Problem 8 - Prealgebra

Question

Make the following conversions in the U.S. system by multiplying by the appropriate conversion factor. Write your answers as whole numbers or mixed numbers. 9.5 yd to inches

Step-by-Step Solution

Answer

9.5 yards is equal to 342 inches.

Step 1: Identify the Conversion Factor

To convert yards to inches, we need to know how many inches are in one yard. There are 36 inches in one yard, so our conversion factor will be 36.

Step 2: Set Up the Multiplication

We have 9.5 yards that we need to convert into inches. To do this, we multiply 9.5 by the conversion factor of 36: \[ 9.5 \text{ yd} \times 36 \frac{\text{inches}}{\text{yd}} \]

Step 3: Perform the Multiplication

Now, calculate the multiplication: \[ 9.5 \times 36 = 342 \]Thus, 9.5 yards is equal to 342 inches.

Key Concepts

Conversion Factor

When dealing with unit conversion, a conversion factor is an essential tool. It tells us how many parts—like inches, feet, or meters—fit into another unit, such as yards or miles. Think about it as a bridge that allows you to move from one measurement to another seamlessly.
It's important to choose the correct conversion factor. If you're converting yards to inches, you need the conversion factor of 36, because 1 yard equals 36 inches. By using this factor, you maintain the accuracy of your conversion.
To apply a conversion factor, simply set it up in a fraction, with the new unit on the top: for converting yards to inches, use \( \frac{36\text{ inches}}{1\text{ yard}} \). This fraction serves as your multiplier for a straightforward conversion, ensuring the units align and the math works out correctly.

U.S. Customary Units

U.S. customary units are a system of measurements that include familiar units such as inches, feet, yards, and miles. It is predominantly used in the United States, contrasting the metric system which is used in most other countries.
Each unit in the U.S. customary system has a specific relation to others. For example:

• 12 inches make up 1 foot.
• 3 feet equal 1 yard.
• 5,280 feet is 1 mile.

You might often need to convert from one of these units to another, especially in everyday tasks like measuring fabric for sewing or calculating distances for a project. Understanding and memorizing these key relationships, like the conversion between yards and inches, is incredibly useful and simplifies making conversions using multiplication.

Multiplication

In unit conversion, multiplication is the process you use to apply the conversion factor. It allows you to scale your initial measurement into the desired unit.
This works because each unit multiplication involves multiplying by a number, which corresponds to the amount of the new unit in the old unit. For instance, when converting \(9.5\) yards to inches, you multiply \(9.5\) by \(36\), the conversion factor, which results in \(342\) inches.
Here's how it works for converting yards to inches:

• Identify the starting measurement (e.g., \(9.5\) yards).
• Apply the conversion factor (\(36\)).
• Perform the multiplication: \(9.5 \times 36 = 342\).

Using multiplication keeps the conversion process simple and ensures that you end up with an accurate measurement in the new unit.