Question

which statement would be the most important in explaining why $\frac{2}{3}=\frac{6}{9}$?

Explanation:

Step1: Recall fraction equivalence rule

A fraction is equivalent if we multiply numerator and denominator by the same non-zero number.

Step2: Apply rule to $\frac{2}{3}$

Multiply numerator and denominator by 3: $\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$

Step3: Connect to the visual model

The grid has 9 total squares. $\frac{2}{3}$ means $\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$, so 6 out of 9 shaded squares match $\frac{6}{9}$, which is the same proportion as $\frac{2}{3}$.

Answer:

The most important statement is: If you multiply both the numerator and denominator of $\frac{2}{3}$ by 3, you get $\frac{6}{9}$, and the grid shows 6 out of 9 squares shaded, representing the same proportional value.