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Chapter 9: Problem 54

Complete. \(72 \mathrm{ft}=\) _______ yd.

Short Answer

Expert verified
24 yd

Step by step solution

01

Understand the Conversion Factor

Understand the conversion factor between feet and yards. There are 3 feet in 1 yard.
02

Set Up the Conversion Equation

Set up the equation to convert feet to yards. Since there are 3 feet in 1 yard, you have to divide the number of feet by 3 to get the number of yards.
03

Perform the Division

Divide 72 feet by 3 to find the equivalent number of yards. \[ 72 \text{ ft} \times \frac{1 \text{ yd}}{3 \text{ ft}} = \frac{72}{3} \text{ yd} = 24 \text{ yd} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Feet to Yards Conversion
Understanding unit conversions is essential in many contexts, especially when dealing with measurements. To convert from feet to yards, you need to know the conversion factor between these two units. Specifically, 1 yard is equal to 3 feet. This relationship allows you to convert any measurement in feet to yards by dividing the number of feet by 3. For example, if you have 72 feet and want to know how many yards that is, you simply divide 72 by 3. By understanding this basic conversion, you can easily switch between these units as needed.
Mathematical Division
Division is a fundamental mathematical operation used in numerous applications, including unit conversion. In the context of converting feet to yards, division helps you determine how many smaller units (yards) fit into a larger one (feet). When you split 72 feet into groups of 3 feet (since 3 feet make 1 yard), you are essentially dividing 72 by 3. This gives you \( \frac{72}{3} = 24 \). So, 72 feet is equal to 24 yards. Performing division steps correctly ensures that you get accurate and meaningful results in conversions and other calculations.
Conversion Factor
A conversion factor is a number used to change one set of units to another by multiplying or dividing. In unit conversion, understanding the correct conversion factor is crucial. For feet to yards, the conversion factor is 1 yard for every 3 feet. This means that for every 3 feet, you have 1 yard, and you use this factor to perform your conversion. Simply put, you multiply the number of feet by \( \frac{1 \text{ yd}}{3 \text{ ft}} \) to get the number of yards. For instance, \( 72 \text{ ft} \times \frac{1 \text{ yd}}{3 \text{ ft}} = 24 \text{ yd} \). Conversion factors like these are a vital tool in navigating both everyday measurements and more complex scientific calculations.

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