Model Fraction Multiplication with Area Models

Property To model the multiplication of a whole number $c$ and a fraction $\frac{a}{b}$, you can use area models. Draw $c$ identical shapes, each divided into $b$ equal parts. Then, shade $a$ parts in each of the $c$ shapes to represent the product $c \times \frac{a}{b}$.

Examples To model $3 \times \frac{2}{5}$, draw 3 rectangles, each divided into 5 equal parts. In each of the 3 rectangles, shade 2 parts. Counting the total shaded parts gives $\frac{6}{5}$. To model $4 \times \frac{1}{3}$, draw 4 circles, each divided into 3 equal parts. In each of the 4 circles, shade 1 part. The total shaded area represents $\frac{4}{3}$.

Explanation Using area models helps visualize multiplying a fraction by a whole number. This method connects the idea of repeated addition to a visual representation. By drawing the whole number of groups and shading the fractional amount in each, you can count the total number of shaded parts to find the resulting fraction. This provides a concrete way to understand why you multiply the whole number by the numerator.