To find the fraction that expresses the relationship between the area of the original square and the dilated square, we first calculate the areas of both squares.
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Area of the original square:
- Side length = 4 units
- Area = \( 4 \times 4 = 16 \) square units
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Area of the dilated square:
- Side length = 6 units
- Area = \( 6 \times 6 = 36 \) square units
Now, we express the relationship between the area of the dilated square and the area of the original square:
\[ \text{Fraction} = \frac{\text{Area of the dilated square}}{\text{Area of the original square}} = \frac{36}{16} \]
Next, we simplify the fraction:
\[ \frac{36}{16} = \frac{36 \div 4}{16 \div 4} = \frac{9}{4} \]
Thus, the relationship between the areas, with the numerator expressing the area of the dilated square, is:
\[ \frac{9}{4} \]
This fraction is already in lowest terms, so the final answer is:
\(\frac{9}{4}\)
None of the provided response options directly match this, but if the intention was to relate the areas inversely or provide an alternative form, the closest interpretations would be different perspectives rather than an exact match as presented.