rosie is building two dog houses, one for each of her dogs. one dog is bigger than the other, so she decides to make one house 1/2 the size of the other. how much smaller will the surface area of the small house be compared to that of the big house? write your response as a fraction

Answer 1

Let the surface area of the larger dog house be represented as \( S \).

Since the smaller dog house is 1/2 the size of the larger one, its surface area will be \( \frac{1}{2}S \).

To find out how much smaller the surface area of the small house is compared to the big house, we can calculate the difference in their surface areas:

\[ S - \frac{1}{2}S = \frac{1}{2}S \]

Now, to express this as a fraction of the surface area of the bigger house:

\[ \text{Difference in surface area} = S - \frac{1}{2}S = \frac{1}{2}S \]

The fraction that represents how much smaller the surface area of the small house is compared to the big house is:

\[ \frac{\frac{1}{2}S}{S} = \frac{1}{2} \]

Thus, the surface area of the small house is \(\frac{1}{2}\) smaller than that of the big house.