Okay, let's solve the expression step by step.
We need to calculate \(10 \cdot \frac{1}{6}\).
Step 1: Multiply the whole number by the numerator of the fraction.
\(10 \cdot 1 = 10\)
Step 2: Keep the same denominator.
So we have \(\frac{10}{6}\).
Step 3: Simplify the fraction if possible. Both 10 and 6 are divisible by 2.
\(\frac{10 \div 2}{6 \div 2} = \frac{5}{3}\)
Step 4: Convert the improper fraction to a mixed number.
\(\frac{5}{3} = 1 \frac{2}{3}\)
So, \(10 \cdot \frac{1}{6} = \frac{5}{3} = 1 \frac{2}{3}\).
Final Answer: The final answer is \(\frac{5}{3}\) or \(1 \frac{2}{3}\).