When John partitions the three circles into equal parts, he is dividing each circle into smaller segments. The size of each part will depend on the total number of parts he creates.
For example, if John has three circles and initially divides each circle into 2 equal parts, he will have a total of \(3 \times 2 = 6\) parts. Each part will represent \( \frac{1}{6} \) of the total area of the three circles.
If he then decides to partition the same three circles into more equal parts, such as dividing each circle into 4 equal parts, he will have a total of \(3 \times 4 = 12\) parts. Each part will now represent \( \frac{1}{12} \) of the total area of the three circles.
As we can see from these examples, when the whole (in this case, the area of the three circles) is partitioned into more equal parts, the size of each part decreases. This is because the total area is being divided into a greater number of smaller segments. Thus, as the number of parts increases, the size of each individual part becomes smaller.
In mathematical terms, if the whole is partitioned into \( n \) equal parts, the size of each part is \( \frac{1}{n} \) of the whole. Therefore, increasing \( n \) leads to a smaller size for each part.
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