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When we talk about algebraic expressions, we refer to mathematical phrases that can contain numbers, variables (like x or y), and operational symbols such as addition and subtraction. Unlike equations, algebraic expressions don't have an equality sign. Instead, they provide a way to represent relationships between quantities.
For example, if you see an expression like \(3x + 4\), it means "three times a number, plus four." The number here is represented by the variable 'x'. Variables stand in for numbers that can change, or that we don't yet know.
Algebraic expressions can get more complex by combining variables and numbers in various ways, including multiplication and division, as seen in the given exercise where variables interact within a fraction: \(\frac{y}{|y|}\). This expression combines algebraic concepts with the absolute value, necessitating a clear understanding of how both elements work together.

Simplifying expressions is about making them more straightforward while keeping their value the same. When simplifying expressions that include absolute values, we need to remember that absolute value represents the distance of a number from zero on the number line, hence it is always non-negative.
In the expression \(\frac{y}{|y|}\), simplifying it involves first computing the absolute value of 'y'. For instance, the absolute value of \(-5\) is \(5\) because distance is always positive.
Simplifying an expression can also involve performing basic arithmetic operations like division or multiplication. Here, once the absolute value is simplified, the original expression becomes \(\frac{-5}{5}\), which can then be further simplified into a simpler form by carrying out the division.

Evaluating algebraic expressions involves two primary steps: substituting values and computing the result. You begin by replacing each variable with given numbers. In our exercise, 'y' was replaced by \(-5\).
When variables have specified values, the algebraic expression transforms into a numerical expression consisting only of numbers. Here, \(y\) is replaced with \(-5\), turning \(\frac{y}{|y|}\) into \(\frac{-5}{5}\).
The next step involves calculating the final value through any operations indicated. In this scenario, you perform the division which results in \(-1\).

• Start by substituting the variable values.
• Compute absolute values if needed.
• Perform arithmetic operations to find the answer.

This process results in a complete understanding of how input values affect the outcome of an expression.