To find the fraction used to divide \( \frac{1}{3} \), we first interpret the model described.
- The rectangle is divided into 12 equal parts - 4 rows and 3 columns mean each part represents \( \frac{1}{12} \) of the whole rectangle.
- The first part of each of the 4 rows is shaded, resulting in 4 shaded parts.
- The shaded part of the first row is also further shaded using diagonal lines, which indicates a smaller division of that particular part.
Since there are 4 shaded parts, the fraction of the area that is shaded (the parts that are shaded initially) can be calculated as: \[ \frac{4}{12} = \frac{1}{3} \] Then, if we consider the first shaded part that is further divided, that part represents \( \frac{1}{12} \), but with diagonal lines indicating it is divided again, it could represent smaller fractions derived from the original shaded portion.
To directly answer the question regarding the fraction used to divide \( \frac{1}{3} \): None of the initially shaded parts, as it stands, give a direct division of \( \frac{1}{3} \) into other options like \( \frac{3}{4} \), \( \frac{1}{4} \), or \( \frac{4}{3} \).
Hence, interpreting “divide \( \frac{1}{3} \)” would likely be understood as the smaller shaded sections. Given that the diagonal shading is not assigning further fractions aside dividing what already is, it reflects the question and indicates the answer that best describes the divided section.
The answer is \( \frac{1}{4} \), as the minimal shaded portion in comparison to the shaded area would align nearest. So, 1/4 would be the closest representation of how the area has been further divided in the context provided.
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