Question

use the area model to show how the larger unit is composed. then label the equivalent fraction. express each equivalence by using division.
1.
\\(\frac{2}{8} = \frac{2\div2}{8\div2} = \frac{\square}{\square}\\)
2.

Explanation:

Step1: Simplify the first fraction

$\frac{2}{8} = \frac{2\div2}{8\div2} = \frac{1}{4}$
Label the area model: The shaded 2 out of 8 parts can be grouped into 1 out of 4 equal larger units, so label the equivalent fraction $\frac{1}{4}$.

Step2: Analyze the second area model

The model has 5 shaded parts out of 10 total. Simplify $\frac{5}{10}$:
$\frac{5}{10} = \frac{5\div5}{10\div5} = \frac{1}{2}$
Label the area model: The shaded 5 out of 10 parts can be grouped into 1 out of 2 equal larger units, so label the equivalent fraction $\frac{1}{2}$.

Answer:

1. Simplified fraction: $\frac{1}{4}$; Label for the first model: $\frac{1}{4}$
2. Simplified fraction: $\frac{1}{2}$; Label for the second model: $\frac{1}{2}$