Question

1. consider the equation.

$\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$
which model represents the equation?
images of models a, b, c, d (grid models with shaded regions)

Explanation:

Answer:

To solve the problem, we analyze the equation \(\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}\) and the models:

Step 1: Interpret the first fraction (\(\frac{1}{4}\))

The equation starts with \(\frac{1}{4}\). Visually, this means dividing a whole into 4 equal parts and shading 1 part. Looking at the models, the top row of each option (A, B, C, D) shows the first fraction. For \(\frac{1}{4}\), we need 1 out of 4 parts shaded.

Step 2: Interpret the multiplication by \(\frac{1}{2}\)

Multiplying by \(\frac{1}{2}\) means taking the shaded part from the first step (\(\frac{1}{4}\) of the whole) and dividing it by 2 (or shading \(\frac{1}{2}\) of the already shaded \(\frac{1}{4}\) region).

Step 3: Analyze each option

• Option A: The top row has 1 out of 4 parts shaded (representing \(\frac{1}{4}\)). The bottom row (or the "second layer" of shading) takes that 1 shaded part and shades \(\frac{1}{2}\) of it (since the shaded region in the top is split into 2, and 1 is shaded). This matches \(\frac{1}{4}\times\frac{1}{2}\): \(\frac{1}{4}\) of the whole, then \(\frac{1}{2}\) of that \(\frac{1}{4}\) region.
• Option B: The top row shades 2 out of 4 parts (representing \(\frac{2}{4}=\frac{1}{2}\)), not \(\frac{1}{4}\). Eliminate B.
• Option C: The top row shades 3 out of 4 parts (representing \(\frac{3}{4}\)), not \(\frac{1}{4}\). Eliminate C.
• Option D: The top row shades 4 out of 4 parts (representing \(1\)), not \(\frac{1}{4}\). Eliminate D.

Thus, the model that represents \(\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}\) is A.

(Note: If the final answer is the option letter, the answer is "A".)