Problem 30 - Algebra 1: Concepts and Skills

Question

Write the appropriate unit. $$108 \text { inches } \cdot \frac{1 \text { foot }}{12 \text { inches }}=9 \stackrel{?}{\longrightarrow}$$

Step-by-Step Solution

Answer

The unit for the final answer is feet.

Step 1: Identify the Conversion Factor

The given exercise uses a conversion factor to convert from inches to feet. The conversion factor is \(\frac{1 \text { foot }}{12 \text { inches }}\), which means that there are 12 inches in 1 foot.

Step 2: Carry Out the Conversion

The given amount, 108 inches, is multiplied by the conversion factor. This gives us \(108 \text { inches } \cdot \frac{1 \text { foot }}{12 \text { inches }} = 9\).

Step 3: Determine the Correct Unit

Since the original quantity was in inches and it was converted to feet, the resulting quantity will be in feet.

Key Concepts

Conversion Factor

In the world of unit conversion, a conversion factor is fundamentally important. It helps us translate quantities from one measurement unit to another. A conversion factor is a fraction or a ratio that represents how many of one unit are equal to another unit. For example, in our exercise, the conversion factor is \( \frac{1 \text{ foot }}{12 \text{ inches }} \). This specific conversion factor indicates that 1 foot is equivalent to 12 inches. Every time we need to convert inches into feet, we use this relationship.

• Conversion factors are essential for standardizing measurements.
• They always involve equivalent measures but in different units.
• Look for conversion factors when changing from one unit system to another.

By using the proper conversion factor, you ensure accurate conversions, maintaining the integrity of measurements. Understanding and utilizing conversion factors streamlines measurements across various contexts, whether you're dealing with length, area, volume, or other units.

Inches to Feet

Converting from inches to feet is a common task, especially in the United States where both units are frequently used. To convert inches to feet, you apply the conversion factor \( \frac{1 \text{ foot }}{12 \text{ inches }} \). This means you divide the number of inches by 12 to find out how many feet you have.
For example, if you have 108 inches as in the exercise, you perform the calculation \( 108 \text{ inches } \times \frac{1 \text{ foot }}{12 \text{ inches }} \) which simplifies to 9 feet. This gives you a reliable way to change one measurement unit into another accurately.

• Start with the number of inches you want to convert.
• Divide by 12 because there are 12 inches in a foot.
• The result will tell you how many feet correspond to that number of inches.

Being able to convert inches to feet is handy in many real-life situations such as carpentry, sewing, and real estate to ensure precision.

Measurement Units

Measurement units are the standards we use to quantify different dimensions like length, weight, and volume. These units provide a reference and allow us to express quantities in a way that's understood universally. Common length units include inches and feet, which are part of the Imperial system.
Measurement units help keep information standardized, ensuring that everyone can understand and use data effectively. For instance, using inches and feet makes it easier to communicate lengths in a consistent manner.

• Measurement units help maintain clarity in communication.
• They enable easier comparisons of different quantities.
• Using standardized units helps avoid confusion and errors.

When working with measurements, it's important to familiarize yourself with the common units used in various fields. This ensures you can accurately interpret and convert measurements as needed, like turning inches into feet.