Final answer:
To determine the total number of pieces in the full pie, we set up the proportion 2/3 = 6/x and solve for x, finding that the full pie has 9 pieces.
Step-by-step explanation:
The question you've asked pertains to determining the total number of pieces in a full pie when you know the number of pieces that represent a certain fraction of that pie. To solve this, we use the concept of proportions.
If 2/3 of the pie equals 6 pieces, we can set up a proportion where x represents the total number of pieces in the full pie. The proportion will therefore be 2/3 = 6/x. To find the value of x, we cross-multiply and divide.
Step-by-step solution:
2/3 = 6/x (this is our original proportion)
2x = 18 (cross-multiplying gives us this equation, 3 * 6 = 2 * x)
x = 9 (dividing both sides by 2, we get the total number of pieces)
Thus, when the pie is full, it has 9 pieces.