Question

which visual fraction model correctly shows the shaded region for the expression \\(\frac{1}{2} \div 6\\)? a. image of a rectangle divided into 12 small squares, 1 shaded b. image of a rectangle divided into 6 small rectangles, 1 shaded c. image of a rectangle divided into 6 small rectangles, 3 shaded d. image of a rectangle divided into 12 small squares, 6 shaded

Explanation:

Step1: Understand the division of fractions

To model \(\frac{1}{2}\div6\), we first represent \(\frac{1}{2}\) and then divide it into 6 equal parts. Mathematically, \(\frac{1}{2}\div6=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}\), but visually, we can also think of dividing the \(\frac{1}{2}\) region into 6 parts.

Step2: Analyze each option

• Option A: The total number of small rectangles is 12 (2 rows of 6). The shaded part is 1, which is \(\frac{1}{12}\), but let's check the process. Wait, actually, when we divide \(\frac{1}{2}\) by 6, we first take \(\frac{1}{2}\) (which could be a row of 6, so \(\frac{1}{2}\) of the total 12 is 6, i.e., one row). Then dividing that row (6 units) into 6 parts, each part is 1 unit. But in option A, the shaded is 1 in 12, but let's re - evaluate.
• Option B: The figure has 6 rectangles in a row. If we consider the \(\frac{1}{2}\) of the whole (assuming the whole is 12, but here it's a single row of 6, maybe the \(\frac{1}{2}\) is this row? Wait, no. Wait, \(\frac{1}{2}\div6\) means we take \(\frac{1}{2}\) of a whole and then divide it into 6 equal parts. Let's think of the whole as a rectangle. First, shade \(\frac{1}{2}\) of it (for example, a row of 6, so \(\frac{1}{2}\) of a 2 - row rectangle is 6). Then divide that 6 - unit region into 6 parts, so each part is 1 unit. Option B shows a single row of 6, with 1 shaded, which represents taking \(\frac{1}{2}\) (the row) and dividing by 6 (so 1 part out of 6 in the \(\frac{1}{2}\) region).
• Option C: Shaded 3 out of 6, which is \(\frac{3}{6}=\frac{1}{2}\), not related to \(\frac{1}{2}\div6\).
• Option D: Shaded 6 out of 12, which is \(\frac{6}{12}=\frac{1}{2}\), not related to the division result.

So the correct visual model is Option B.

Answer:

B. The visual fraction model with one shaded rectangle out of six in a row (the second option)