Question

which model correctly shows the problem $\frac{2}{6} \times \frac{1}{5}$? (with four grid models as images)

Explanation:

Step1: Understand fraction multiplication model

To model $\frac{2}{6} \times \frac{1}{5}$, first identify a grid with $6$ rows (total rows) and $5$ columns (total columns), so total cells $6 \times 5 = 30$.

Step2: Highlight first fraction $\frac{2}{6}$

Shade $\frac{2}{6}$ of the grid: this means shading $2$ out of $6$ full rows. For 5 columns per row, that's $2 \times 5 = 10$ cells (the pink shaded area in the correct model).

Step3: Highlight second fraction $\frac{1}{5}$

Now, shade $\frac{1}{5}$ of the already shaded pink area. This means shading $1$ out of $5$ columns within the 2 pink rows, which is $2 \times 1 = 2$ cells (the overlapping purple area in the correct model).

Step4: Match to the correct grid

The top-most grid has 2 full rows (10 cells) shaded pink, and 1 column within those 2 rows (2 cells) shaded purple, which matches $\frac{2}{6} \times \frac{1}{5}$.

Answer:

The top-most grid (first model, with 2 full pink rows and 1 purple column in those rows) correctly shows $\frac{2}{6} \times \frac{1}{5}$.