Question

Stefan is decorating a rectangular cake. He will put blue icing on the top 3/4 of the cake and he will put red dots on the left 1/5 of the cake. What fraction of the cake will have both blue icing and red dots?

Answer 1

To solve the problem, we need to determine the fraction of the cake that will have both blue icing and red dots.

1. **Identify the areas covered by each decoration**:
- The blue icing covers the top \( \frac{3}{4} \) of the cake.
- The red dots are placed on the left \( \frac{1}{5} \) of the cake.

2. **Determine the area that is both blue and red**:
- To find out the area that has both blue icing and red dots, we need to find the overlap between the blue area and the red area. This overlap will be in the area that is both \( \frac{3}{4} \) of the height (for the blue icing) and \( \frac{1}{5} \) of the width (for the red dots).

3. **Calculate the area of overlap**:
- We can think of this as a rectangular area in an overall rectangle that has dimensions \( 1 \times 1 \) (representing the whole cake).
- The area covered by blue icing is \( \frac{3}{4} \) of height and the area covered by red dots is \( \frac{1}{5} \) of the width.

Therefore, the area that has both blue icing and red dots can be calculated as follows:
\[
\text{Area with both blue icing and red dots} = \text{(Height fraction for blue)} \times \text{(Width fraction for red)} = \frac{3}{4} \times \frac{1}{5}
\]

4. **Perform the multiplication**:
\[
\frac{3}{4} \times \frac{1}{5} = \frac{3 \cdot 1}{4 \cdot 5} = \frac{3}{20}
\]

Thus, the fraction of the cake that will have both blue icing and red dots is \( \frac{3}{20} \).

\[
\boxed{\frac{3}{20}}
\]