Lesson 3: Multiplying Fractions Using Area Models

Property

Multiplying two fractions, $\frac{a}{b} \times \frac{c}{d}$, is equivalent to finding a part of a part, or $\frac{a}{b}$ of $\frac{c}{d}$.
An area model visualizes this by partitioning a whole into $b \times d$ smaller rectangles.
The product is the fraction of the whole that is represented by the $a \times c$ double-shaded area.

Examples

Property

To multiply two fractions, we can find a "fraction of a fraction." An area model visualizes this by representing the first fraction with vertical divisions and the second fraction with horizontal divisions. The product is the area where the shaded parts of both fractions overlap.

Examples