Lesson 6

As in previous lessons, students represent a product of fractions with a diagram. This diagram represents the product \(\frac{3}{6} \times \frac{4}{5}\). The diagram shows \(\frac{3}{6}\) of \(\frac{4}{5}\) of the square so that’s \(\frac{3}{6}  \times \frac{4}{5}\). The number of shaded pieces is \(3 \times 4\), the product of the numerators. The number of pieces in the whole square is \(6 \times 5\), the product of the denominators. So the value of the product can also be written as \(\frac{3 \times 4}{6 \times 5}\). In the first activity, students relate expressions to the area in diagrams like this and then they use this structure to find products of non-unit fractions in the second activity.