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].
