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When solving equations, our first objective is to isolate the variable. In this case, the variable is \(p\). Isolating the variable means getting \(p\) by itself on one side of the equation. To achieve this, you need to perform operations that will cancel out the coefficients and other terms around \(p\).
For the equation $$ 0.4p=9.2 $$, we will need to divide both sides by 0.4. This step is crucial because it simplifies the equation, allowing us to clearly solve for \(p\).
Remember, whatever operation you perform on one side of the equation, you must also perform on the other side to maintain the balance of the equation. Keeping this balance is key to solving equations accurately.

Division is one of the fundamental operations in algebra, especially in prealgebra. When you're dividing, you're essentially distributing a quantity into smaller, equal parts. The division in our problem helps to isolate the variable from its coefficient. Here's how we do it:
We start with the equation $$ 0.4p = 9.2 $$, then we divide both sides by 0.4: \[ p = \frac{9.2}{0.4} \]
Performing the division, we get \( p = 23 \). Practicing division in these scenarios is essential because it will come up often, especially when isolating variables. Remember to check your calculations to ensure accuracy.

Prealgebra introduces foundational concepts in math that prepare students for more advanced work in algebra. It simplifies problems and teaches core skills like operations with numbers, basic properties of numbers, and early equation solving. In our problem, the equation $$ 0.4p = 9.2 $$ fits perfectly into prealgebra's scope as it involves straightforward arithmetic and the fundamental skill of solving for a variable. Addressing this problem requires understanding:

• Basic arithmetic operations (e.g., multiplication and division)
• The equality principle (balancing equations)
• Translating word problems into mathematical equations (sometimes essential in prealgebra)

Mastery of these concepts at the prealgebra level is vital. It builds the foundation for solving more complex equations and mathematical problems later on.