Of 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 simplified fraction form
Let's say there are a total of x cars on the lot.
Since 2/5 of them are gray, the number of gray cars is (2/5)x.
Out of the gray cars, 1/3 of them are electrically powered, so the fraction of gray and electric cars is (1/3)(2/5)x = (2/15)x.
Hence, the fraction of cars on the lot that are both gray and electrically powered is 2/15.
To find the fraction of cars on the lot that are both gray and electrically powered, we need to multiply the fraction of cars that are gray by the fraction of gray cars that are electrically powered.
Fraction of cars that are gray: 2/5
Fraction of gray cars that are electrically powered: 1/3
Multiplying these fractions, we get:
(2/5) * (1/3)
= 2/15
Therefore, the fraction of cars on the lot that are both gray and electrically powered is 2/15.
To find the fraction of cars on the lot that are both gray and electrically powered, we need to multiply the fractions representing the proportion of gray cars and the proportion of electrically powered cars among the gray cars.
Let's start with the fraction of gray cars. We are told that 2/5 of the cars on the lot are gray. So, if we let the total number of cars on the lot be represented by the variable "x," the number of gray cars would be (2/5)x.
Next, we need to find the fraction of electrically powered cars among the gray cars. We are told that 1/3 of the gray cars are electrically powered. So, if we multiply the number of gray cars by 1/3, we get (1/3) * (2/5)x = (2/15)x.
Therefore, the fraction of cars on the lot that are both gray and electrically powered is (2/15)x / x. Notice that the "x" cancels out, leaving us with the simplified fraction:
2/15
So, the fraction of cars on the lot that are both gray and electrically powered is 2/15.