To solve the expression \( 6 \times \left(\frac{1}{3}\right)^2 - 17 \times \frac{1}{3} \), let's break it down step by step.
Calculate \(\left(\frac{1}{3}\right)^2\): \[ \left(\frac{1}{3}\right)^2 = \frac{1}{9} \]
Now, substitute \(\frac{1}{9}\) into the expression: \[ 6 \times \frac{1}{9} - 17 \times \frac{1}{3} \]
Calculate \(6 \times \frac{1}{9}\): \[ 6 \times \frac{1}{9} = \frac{6}{9} = \frac{2}{3} \]
Calculate \(17 \times \frac{1}{3}\): \[ 17 \times \frac{1}{3} = \frac{17}{3} \]
Now, we have: \[ \frac{2}{3} - \frac{17}{3} \]
Since both fractions have the same denominator, we can subtract them: \[ \frac{2 - 17}{3} = \frac{-15}{3} = -5 \]
Thus, the final result is: \[ \boxed{-5} \]
