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Simplification is a key concept in mathematics where we aim to transform an expression into its simplest form. This process helps to make calculations easier and more intuitive. Let's take the given expression \((213) \times 2\) as an example. Here, our objective is to simplify the equation into a more straightforward result.
We start by breaking down the arithmetic operation to ensure clarity and understanding. By simplifying, we reduce errors and make further mathematical processes smoother. Simplification can involve several methods, such as canceling out terms, reducing fractions, or as in this case, performing multiplication to derive a concise numerical result.

Arithmetic operations are the basic building blocks of mathematics, encompassing addition, subtraction, multiplication, and division. They are fundamental tools we use to solve various mathematical problems. In our specific exercise, we focus on multiplication, an operation that involves combining equal groups or quantities.
When we multiply 213 by 2, we are effectively adding 213 to itself. This operation is not only about obtaining the product, but also about understanding the process involved in achieving it. By involving the digits separately as in the provided solution—multiplying 2 by each digit of 213, and subsequently combining the results—we see the value of organizing calculations methodically.

• Multiply 2 by the ones digit: \(2 \times 3 = 6\)
• Multiply 2 by the tens digit: \(2 \times 10 = 20\), accounting for place value
• Multiply 2 by the hundreds digit: \(2 \times 100 = 400\)

Putting these together gives us the final product of 426.

Breaking down problems into step-by-step solutions is invaluable in understanding and accurately carrying out mathematical operations. It allows us to tackle complex problems by addressing simpler, more manageable parts. In solving \((213) \times 2\), following a step-by-step solution ensures that each part of the problem is addressed correctly.
We started by recognizing the operation: multiplying 213 by 2. Then, breaking the problem into parts, we handled each digit multiplication separately. This methodical approach makes the multiplication process clear and accessible.
Finally, the results obtained from multiplying each individual digit (3, 1, and 2) with 2 are added together. By taking these small, deliberate steps, we minimize errors and misunderstandings, thus arriving confidently at the final solution: 426. This approach emphasizes learning through structured steps, fostering an understanding that lasts and enhances problem-solving skills in mathematics.