Four friends are sharing a pizza. One friend eats half of the pizza. The other three friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?
A.
1/5
B.
1/3
C.
¼
D.
1/6
The Correct Answer and Explanation is :
The correct answer is D. 1/6.
Explanation:
To solve this problem, let’s break it down step-by-step:
- Determine the portion of the pizza eaten by the first friend:
- The first friend eats half of the pizza. In fraction form, this is represented as 12\frac{1}{2}21.
- Calculate the remaining portion of the pizza:
- Since the entire pizza is considered to be 1 (or 11\frac{1}{1}11), if half of it is eaten by the first friend, the remaining portion of the pizza is: 1−12=121 – \frac{1}{2} = \frac{1}{2}1−21=21
- Divide the remaining portion among the other three friends:
- The remaining 12\frac{1}{2}21 of the pizza needs to be equally divided among the three remaining friends. To find out what portion each of these three friends receives, we need to divide 12\frac{1}{2}21 by 3. In mathematical terms, this can be represented as: 123\frac{\frac{1}{2}}{3}321
- To divide a fraction by a whole number, you multiply the fraction by the reciprocal of that number. The reciprocal of 3 is 13\frac{1}{3}31. Therefore: 12×13=1×12×3=16\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}21×31=2×31×1=61
- Verify the result:
- Each of the three friends will receive 16\frac{1}{6}61 of the pizza. To check this, you can multiply the portion each friend gets by the number of friends: 3×16=36=123 \times \frac{1}{6} = \frac{3}{6} = \frac{1}{2}3×61=63=21
- This confirms that the division of the remaining 12\frac{1}{2}21 of the pizza among three friends is correct, as it sums up to the remaining portion of the pizza.
Thus, each of the other three friends receives 16\frac{1}{6}61 of the pizza, which is option D.