5. Mrs. Washer filled the gas tank of her car. She used \( \frac{2}{3} \) of a tank of gasoline while driving to the beach. She used another \( \frac{1}{6} \) of the tank driving to her hotel. How much gasoline is left in the tank?

To find out how much gasoline is left in Mrs. Washer's tank, we first need to add the fractions she used for both trips. She used \( \frac{2}{3} \) of a tank to the beach and \( \frac{1}{6} \) of a tank to the hotel. To add these fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. Convert \( \frac{2}{3} \) to a fraction with a denominator of 6: \[ \frac{2}{3} = \frac{4}{6} \] Now add \( \frac{4}{6} + \frac{1}{6} = \frac{5}{6} \). Since Mrs. Washer started with a full tank (1 tank = \( \frac{6}{6} \)), we subtract the amount used from the full tank: \[ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} \] So, the amount of gasoline left in the tank is \( \frac{1}{6} \) of a tank.