Represent fractions using area models

An area model represents a fraction by partitioning one or more wholes into equal-area parts: the denominator names the total number of equal parts in each whole, and the numerator names the parts represented or shaded. The model can show proper fractions, mixed numbers, and fractions greater than one across multiple wholes, while making equivalence visible when parts are subdivided without changing the total area; unequal partitions do not provide a valid fraction model.

Detailed Explanation: Represent fractions using area models

An area model shows a fraction by dividing a whole into equal-area parts.

The denominator tells how many equal parts are in each whole.
The numerator tells how many parts are shaded or represented.

Example: Represent $\frac{7}{4}$ with an area model

Step 1: Look at the denominator.
The denominator is $4$ , so divide each whole into $4$ equal parts.

Step 2: Look at the numerator.
The numerator is $7$ , so shade $7$ of the equal parts.

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

Each rectangle is one whole. The first whole has $4$ shaded parts, and the second whole has $3$ shaded parts.

So there are $7$ shaded parts total, with $4$ equal parts in each whole:

\frac{7}{4}=1\frac{3}{4}.

Make sure every part in a whole has the same area. Unequal parts would not make a correct area model.

Learn by doing: Represent fractions using area models

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Fraction Concept Intro - Fraction to Picture, Mixed Fraction

Earned ?