Question

Change \(34,848\) feet to miles. A. \(2.2 \mathrm{m}\) B. \(4.4 \mathrm{mi}\) C. \(8.8 \mathrm{mi}\) D. \(6.6 \mathrm{mi}\)

Short answer

The correct answer is D. \(6.6 \mathrm{mi}\).

Step-by-step solution

Understand the Problem

We need to convert a distance from feet to miles. Specifically, we want to find out how many miles are equivalent to 34,848 feet.

Recall the Conversion Factor

The conversion factor between feet and miles is: 1 mile = 5,280 feet.

Set Up the Equation

To convert from feet to miles, we use the equation: \[\text{miles} = \frac{\text{feet}}{5,280}\]So we set up the equation using our specific numbers: \[\text{miles} = \frac{34,848}{5,280}\]

Perform the Division

Now, divide 34,848 by 5,280: \[\frac{34,848}{5,280} = 6.6\]

Select the Correct Answer

The result from our calculation is 6.6 miles, which matches with option D. Therefore, the correct answer is D. \(6.6 \mathrm{mi}\).

Key concepts

Understanding Distance Conversion

Distance conversion is a fundamental skill in mathematics that allows us to change measurements from one unit to another. In this context, we're focusing on converting from feet to miles. Such conversions are essential for solving real-world problems, like determining travel distances, mapping out journeys, or even planning athletic events.

• Distance conversion helps simplify calculations by using standardized units.
• It provides a way to express larger distances in more manageable terms.
• Understanding this concept aids in developing critical thinking and problem-solving skills.

By mastering distance conversion, you engage in a practical application of math that is widely used in everyday life. Whether measuring lengths for a construction project or calculating distances for travel, being proficient in converting units is invaluable.

Feet to Miles Conversion

Feet to miles conversion is a specific type of distance conversion where we change a measurement from feet, typically a smaller unit, to miles, a larger unit.

• There are 5,280 feet in a mile, which is the key conversion factor used in calculations.
• This conversion is frequently needed in geography and travel scenarios.
• When converting, it helps to understand why and how the conversion factor is applied.

The purpose of converting feet to miles is to make understanding and communication of large distances easier. For example, saying that you traveled 10,560 feet may not provide as clear a picture as saying you traveled 2 miles. This conversion simplifies large numbers into practical, human-friendly terms.

Role of the Conversion Factor

A conversion factor is a numerical value used to change a measurement from one unit to another. It serves as a multiplier or divider, depending on the direction of conversion.

• For feet to miles, the conversion factor is 5,280 feet per mile.
• Using this factor allows you to accurately express large quantities in a different unit.
• This factor is essential for keeping equivalence between units, ensuring calculations are correct.

In mathematical problems, knowing the correct conversion factor ensures accuracy and consistency. It helps standardize measurements across various applications, allowing for seamless integration of data across different fields like science, engineering, and daily calculations.

Effective Mathematics Problem-Solving

Mathematics problem-solving involves a series of logical steps to reach a solution. In distance conversions, like feet to miles, following these steps accurately is crucial for arriving at the correct answer.

• Identify the problem and understand the conversion required.
• Recall and accurately use the conversion factor.
• Set up the equation correctly to ensure proper calculations.
• Perform arithmetic operations with precision to avoid errors.

By following these structured steps, solving conversion problems becomes more manageable and less intimidating. The process not only helps in getting the right answer but also reinforces mathematical reasoning and analytical thinking. Emphasizing these skills prepares you for more complex problems and enhances your overall mathematical aptitude.