Let's start by breaking down the problem and performing the subtraction step-by-step.
First, we need to convert the mixed number [tex]\(-3 \frac{3}{8}\)[/tex] into an improper fraction. To do this:
1. Multiply the whole number part by the denominator of the fractional part: [tex]\(-3 \times 8 = -24\)[/tex].
2. Add the numerator of the fractional part: [tex]\(-24 + (-3) = -27\)[/tex].
So, [tex]\(-3 \frac{3}{8}\)[/tex] as an improper fraction is [tex]\(\frac{-27}{8}\)[/tex].
Next, we need to subtract the fraction [tex]\(\frac{-7}{8}\)[/tex] from [tex]\(\frac{-27}{8}\)[/tex]. Since the fractions have the same denominator, we can subtract the numerators directly while keeping the same denominator.
[tex]\[
\frac{-27}{8} - \frac{-7}{8} = \frac{-27 - (-7)}{8}
\][/tex]
Simplify the subtraction in the numerator:
[tex]\[
-27 - (-7) = -27 + 7 = -20
\][/tex]
So, the resulting fraction is:
[tex]\[
\frac{-20}{8}
\][/tex]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{-20 \div 4}{8 \div 4} = \frac{-5}{2}
\][/tex]
Therefore, the simplified fraction is:
[tex]\[
\boxed{\frac{-5}{2}}
\][/tex]
