} \][/tex]
