Let the surface area of the smaller dog house be \( S \), and let the surface area of the larger dog house be \( L \). According to the problem, the larger dog house is 12 times the size of the smaller one. Thus, we can express this relationship as:
\[ L = 12S \]
To find out how much smaller the surface area of the small house is compared to that of the big house, we need to calculate the difference in their surface areas:
\[ L - S = 12S - S = 11S \]
Now, if we want to express how much smaller the small house's surface area is compared to the big house's surface area as a fraction of the larger:
- The difference in surface area is \( 11S \).
- The surface area of the larger house is \( L = 12S \).
Now, we can express the difference as a fraction of the larger house's surface area:
\[ \text{Fraction} = \frac{L - S}{L} = \frac{11S}{12S} = \frac{11}{12} \]
Thus, the surface area of the small house is \( \frac{11}{12} \) smaller than that of the big house.
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