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Substitution is a fundamental concept in prealgebra. It allows us to replace variables in an expression with actual numbers. This makes solving mathematical problems more straightforward.
In our exercise, we needed to evaluate the expression \( y - 10 \) when \( y = 8 \). This means that wherever there is a \( y \) in the expression, we replace it with the number 8. By doing so, the expression becomes \( 8 - 10 \). Substitution helps in transforming variables into specific numeric values, allowing for easy calculation. Without substitution, it would be challenging to get a definite answer when variables are involved.
Remember, the key to substitution is correctly identifying which values replace which variables. Each variable gets replaced only by its designated value, as provided in the problem statement.

Arithmetic operations are basic calculations that we frequently perform. They include addition, subtraction, multiplication, and division.
In our exercise, after substituting \( y = 8 \) into the expression \( y - 10 \), we need to calculate \( 8 - 10 \). This is a subtraction operation. Here's how subtraction works:

• Subtraction involves taking one number away from another.
• If the number being subtracted is larger than the one being subtracted from, the result is negative.
• In our case, subtracting 10 from 8 results in \( 8 - 10 = -2 \).

Understanding and getting comfortable with basic arithmetic operations like subtraction helps in accurately evaluating expressions.

Evaluating expressions involves simplifying them to a single numerical value using substitution and arithmetic operations. It's like solving a puzzle by following a few essential steps.
For the expression \( y - 10 \) with \( y = 8 \), we substitute 8 for \( y \) (the substitution step), turning it into \( 8 - 10 \) and then solve it to reach \( -2 \).

• Start by identifying the values you need for substitution.
• Perform necessary arithmetic operations.
• Simplify the expressions to result in one clear value.

By practicing how to evaluate such expressions, students can get a stronger grasp of algebra and prealgebra concepts. The method of breaking down steps; substitution followed by calculation, makes daunting problems more manageable and enjoyable!