Problem 9 - Prealgebra

Question

Because there are 3 feet in every yard, the formula \(F=3 \cdot Y\) will convert \(Y\) yards into \(F\) feet. find \(F\). \(Y=4\) yards

Step-by-Step Solution

Answer

4 yards is 12 feet.

Step 1: Identify the Given Information

We are given the number of yards as \(Y = 4\) yards. We need to convert this into feet using the formula provided.

Step 2: Understand the Conversion Formula

The formula given for converting yards to feet is \(F = 3 \cdot Y\), where \(F\) is the number of feet, and \(Y\) is the number of yards.

Step 3: Substitute the Known Value into the Formula

Insert \(Y = 4\) into the formula: \[F = 3 \cdot Y = 3 \cdot 4\].

Step 4: Perform the Calculation

Now, multiply 3 by 4 to convert the yards to feet: \[F = 3 \times 4 = 12\].

Step 5: State the Result

The result of the calculation shows that \(F = 12\) feet. Therefore, 4 yards is equivalent to 12 feet.

Key Concepts

Conversion Formula

Understanding the concept of a conversion formula is essential for tackling unit conversion problems. A conversion formula is a mathematical expression that enables you to change one unit of measurement to another. This is vital when needing a consistent unit to compare or compute measurements.
In the context of converting yards to feet, the specific conversion formula we use is:

• \( F = 3 \cdot Y \)

In this formula, \( F \) represents the feet, while \( Y \) denotes the yards. The conversion factor here, 3, indicates that each yard is equivalent to 3 feet.
This formula simplifies the process by allowing a straightforward multiplication to switch from yards to feet, making it a powerful tool for quick conversions.

Multiplication

Multiplication is a fundamental mathematical operation that we often use in unit conversion. It involves combining equal groups, which aligns perfectly with our need to convert units like yards to feet.
In the conversion problem, recognize that you're dealing with a conversion factor of 3. This indicates that every group, or in this case, every yard, contains 3 feet. To multiply the number of yards by this conversion factor, follow these steps:

• Take the number of yards, which is 4, in our example.
• Multiply it by the conversion factor: \( 3 \times 4 \)

When carried out, this multiplication gives you 12, showing that 4 yards are indeed 12 feet.
Thus, multiplication acts as the bridge in our conversion formula, fulfilling the role of translating between units.

Yard to Feet Conversion

Converting yards to feet is a common task in measuring distances or lengths, especially in countries using the imperial system. This conversion is straightforward once you know the conversion factor, which is simple yet crucial.
The conversion factor is 3, implying 1 yard equals 3 feet. So, to find out how many feet certain number of yards represent, you multiply the yards by 3. In mathematical terms, for the conversion:

• Take the given yards, for instance, 4 yards.
• Multiply with the conversion factor: \( 4 \times 3 = 12 \).

By doing this, 4 yards are found to equate to 12 feet.
Remembering this conversion factor and process simplifies many real-world problems, whether you're measuring out a playing field or converting fabric lengths.