Answer :

Let's simplify the expression [tex]\(-\frac{31}{5}\)[/tex].

First, we need to convert the improper fraction [tex]\(-\frac{31}{5}\)[/tex] into a mixed number.

1. Determine the whole number part by performing the division of the numerator by the denominator:
[tex]\[ -31 \div 5 = -7 \][/tex]
This gives us [tex]\(-7\)[/tex] as the integer part of the mixed number since [tex]\(-31\)[/tex] divided by [tex]\(5\)[/tex] results in [tex]\(-7\)[/tex] with a remainder.

2. Calculate the remainder of the division:
[tex]\[ -31 \mod 5 = 4 \][/tex]
This tells us that when [tex]\(-31\)[/tex] is divided by [tex]\(5\)[/tex], the remainder is [tex]\(4\)[/tex].

3. Now, put together the whole number part with the fraction formed by the remainder over the original denominator:
[tex]\[ -\frac{31}{5} = -7 \frac{4}{5} \][/tex]

Thus, [tex]\(-\frac{31}{5}\)[/tex], when expressed as a mixed number, is [tex]\(-7 \frac{4}{5}\)[/tex].