Identify equal parts of a whole

A whole is divided into equal parts when every part has the same area, even if the parts differ in shape; unequal-looking regions may still be equal shares, while equal numbers of pieces do not guarantee equal parts. This understanding supports interpreting halves, thirds, fourths, sixths, and eighths as unit fractions and as portions of a whole in area models and number lines, without extending to unlike-fraction comparison or improper fractions.

Detailed Explanation: Identify equal parts of a whole

To identify equal parts of a whole, check whether each part has the same area. The parts can have different shapes and still be equal shares.

Suppose this square is divided into small equal squares. Each letter shows one part:

\begin{array}{|c|c|c|c|} \hline A&A&B&B\\ \hline A&A&B&C\\ \hline D&D&B&C\\ \hline D&D&C&C\\ \hline \end{array}

Step 1: Count the parts

There are $4$ parts: $A$ , $B$ , $C$ , and $D$ .

Step 2: Count the small squares in each part

Part $A$ has $4$ small squares.
Part $B$ has $4$ small squares.
Part $C$ has $4$ small squares.
Part $D$ has $4$ small squares.

Each small square has the same area, so all four parts have the same area.

Step 3: Name the equal parts

The whole is divided into $4$ equal parts. Each part is one-fourth, written as

\frac{1}{4}.

Even though the parts do not all look the same, they are equal because they cover the same amount of area.

Learn by doing: Identify equal parts of a whole

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Fraction Equal Parts - Which Has X Equal Parts - Different Shape

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