Problem 58 - Algebra A Combined Function

Question

Convert as indicated. See Examples 9 through 12. 3.6 square yards = _________ square feet.

Step-by-Step Solution

Answer

3.6 square yards equals 32.4 square feet.

Step 1: Understand the Units

We are asked to convert 3.6 square yards into square feet. We need to know the conversion factor between yards and feet.

Step 2: Conversion Factor

1 yard is equal to 3 feet. Therefore, to convert square yards to square feet, we square the conversion factor: \[ (1 ext{ yard})^2 = (3 ext{ feet})^2 = 9 ext{ square feet} \] Thus, 1 square yard equals 9 square feet.

Step 3: Apply the Conversion

Multiply the given measurement in square yards by the conversion factor (9 square feet per square yard): \[ 3.6 ext{ square yards} imes 9 ext{ square feet/square yard} = 32.4 ext{ square feet} \]

Step 4: Final Calculation

Perform the multiplication from the previous step to find the answer: \[ 3.6 imes 9 = 32.4 \] Hence, 3.6 square yards is equal to 32.4 square feet.

Key Concepts

Square Yards to Square Feet

Converting square yards to square feet might sound confusing at first, but it’s all about understanding how areas relate to each other.
Imagine a square yard as a large square on the ground. Each side of this square measures 1 yard.
Now, if you break it down further, each yard contains 3 feet.
This means that a square yard covers an area that is actually composed of smaller squares, each with sides that measure 3 feet.
The important point here is that when you are talking about an area, both the length and the width of the square will be affected by this conversion.
This means a square yard becomes much larger when you think about it in square feet.

Conversion Factor

To convert one unit of measurement to another, understanding and using the correct conversion factor is essential.
A conversion factor is simply a number that allows you to translate amounts in one set of units to another.
In the case of square yards and square feet, the conversion factor comes from squaring the linear conversion (from yards to feet).
Since 1 yard equals 3 feet, you square this to convert areas:

• The square of 1 yard is (1 yard × 1 yard) which is equivalent to (3 feet × 3 feet), this equals 9 square feet.

Armed with this conversion factor, you can convert any number of square yards to square feet simply by multiplying the number of square yards by 9.

Multiplication in Unit Conversion

Now that we have our conversion factor, how do we use it in practice?
It all boils down to multiplying the measurement you have with the conversion factor.
In this example, if you are asked to convert 3.6 square yards to square feet, you multiply 3.6 by 9.

• 3.6 × 9 = 32.4

This multiplication is straightforward because it allows you to scale the measurement in square yards up to square feet.
It’s crucial to remember that this multiplication step will always involve the conversion factor when converting areas.

Algebraic Problem-Solving

Approaching conversion workouts like algebra problems can make them easier to handle.
First, identify what you have and what you need: you start with square yards and want to end with square feet.
Next, insert the conversion factor into an equation:

• For example, in our conversion, 3.6 square yards becomes 3.6 × 9 = 32.4 square feet.

Each step is methodical and follows logically from the relationship between the units.
What's fantastic about treating the problem this way is that it works for any unit conversion problem, not just square yards to square feet.
With consistency and practice, you can solve these algebraically with ease and confidence.