91Ó°ÊÓ

When you have an equation, isolating the variable means getting that variable by itself on one side of the equation. This can involve using basic arithmetic operations like addition, subtraction, multiplication, and division. In the exercise above, we need to isolate the variable d.
To do this, we start with the equation given: \( C = \pi d \).
Since we want \( d \) by itself, we need to get rid of the \( \pi \) next to it. We can do this by dividing both sides of the equation by \( \pi \). Now, we have: \[ \frac{C}{\pi} = d \].
This step of isolating the variable is crucial to solving many equations, making it a fundamental skill in algebra.

The circumference formula is a key concept in geometry. It relates the circumference \( C \) of a circle to its diameter \( d \) using the constant \( \pi \), which is approximately 3.14159: \[ C = \pi d \].
This formula tells us that if we know the diameter of a circle, we can easily find its circumference by multiplying the diameter by \( \pi \).
Conversely, if we know the circumference, we can find the diameter by dividing the circumference by \( \pi \). This bidirectional relationship is helpful in various real-world applications.
For example, if you have a circle with a circumference of 31.4 units and you want to find the diameter, you can use the formula we rearranged in the previous section: \ \[ d = \frac{31.4}{\pi} \].
This way, the understanding of the circumference formula makes it straightforward to switch between measurements of a circle.

Prealgebra involves understanding and solving simple equations. This builds the foundation for more complex algebraic concepts. Let's break down the steps taken to solve our given equation: \[ C = \pi d \].
First, write down the given equation: \ \[ C = \pi d \].
Next, isolate the variable d by dividing both sides by \( \pi \), which simplifies to \ \[ d = \frac{C}{\pi} \].
Lastly, simplify the expression by performing the division if numerical values are given for C and \( \pi \).
These steps follow a logical progression:

• Start with the equation.
• Identify the variable to isolate.
• Perform the arithmetic operations needed to get the variable by itself.

Practicing these steps helps build confidence in solving various equations which is a vital skill for advancing in mathematics.