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Absolute value is a crucial concept in algebra and can initially seem confusing. The absolute value of a number is essentially its distance from zero on a number line. One important thing to remember about absolute values is that they are always non-negative. For instance, the absolute value of both \(-5\) and \(5\) is \(5\). This is because we only focus on the magnitude, not the direction.

In mathematical terms, the absolute value is represented by the vertical bars on either side of a number, like \(|-5|\). When we determine the absolute value of \(-5\), we simply strip away the negative sign, leaving us with \(5\). The absolute value of a positive number remains unchanged.

Think of distance: If you walked 5 steps forward or 5 steps backward, your distance covered is still 5 steps, not -5. This is why absolute values are always positive.

Multiplication is one of the fundamental operations in arithmetic and algebra. When we multiply two numbers, we are adding one number to itself as many times as the value of the other number. For example, \(5 \times 5\) means adding \(5\) to itself five times ( \(5 + 5 + 5 + 5 + 5\) ), which equals \(25\).

In our exercise, after determining the absolute value of \(-5\) is \(5\), the next step is to multiply this value by the given number, which is also \(5\). The expression changes to \(5 \times 5\). When you compute this, it simplifies to \(25\).

An easy way to remember how multiplication works is to think of it as repeated addition. This can be particularly useful for visual learners when grappling with more complex numbers.

Simplification is the process of reducing an expression to its most basic form. It’s about making an equation easier to understand and work with.

In the given exercise, the simplification process involves two main steps: first, finding the absolute value and then performing the multiplication. Initially, the expression is \(5|-5|\). Breaking this down:

• Step 1: Calculate the absolute value of \(-5\), which is \(5\).
• Step 2: Multiply the absolute value by \(5\), leading to the expression \(5 \times 5\).
• Step 3: Finally, compute the multiplication to get \(25\).

By simplifying each part of the expression step-by-step, we make complex processes more manageable. This way, simplifying algebraic expressions becomes less intimidating and more systematic.