Problem 54 - Prealgebra

Question

Complete. $$\frac{3}{4} \text { yard }=\underline{?} \text { inches }$$

Step-by-Step Solution

Answer

27 inches.

Step 1: Understand 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.

Step 2: Set Up the Conversion

We need to convert \( \frac{3}{4} \) of a yard to inches. This can be set up using the conversion factor that 1 yard equals 36 inches.

Step 3: Multiply by the Conversion Factor

Multiply \( \frac{3}{4} \) yard by 36 inches per yard: \[ \frac{3}{4} \times 36 \].

Step 4: Calculate the Product

Perform the multiplication: \( \frac{3}{4} \times 36 = \frac{108}{4} = 27 \). Therefore, \( \frac{3}{4} \) yard equals 27 inches.

Key Concepts

Understanding Fractions

Fractions are a way to represent parts of a whole. They consist of a numerator and a denominator. The numerator is the top number, showing how many parts we are considering. The denominator is the bottom number, indicating the total number of equal parts the whole is divided into.

For example, in the fraction \( \frac{3}{4} \), 3 is the numerator and 4 is the denominator. This fraction represents three out of four equal parts of something. When working with fractions, it's helpful to remember the following:

• Fractions are essentially division; \( \frac{3}{4} \) means 3 divided by 4.
• They often appear in measurement and conversions, like converting fractions of a yard into inches.
• Simplifying fractions can make calculations easier, but be sure the context doesn't change the need for precision.

Having a good grasp of fractions is essential in solving problems that involve parts of a measurement, like the problem of converting \( \frac{3}{4} \) yard into inches.

The Role of Multiplication in Conversions

Multiplication plays a crucial role when converting measurements from one unit to another. It's the operation we use to scale a number according to a specific factor. In measurement conversions, this factor is often called the conversion factor.

In our example, converting yards to inches involves the conversion factor of 36 because there are 36 inches in one yard. To determine how many inches there are in \( \frac{3}{4} \) of a yard, we multiply by this factor. Here's how multiplication helps:

• It allows scaling properties, such as converting larger units (yards) into smaller units (inches).
• By multiplying \( \frac{3}{4} \times 36 \), we adjust the fraction of the whole yard to its equivalent in inches.
• Multiplication facilitates direct computation, helping to find products like \( \frac{108}{4} \), leading to a simplified answer of 27 inches.

Understanding the multiplication process is vital in solving practical problems involving conversion, ensuring accuracy and confidence in the final result.

Essentials of Measurement Conversions

Measurement conversions involve changing one unit of measurement into another. Knowing conversion factors is key, as these are the numbers used to change from one unit to another.

In order to perform a conversion, follow these essential steps:

• Select the correct conversion factor. For yards to inches, it's 36 inches per yard, because 1 yard equals 36 inches.
• Set up the equation with the given measurement (here, \( \frac{3}{4} \) yard), and multiply by the conversion factor.
• Calculate the product to find the new measurement. In our example, \( \frac{3}{4} \times 36 = \frac{108}{4} = 27 \). Hence, \( \frac{3}{4} \) yard converts to 27 inches.

Successful measurement conversions allow you to work seamlessly between units, whether for academic exercises, everyday situations, or specialized fields like engineering and construction.