Partitioning a shape means dividing a single whole, such as a rectangle or circle, into two, three, or four parts of equal area and identifying the parts as halves, thirds, or fourths. The parts must cover the whole without gaps or overlaps, but equal parts need not have the same shape or orientation; more complex fractional partitions and generalized area relationships are outside this scope.
To partition a shape, divide the whole shape into equal-area parts. The parts must fit together with no gaps or overlaps.
Example: Partition a rectangle into fourths.
Now the rectangle is divided into smaller rectangles:
Each smaller rectangle has area:
All parts have the same area, and together they cover the whole rectangle. Therefore, each part is called one-fourth, or , of the rectangle.
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