Question

build a model to show \\(\frac{4}{9} \times 2\\).

Explanation:

Step1: Rewrite integer as fraction

$2 = \frac{2}{1}$

Step2: Multiply numerators and denominators

$\frac{4}{9} \times \frac{2}{1} = \frac{4 \times 2}{9 \times 1} = \frac{8}{9}$

Step3: Model explanation

To model this:

1. Divide the number line from 0 to 2 into 9 equal segments per whole (so 18 total segments for 2 wholes).
2. Each $\frac{4}{9}$ is 4 segments. Mark 4 segments for the first $\frac{4}{9}$, then another 4 segments for the second $\frac{4}{9}$.
3. The total marked length is 8 segments, which equals $\frac{8}{9}$.

Answer:

$\frac{8}{9}$