Problem 36 - Prealgebra

Question

Tower Height. A transmitting tower is 100 feet tall. How many inches is that?

Step-by-Step Solution

Answer

The tower is 1200 inches tall.

Step 1: Understand the Conversion Factor

To convert feet to inches, we need to know how many inches there are in one foot. There are 12 inches in one foot.

Step 2: Set Up the Conversion Equation

We will use the conversion factor from Step 1 to convert the tower's height from feet to inches. To do so, use the equation: \[ ext{Height in inches} = ext{Height in feet} \times 12\]Substitute the given height of the tower into the equation.

Step 3: Perform the Calculation

Substitute the given tower height of 100 feet into the equation:\[ ext{Height in inches} = 100 \times 12\]Now, perform the multiplication to find the height in inches.

Step 4: Solve the Equation

Carrying out the multiplication gives:\[100 \times 12 = 1200\]So, the tower is 1200 inches tall.

Key Concepts

Measurement Units

Understanding the concept of measurement units is essential in many fields, such as science, engineering, and everyday life. In this exercise, the tower's height was initially provided in feet, which is a standard unit of measurement in the United States for length. However, sometimes we need to convert measurements into different units to make them more understandable or to meet specific requirements. When dealing with length, common units include:

• Inches
• Feet
• Yards
• Miles

Visitors from other countries or regions might use the metric system, which includes centimeters and meters. Regardless of the system, the key to successful conversions is understanding the relationship between these units. Here, the conversion factor was the relationship between feet and inches: 12 inches per foot. It's crucial to remember that such conversions rely on established ratios, making knowledge of common conversion factors highly practical. This way, calculations can maintain accuracy and consistency across different measurement systems.

Arithmetic Operations

Arithmetic operations are the basic mathematical computations that we use in daily life. In this exercise, multiplication was the key operation used to convert the tower's height from feet to inches. Here are some basic arithmetic operations you should know:

• Addition
• Subtraction
• Multiplication
• Division

Multiplication, in this case, allowed us to scale up a given measurement from one unit to another. Since there are 12 inches in a foot, we multiplied the given 100 feet by 12 to convert the entire measurement into inches. Using multiplication: When you know the conversion factor (in this case, 12 inches per 1 foot), you can apply multiplication to adjust the original measurement. This principle is useful in various situations, from simple unit conversions to complex problem-solving in fields like physics and engineering. Confidence in performing arithmetic operations can make problem-solving much more approachable and efficient.

Problem Solving Strategies

Effective problem solving involves a series of steps that enhance understanding and guide you toward a solution. In this exercise, converting the tower's height from feet to inches was achieved by following a simple problem-solving strategy. These steps often include:

• Identifying what information you have
• Recognizing what you need to find
• Using appropriate methods to reach the solution
• Carrying out calculations and checking the results

In the example given, the initial step was recognizing the need to convert the tower's height into inches. Knowing the conversion factor (
2 inches in a foot) prepared us for setting up the calculation. By methodically multiplying the height in feet by this factor, we arrived at the tower's height in inches. Throughout problem-solving, it is vital to ensure each step is done with care, considering the logic applied and validating the results. Strategies like these reinforce critical thinking skills and enable problem-solving across various fields and scenarios, from academic exercises to real-life applications.