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Partition shapes into fourths

A whole shape can be partitioned into four regions of equal area, with each region representing one fourth (¼) of the whole and the four fourths composing the whole. The regions may differ in shape or orientation, so equal shares depend on area rather than appearance; this understanding establishes unit fractions and supports comparing, composing, and representing fractions in later work.

Detailed Explanation: Partition shapes into fourths

To partition a shape into fourths, divide the whole shape into 4 regions with equal area.

Example: Partition a rectangle into fourths.

  1. Start with the whole rectangle.

  2. Draw a line straight down the middle. Now there are 2 equal parts.

  3. Draw a line straight across the middle. This makes 4 equal regions.

+-------+-------+
|       |       |
|       |       |
+-------+-------+
|       |       |
|       |       |
+-------+-------+
  1. Count the equal regions. There are 4 regions, so each region is one fourth, written as 14\frac{1}{4}.

The four fourths together make the whole rectangle:

14+14+14+14=1\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=1

Remember: The regions do not have to look exactly the same. They must have the same area.

Learn by doing: Partition shapes into fourths

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Fractions Fourths - Which Is Divided Evenly


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