Problem 13 - 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. 48 in. to yards

Step-by-Step Solution

Answer

1 and 1/3 yards

Step 1: Identify the Conversion Factor

To convert inches to yards, determine the appropriate conversion factor. There are 36 inches in a yard.

Step 2: Set Up the Conversion Equation

Write the equation to convert 48 inches to yards using the conversion factor determined earlier: \[\text{yards} = \frac{48 \text{ inches}}{36 \text{ inches per yard}}\]

Step 3: Perform the Division

Calculate the division from the equation: \[\frac{48}{36} = \frac{4}{3} \] This gives us \( \frac{4}{3} \) or 1 and \( \frac{1}{3} \) yards.

Key Concepts

Inches to Yards

Converting inches to yards is a fundamental skill when working with measurements in the U.S. customary system. This unit conversion is handy in various scenarios, such as fabric measurements or construction projects. You start by understanding the basic relationship between inches and yards.

There are 36 inches in one yard. This means that whenever you have a measurement in inches and want to express it in yards, you're essentially looking to see how many whole yards (and possibly a fraction of another yard) those inches amount to.

Here's a simplified thought process: imagine you have a tape measure stretched out to 36 inches, and each time the tape reaches 36 inches, you're at one yard. Therefore, with 48 inches, you'll cover a whole yard (36 inches) and then 12 more inches into a second yard. It's all about dividing the inch measurement by 36, which brings us to the core mechanism of conversion factors.

Conversion Factor

The conversion factor is the key that unlocks the door between different units of measurement. Consider it as a bridge that connects the numbers in different measurement systems.

In the U.S. system, converting inches to yards is streamlined by using the conversion factor of 36 inches equals 1 yard. This is often expressed as a fraction:

• 1 yard/36 inches

Using this fraction during conversion helps define how many yards are in a given number of inches.

To convert 48 inches into yards, you multiply 48 by the conversion factor (or more accurately, divide 48 by 36):

• \[\text{yards} = \frac{48 \text{ inches}}{36 \text{ inches/yard}}\]

This computation simplifies the process and effectively changes the unit from inches to yards.

Mixed Numbers

Sometimes, conversions result in measurements that aren't whole numbers, but rather partial or mixed numbers. A mixed number includes both a whole number and a fraction.

When converting 48 inches to yards, the straightforward division yields \(\frac{48}{36}\), simplifying to \(\frac{4}{3}\). This fraction means you have more than one yard but less than two. To understand better, convert \(\frac{4}{3}\) into a mixed number: 1 whole yard and \(\frac{1}{3}\) more yard.

Mixed numbers are practical as they offer a clearer, more intuitive understanding of measurement, presenting an amount as a whole part plus a fraction, which can be particularly useful in real-world physical applications like cutting materials or allocating space.