Problem 21 - Prealgebra

Question

Perform the indicated operation. Again, remember to use the appropriate conversion factor. [Examples \(2,3]\) Add 8 feet 10 inches and 13 feet 6 inches

Step-by-Step Solution

Answer

The sum is 22 feet 4 inches.

Step 1: Convert Measurements to Inches

First, we'll convert both measurements from feet and inches to inches only. Remember, there are 12 inches in a foot.- For 8 feet 10 inches: Convert the feet to inches: \(8 \times 12 = 96\) inches. Add the remaining 10 inches: \(96 + 10 = 106\) inches. - For 13 feet 6 inches: Convert the feet to inches: \(13 \times 12 = 156\) inches. Add the remaining 6 inches: \(156 + 6 = 162\) inches.

Step 2: Add the Inches

Add the total inches from both measurements together: \(106 + 162 = 268\) inches.

Step 3: Convert Total Inches Back to Feet and Inches

Convert 268 inches back to feet and inches. Divide 268 by 12 to convert inches to feet: \(268 \div 12 = 22.333\). This gives us 22 feet with a remainder of approximately 4 inches (since \(22 \times 12 = 264\) inches, there are 4 inches remaining).

Key Concepts

Adding Measurements

When it comes to adding measurements, the key is to ensure that you are working with the same units before adding them together. This means if you are dealing with measurements involving both feet and inches, you need to first consider how they interrelate. Measurements should be unified into a single unit to avoid errors. For example, in adding measurements like 8 feet 10 inches and 13 feet 6 inches, you first need to convert all measurements to inches. This way, you add the total inches, ensuring every part of your measurement is correctly counted.
Planning before adding, such as identifying whether you'll do conversion first or add separately, can save time and effort.

Unit Conversion

Unit conversion is a fundamental skill in measurement. Luckily, the process is fairly straightforward when you follow the proper guidelines. The key is knowing the right conversion factor, which tells you how one unit relates to the other. In our case, the conversion factor between feet and inches is 12, meaning 1 foot equals 12 inches.
Whenever dealing with problems involving units, first decide which unit is easier to work with. Once you've chosen, look up or remember the conversion factor. Multiply to go from a larger unit to a smaller one (like feet to inches) and divide for the opposite (like inches to feet).

• To convert feet to inches, multiply by 12.
• To convert inches to feet, divide by 12.

Understanding these basics helps you work with mixed units reliably and efficiently.

Inches to Feet Conversion

Converting from inches to feet involves straightforward division. Since 12 inches make up one foot, the process requires dividing the total inches by 12. Using our example, where we had a total of 268 inches after combining all measurements, dividing 268 by 12 yielded 22.333.
Here's what happens in this conversion: - The whole number part of the division (22 in this example) becomes the feet. - The remainder (4 inches in this case) is what's left over once you subtract 264 inches (22x12) from the total. Applying these simple steps ensures the measurement can be expressed in a clear and accurate format of feet and inches. Remember, understanding these conversions lets you easily switch between units, catering to different needs and conventions.