Represent fractions with area models

An area model represents a fraction of a whole by partitioning a shape into equal-area parts: the denominator names the total number of equal parts, and the numerator names how many parts are selected. The representation connects unit fractions, such as $1/4$ , to larger fractions with the same denominator and makes clear that unequal regions do not form valid fractional parts; the scope is fractions from 0 to 1, not mixed numbers or more advanced generalizations.

Detailed Explanation: Represent fractions with area models

Start with the denominator. It tells how many equal-area parts the whole must have.

Then use the numerator. It tells how many of those parts to select or shade.

Example: Represent $\frac{3}{4}$ with an area model

Draw one rectangle to represent the whole.
The denominator is $4$ , so divide the rectangle into 4 equal-area parts.

\begin{array}{|c|c|c|c|} \hline & & & \\ \hline \end{array}

The numerator is $3$ , so shade 3 of the 4 parts.

\begin{array}{|c|c|c|c|} \hline \blacksquare & \blacksquare & \blacksquare & \square \\ \hline \end{array}

The model shows $\frac{3}{4}$ because:

There are $4$ equal parts in the whole.
$3$ parts are shaded.

The parts must be equal in area. If one part were larger or smaller than the others, the model would not correctly represent fourths.

Learn by doing: Represent fractions with area models

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Fraction Concept Intro - Fraction to Picture, Mixed Fraction

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