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The number line is a straight line on which every point corresponds to a real number. It is used to represent numbers graphically. Positive numbers are located to the right of zero and negative numbers to the left.
You can use the number line to visually understand the concept of absolute value. For instance, if you place \(-\frac{4}{5}\) on the number line, it will be to the left of zero. Its distance from zero, irrespective of direction, is the absolute value.
This distance, seen on the number line, is always a non-negative value. Thus, when we say \(|-\frac{4}{5}| = \frac{4}{5}\), we are essentially measuring how far it is from zero.

A non-negative value is a value that is either positive or zero. It can never be negative. This is a critical concept in understanding absolute value.
The absolute value of a number represents its distance from zero, and distances are always non-negative. Therefore, irrespective of whether the number itself is negative, positive or zero, its absolute value will always be a non-negative value.
For example, the absolute value of \(-\frac{4}{5}\) is \(\frac{4}{5}\), which is a non-negative value. Similarly, the absolute value of any positive number, like \(+\frac{4}{5}\), will remain \(+\frac{4}{5}\). It shows that absolute value can never be negative, reinforcing the idea that absolute values are always non-negative.

Simplifying expressions involves making them easier to work with or understand. In the context of absolute value, this often requires stripping away unnecessary negative signs and reducing the expression to its simplest form.
For example, let's take the given exercise \(- | - \frac{4}{5} |\). Here’s how you can simplify it step-by-step:

• First, find the absolute value of \(- \frac{4}{5}\). Absolute value removes the negative sign, so \(| - \frac{4}{5} | = \frac{4}{5}\).
• Next, substitute this value back into the expression to get \(- \frac{4}{5}\).

This process shows that simplification often involves using fundamental properties of mathematical operations to make expressions more manageable.