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Partition shapes into smaller shapes

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.

Detailed Explanation: Partition shapes into smaller shapes

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.

  1. Imagine the rectangle is 88 squares long and 44 squares wide.
  2. Divide the long side into 44 equal sections. Each section is 22 squares long.
  3. Draw a line from top to bottom at each section mark.

Now the rectangle is divided into 44 smaller rectangles:

8×4=32 square units8 \times 4 = 32 \text{ square units}

Each smaller rectangle has area:

2×4=8 square units2 \times 4 = 8 \text{ square units}

All 44 parts have the same area, and together they cover the whole rectangle. Therefore, each part is called one-fourth, or 14\frac14, of the rectangle.

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Fractions Thirds - Which Shows One Third


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