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In algebra, variable substitution is a fundamental technique. When you see an expression with a variable like \(\frac{x-2}{5}\), you can replace that variable with a given number. This is helpful for solving expressions or equations. For example:
1. The original expression is \(\frac{x-2}{5}\).
2. If we are given \(x=4\), we substitute 4 for x. The expression then becomes \(\frac{4-2}{5}\).
3. Similarly, if \(x=6\), we substitute 6 for x. The expression then becomes \(\frac{6-2}{5}\).
This method helps in evaluating the expression for different values of the variable. Variable substitution is especially important as it's a stepping stone for more complex algebra problems.

Simplifying expressions means reducing them to their simplest form. After substituting the variable, you'll often need to perform simplification:
1. For \(x=4\), the substituted expression becomes \(\frac{4-2}{5}\).
2. First, solve the inside of the numerator: \(4-2=2\).
3. Now the expression is \(\frac{2}{5}\).
4. This fraction represents a division: 2 divided by 5 equals 0.4.
The key steps are performing operations inside the parentheses first, then dividing the result by the number in the denominator. This process ensures the expression is always in its simplest form, making it easier to understand and work with.

Fractions are a significant part of algebra, often seen in various expressions and equations. Understanding how to work with fractions is crucial:
1. A fraction consists of a numerator and a denominator. In \(\frac{x-2}{5}\), \(x-2\) is the numerator and 5 is the denominator.
2. After variable substitution, like \(x=6\), the expression becomes \(\frac{6-2}{5}\).
3. Simplify the numerator: \(6-2=4\). The expression is now \(\frac{4}{5}\).
4. Perform the division: 4 divided by 5 equals 0.8.
This shows the importance of grasping how fractions work in algebra, helping you handle more complex algebraic problems later on. Alleviating the fear of fractions in algebra can open doors to better problem-solving skills in mathematics.