For a school event, 1/6 of the athletic field is reserved for the fifth grade classes. The reserved part of the field is divided equally among the 4 fifth grade classes in the school. What fraction of the whole athletic field is reserved for each fifth grade class? OPTIONS: 2/3. 1/101/243/2
The correct answer and explanation is:
Let’s analyze the problem step by step:
Problem Recap:
- 1/6 of the athletic field is reserved for all the fifth grade classes combined.
- There are 4 fifth grade classes.
- The reserved part (1/6 of the field) is divided equally among these 4 classes.
- We need to find the fraction of the whole athletic field that is reserved for each fifth grade class.
Step 1: Understand what 1/6 represents
- The total field is 1 whole unit.
- The fifth grade classes get 1/6 of the whole field.
Step 2: Divide the 1/6 equally among 4 classes
- Since the reserved 1/6 is shared equally, each class gets: 16÷4=16×14=124\frac{1}{6} \div 4 = \frac{1}{6} \times \frac{1}{4} = \frac{1}{24}
Step 3: Interpret the result
- Each fifth grade class is allocated 1/24 of the entire athletic field.
Step 4: Compare with the provided options:
- 2/3
- 1/10
- 1/24
- 3/2
Clearly, 1/24 matches the calculation.
Explanation Summary (300 words):
The problem involves dividing a portion of the athletic field equally among a number of classes. First, we identify that the total field is considered as 1 whole unit. The fifth grade classes collectively are allocated 1/6 of this whole field. This fraction means that the fifth graders, as a group, have access to one-sixth of the total area of the field.
Since this portion (1/6) is shared equally among 4 fifth grade classes, we need to split this fraction into 4 equal parts. When dividing a fraction by a whole number, the operation is equivalent to multiplying the fraction by the reciprocal of the whole number. Here, dividing 1/6 by 4 means multiplying 1/6 by 1/4: 16÷4=16×14=124\frac{1}{6} \div 4 = \frac{1}{6} \times \frac{1}{4} = \frac{1}{24}
This result means each fifth grade class receives one twenty-fourth of the entire field. This fraction is smaller than the original 1/6 portion because the reserved area is divided into four smaller equal parts.
The options given include 2/3, 1/10, 1/24, and 3/2. The only fraction that fits the calculation correctly is 1/24.
Thus, the fraction of the whole athletic field reserved for each fifth grade class is 1/24.