Answer :
- Convert the mixed number to an improper fraction: $12 \frac{1}{2} = \frac{25}{2}$.
- Multiply the improper fraction by the width: Area = $\frac{25}{2} \times 15 = \frac{375}{2}$.
- Convert the improper fraction to a mixed number: $\frac{375}{2} = 187 \frac{1}{2}$.
- State the final answer with correct units: The area of the floor is $\boxed{187 \frac{1}{2} \text{ square feet}}$.
### Explanation
1. Problem Analysis
The problem asks us to find the area of a floor that measures $12 \frac{1}{2}$ feet by 15 feet. The area of a rectangle is given by the formula: Area = length × width. In this case, the length is $12 \frac{1}{2}$ feet and the width is 15 feet. We need to multiply these two values to find the area.
2. Convert Mixed Number to Improper Fraction
First, we convert the mixed number $12 \frac{1}{2}$ to an improper fraction. To do this, we multiply the whole number (12) by the denominator (2) and add the numerator (1): $12 \times 2 + 1 = 24 + 1 = 25$. So, $12 \frac{1}{2} = \frac{25}{2}$.
3. Multiply to Find the Area
Now, we multiply the improper fraction $\frac{25}{2}$ by 15: Area = $\frac{25}{2} \times 15 = \frac{25 \times 15}{2} = \frac{375}{2}$.
4. Convert Improper Fraction to Mixed Number/Decimal
Next, we convert the improper fraction $\frac{375}{2}$ back to a mixed number or a decimal. Dividing 375 by 2, we get 187 with a remainder of 1. So, $\frac{375}{2} = 187 \frac{1}{2}$. Alternatively, we can express it as a decimal: $\frac{375}{2} = 187.5$.
5. State the Final Answer
The area of the floor is $187 \frac{1}{2}$ square feet or 187.5 square feet. Therefore, the correct answer is $187 \frac{1}{2}$ square feet.
### Examples
When planning to install new flooring in a room, knowing how to calculate the area is essential. For instance, if you're tiling a rectangular kitchen floor, you need to determine the square footage to purchase the correct amount of tiles. This ensures you buy enough material to cover the entire floor without running short, saving time and money.
- Multiply the improper fraction by the width: Area = $\frac{25}{2} \times 15 = \frac{375}{2}$.
- Convert the improper fraction to a mixed number: $\frac{375}{2} = 187 \frac{1}{2}$.
- State the final answer with correct units: The area of the floor is $\boxed{187 \frac{1}{2} \text{ square feet}}$.
### Explanation
1. Problem Analysis
The problem asks us to find the area of a floor that measures $12 \frac{1}{2}$ feet by 15 feet. The area of a rectangle is given by the formula: Area = length × width. In this case, the length is $12 \frac{1}{2}$ feet and the width is 15 feet. We need to multiply these two values to find the area.
2. Convert Mixed Number to Improper Fraction
First, we convert the mixed number $12 \frac{1}{2}$ to an improper fraction. To do this, we multiply the whole number (12) by the denominator (2) and add the numerator (1): $12 \times 2 + 1 = 24 + 1 = 25$. So, $12 \frac{1}{2} = \frac{25}{2}$.
3. Multiply to Find the Area
Now, we multiply the improper fraction $\frac{25}{2}$ by 15: Area = $\frac{25}{2} \times 15 = \frac{25 \times 15}{2} = \frac{375}{2}$.
4. Convert Improper Fraction to Mixed Number/Decimal
Next, we convert the improper fraction $\frac{375}{2}$ back to a mixed number or a decimal. Dividing 375 by 2, we get 187 with a remainder of 1. So, $\frac{375}{2} = 187 \frac{1}{2}$. Alternatively, we can express it as a decimal: $\frac{375}{2} = 187.5$.
5. State the Final Answer
The area of the floor is $187 \frac{1}{2}$ square feet or 187.5 square feet. Therefore, the correct answer is $187 \frac{1}{2}$ square feet.
### Examples
When planning to install new flooring in a room, knowing how to calculate the area is essential. For instance, if you're tiling a rectangular kitchen floor, you need to determine the square footage to purchase the correct amount of tiles. This ensures you buy enough material to cover the entire floor without running short, saving time and money.
