Jess ate 1/4 of a pizza.Jack ate 1/3 of the same pizza.Dennis ate 1/2 of the same pizza.Explain and show with math if this is possible?
The pizza is cut into 12 slices.
Jess ate 3 slices (1/4 = 3/12).
Jack ate 4 slices (1/3 = 4/12).
Dennis ate 6 slices (1/2 = 6/12).
Add: 3+4+6 = ??
1/4 + 1/3 + 1/2 = 3/12 + 4/12 + 6/12 = 13/12 = 1 1/12. Impossible, because 13/12 is more than a whole pizza.
To determine if it is possible for Jess, Jack, and Dennis to have eaten fractions of the same pizza, we need to check if the sum of their fractions is equal to 1 (representing the whole pizza).
Let's calculate:
Jess ate 1/4 of the pizza.
Jack ate 1/3 of the pizza.
Dennis ate 1/2 of the pizza.
To find the total fraction of the pizza eaten, we add these fractions:
1/4 + 1/3 + 1/2 = (3/12) + (4/12) + (6/12) = 13/12
The total fraction eaten sums up to 13/12, which is greater than 1.
Since the sum of the fractions exceeds 1, it is not possible for Jess, Jack, and Dennis to have eaten fractions of the same pizza.
To determine if it is possible for Jess, Jack, and Dennis to have each eaten a portion of the same pizza, we need to calculate the total amount of pizza consumed.
First, let's assume that the pizza is divided into equal-sized portions.
Jess ate 1/4 of the pizza, so the remaining portion can be calculated using the fraction: 1 - 1/4 = 3/4.
Next, Jack ate 1/3 of the remaining pizza (3/4). To calculate the portion remaining after Jack's consumption, we multiply 3/4 by 1/3:
(3/4) * (1/3) = 3/12 = 1/4.
Lastly, Dennis ate 1/2 of the last remaining portion (1/4). Multiplying 1/4 by 1/2 gives us:
(1/4) * (1/2) = 1/8.
The final portion remaining after Dennis's consumption is 1/8 of the original pizza size.
Therefore, it is possible for Jess, Jack, and Dennis to have each eaten a portion of the same pizza, with a remaining portion of 1/8. The calculations demonstrate that the fractions consumed by each person add up correctly.