At the cars in a used car lot 2/5 are the color gray 1/3 of the gray cars are electrically powered vehicles what fraction of the cars on the lot are both gray and electrically powered leave your answer in a simplified fraction form

Answer 1

To find the fraction of cars in the lot that are both gray and electrically powered, we can follow these steps:

1. Identify the fraction of gray cars: According to the problem, \( \frac{2}{5} \) of the cars are gray.
2. Identify the fraction of gray cars that are electrically powered: We know that \( \frac{1}{3} \) of the gray cars are electrically powered.

Now, we will calculate the fraction of the total cars that are both gray and electrically powered by multiplying the two fractions:

\[ \text{Fraction of gray and electrically powered cars} = \text{Fraction of gray cars} \times \text{Fraction of gray cars that are electrically powered} \]

\[ = \frac{2}{5} \times \frac{1}{3} \]

Next, we multiply the numerators and denominators:

\[ = \frac{2 \times 1}{5 \times 3} = \frac{2}{15} \]

Thus, the fraction of the cars on the lot that are both gray and electrically powered is \(\frac{2}{15}\).