Question

use a model to divide by a fraction.
$5 \div \frac{1}{2} = 10$

Explanation:

Step1: Interpret the number line model

The number line spans 0 to 5, and each whole number (1,2,3,4,5) is split into 2 equal parts, each representing $\frac{1}{2}$.

Step2: Count total $\frac{1}{2}$ segments

Each whole has 2 segments, so for 5 wholes: $5 \times 2 = 10$. This matches $5 \div \frac{1}{2}$, since dividing by a fraction is multiplying by its reciprocal: $5 \times \frac{2}{1} = 10$.

Answer:

The model confirms that $5 \div \frac{1}{2} = 10$, as the 5-unit length is divided into 10 equal $\frac{1}{2}$-unit segments.