To solve [tex]\( 5 \frac{1}{6} \cdot \left( -\frac{2}{5} \right) \)[/tex]:
1. First, we need to convert the mixed number [tex]\( 5 \frac{1}{6} \)[/tex] into an improper fraction.
[tex]\[
5 \frac{1}{6} = \frac{5 \cdot 6 + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6}
\][/tex]
2. Next, we'll multiply this improper fraction by the negative fraction [tex]\(-\frac{2}{5}\)[/tex].
[tex]\[
\frac{31}{6} \cdot \left( -\frac{2}{5} \right)
\][/tex]
3. Multiply the numerators together and the denominators together:
[tex]\[
\frac{31 \cdot (-2)}{6 \cdot 5} = \frac{-62}{30}
\][/tex]
4. Simplify this fraction by finding the greatest common divisor of 62 and 30. The simplest form of [tex]\(\frac{-62}{30}\)[/tex] is [tex]\(\frac{-31}{15}\)[/tex].
So, the answer to [tex]\( 5 \frac{1}{6} \cdot \left( -\frac{2}{5} \right) \)[/tex] is:
[tex]\[
\frac{-31}{15}
\][/tex]
