Let x be the capacity of the tank in gallons. We know that 12 gallons fill the tank to 2/3 capacity, so we can set up the following equation:
12 = (2/3)x
To solve for x, we can multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:
12 * (3/2) = x
Simplifying the left side of the equation, we get:
18 = x
Therefore, the capacity of the tank is 18 gallons.
To write out the division problem, we can divide both sides of the equation by 2/3:
12 ÷ (2/3) = x
Simplifying the right side of the equation by multiplying by the reciprocal of 2/3, we get:
12 * (3/2) = x
Dividing 12 by 2/3 is the same as multiplying 12 by the reciprocal of 2/3, which is 3/2:
12 ÷ (2/3) = 12 * (3/2) = 18
Therefore, the division problem is:
12 ÷ (2/3) = 18