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Simplification is all about making an expression easier to understand and work with. When simplifying, we break down complex expressions into simpler parts. For example, in our exercise, we start with a somewhat complicated expression: \(-\left|-\frac{4}{5}\right|\).
We first recognize that we need to address the absolute value inside the expression. By understanding and applying the absolute value, we simplify the expression significantly.
Remember, the goal of simplification is to get the simplest and most easily understandable form of the expression. It can involve removing parentheses, combining like terms, or reducing fractions.

A number line is a straight line on which every point corresponds to a real number. It's useful for visualizing and understanding numbers, especially when dealing with absolute values.
Think of the absolute value as the distance from zero on this line. For instance, \(-\frac{4}{5}\) is to the left of zero, but distance (absolute value) is always a positive measure. On the number line, you always move right when measuring distance, regardless of the original direction.
This visualization helps us see that \(-\frac{4}{5}\) and \(\frac{4}{5}\) are both \(\frac{4}{5}\) units away from zero, but on different sides. It's all about how far and not which direction.

The term non-negative simply means not negative, so it includes all positive numbers and zero. The absolute value of any number is always non-negative. This is a fundamental property of absolute value.
In our exercise, when we took the absolute value of \(-\frac{4}{5}\), we got \(\frac{4}{5}\), since the absolute value removes the negative sign.
The key point to remember is that the absolute value function never results in a negative number. No matter which number you start with—positive, negative, or zero—the output is always non-negative. This is why \(|-x| = x\) for any positive \(x\).
Practicing this concept helps build a solid foundation in understanding and simplifying expressions involving absolute value.