Problem 32 - Prealgebra

Question

Complete each sentence. 5 feet \(=\quad\) inches

Step-by-Step Solution

Answer

5 feet equals 60 inches.

Step 1: Understanding the Conversion Rate

To convert feet to inches, we need to know that 1 foot is equivalent to 12 inches. This is the basic conversion factor that will help us determine how many inches are in 5 feet.

Step 2: Setting Up the Equation

Using the conversion factor from Step 1, set up the equation: \[ 1\, \text{foot} = 12\, \text{inches} \]We need to convert 5 feet into inches. Therefore, we multiply 5 by the conversion rate of 12.

Step 3: Multiplying to Find the Total

Multiply the number of feet (which is 5) by the number of inches in one foot (which is 12):\[ 5 \times 12 = 60 \]So, 5 feet is equal to 60 inches.

Step 4: Conclusion

After completing the multiplication, we find that 5 feet equals 60 inches. Therefore, the sentence would be completed as "5 feet = 60 inches."

Key Concepts

Measurement

Measurement is the process of determining the size, length, or amount of something, typically using standard units. In our exercise example, we are dealing with measuring length. Different systems use different units like feet, inches, centimeters, and meters. - **Standard Length Units:** In the United States, length is often measured using feet and inches. - **Importance:** Understanding measurement is essential as it helps us quantify objects in everyday life, from height and depth to distance. When converting between units, it is vital to be aware of how these units relate to each other. For example, since 1 foot equals 12 inches, knowing these basic conversions allows us to switch between units without losing accuracy.

Multiplication

Multiplication is a mathematical operation that lets you add a number to itself a certain number of times. It is one of the four elementary arithmetic operations and is essential for unit conversion.- **How It Works:** If you need to calculate how many inches are in 5 feet and you know there are 12 inches in a foot, you multiply 5 (the number of feet) by 12 (the number of inches per foot).The formula looks like this:- \[ 5\,\text{feet} \times 12\,\text{inches/foot} = 60\,\text{inches} \]Using multiplication ensures you can easily scale any measurement up or down. This skill is not only useful for converting units but also for working with quantities in many areas of math and science. Multiplication makes handling larger numbers and complex equations simpler.

Conversion Factors

Conversion factors are critical when converting one unit of measure to another. They act as a bridge that connects different units.- **What Are They?** A conversion factor is a ratio expressing how many of one unit are equal to another unit. In our example, the conversion factor between feet and inches is:- \[1\,\text{foot} = 12\,\text{inches} \]Employing a correct conversion factor is crucial because it guides the process of changing units effectively without altering the physical quantity being measured. Always ensure:- You use the correct conversion factor to maintain accuracy.- Multiply or divide by the conversion factor as appropriate.When converting 5 feet to inches, we multiplied by the conversion factor of 12 inches per foot. This straightforward multiplication guided by a conversion factor helped us seamlessly transition from feet to inches.