Question

Translate to an equation and solve. In a 1860 -square-foot house, the living room is 16 feet wide by 20 feet long. What percent of the total area of the house is the living room area?

Short answer

Answer: Approximately 17.2%.

Step-by-step solution

Calculate the living room area.

To find the area of the living room, we will multiply its width (16 feet) by its length (20 feet). So, Area of living room = 16 feet × 20 feet = 320 square feet.

Calculate the percentage of the living room area in the total house area.

To find the percentage, we will divide the living room area (320 square feet) by the total house area (1860 square feet) and multiply by 100. Percentage = (Living room area / Total House area) × 100 Percentage = (320 / 1860) × 100

Calculate the final result.

Now, let's calculate the percentage. Percentage = (320 / 1860) × 100 ≈ 17.2 % So, the living room area is approximately 17.2% of the total house area.

Key concepts

Calculating Area

Understanding how to calculate area is crucial for solving many real-world problems, including those involving floor space in a house. The area represents the amount of two-dimensional space covered by a shape or object, often measured in square units, such as square feet or square meters.

In our exercise, the task was to find the area of a living room, which is a rectangular space. To calculate the area of a rectangle, the formula is simple: area equals length times width. For this scenario, we multiply the living room's length (20 feet) by its width (16 feet) to find an area of 320 square feet. This formula is vital in many prealgebra and geometry problems and serves as a foundation for more complex mathematical calculations.

Percentage Calculation

Calculating percentages is a necessary skill that extends beyond classroom exercises to everyday life, such as determining discounts during shopping or understanding statistics mentioned in the news. A percentage represents a fraction of 100, and to calculate it, we use a basic formula.

In the context of our original problem, we calculated what percentage of the total area of the house is taken up by the living room. The formula used is: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \). Here, we divide the 'part' (the area of the living room) by the 'whole' (the total area of the house) and then multiply by 100 to convert it to a percentage. Understanding this process is essential for accurately interpreting data and proportions in various situations.

Prealgebra Word Problems

Prealgebra word problems often involve real-life scenarios that require us to apply basic arithmetic operations to find a solution. These word problems help students develop critical thinking and problem-solving skills. They often require multiple steps to solve, as seen in the exercise where we determine the area of the living room first, and then use that to find out what percentage that area is of the entire house.

Approaching word problems involves careful reading, identifying relevant information, translating words into mathematical operations, and then applying the appropriate formulas or processes. Practice with these problems enhances the ability to tackle a wide range of mathematical and practical challenges.

Basic Arithmetic Operations

The foundation of all mathematics lies in understanding and utilizing basic arithmetic operations: addition, subtraction, multiplication, and division. These operations are used universally in various contexts, including simple budgeting or complex scientific calculations.

In our example, we use multiplication to calculate the area of the living room and division to determine the percentage that represents of the total house area. Mastering these basic operations not only helps in solving straightforward problems but also in understanding more advanced mathematics. It is important to execute these operations precisely and to understand their applicability in diverse situations.