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.

Question

The surface area of the small house will be __ the size of the big house.

Answer 1

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

To find how much smaller the surface area of the small house is compared to the big house, we can use the formula:

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

Now, we need to express this difference as a fraction of the surface area of the big house \( S \):

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

Thus, we can conclude that the surface area of the small house will be \( \frac{1}{2} \) the size of the big house. Therefore, the answer is:

The surface area of the small house will be \(\frac{1}{2}\) the size of the big house.