To solve [tex]\( 5 \frac{1}{6} \cdot \left(-\frac{2}{5}\right) \)[/tex], follow these steps:
1. Convert the mixed number to an improper fraction:
- The mixed number [tex]\(5 \frac{1}{6}\)[/tex] can be converted by multiplying the whole number part by the denominator and adding the numerator.
- [tex]\(5 \frac{1}{6} = \frac{5 \cdot 6 + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6}\)[/tex].
2. Recognize the other fraction to be multiplied:
- The second fraction is [tex]\(-\frac{2}{5}\)[/tex].
3. Multiply the fractions:
- Multiply the numerators and the denominators: [tex]\(\frac{31}{6} \cdot \left(-\frac{2}{5}\right) = \frac{31 \cdot (-2)}{6 \cdot 5} = \frac{-62}{30}\)[/tex].
4. Simplify the resulting fraction, if possible:
- The fraction [tex]\(\frac{-62}{30}\)[/tex] simplifies by finding the greatest common divisor (GCD) of 62 and 30, which is 2.
- Divide both the numerator and the denominator by 2: [tex]\(\frac{-62 \div 2}{30 \div 2} = \frac{-31}{15}\)[/tex].
So, the answer is:
[tex]\[
\boxed{-31/15}
\][/tex]
