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Substitution is a fundamental concept in algebra that involves replacing a variable with a given numerical value or another expression. In the context of the exercise, you were asked to evaluate the expression involving the variable \( p \) given that \( p = 4.1 \). To perform substitution:

• First, identify the variable in the expression and the value it is meant to represent.
• Replace every occurrence of the variable in the expression with the provided value.

For example, you substitute \( p = 4.1 \) into the expression \( 4.2p \), turning it into \( 4.2 \times 4.1 \). Substitution transforms an algebraic expression into a numerical one, which can then be calculated directly. Remember, accurate substitution is crucial as any mistakes could result in incorrect evaluations.

Multiplication is one of the basic operations of arithmetic and is fundamental in algebra for evaluating expressions after substitution. Once you have successfully substituted a variable with a number, the next step is to perform the multiplication.In this exercise, after substituting \( p = 4.1 \), the expression becomes \( 4.2 \times 4.1 \). Multiplication involves finding the product of these two numbers. Here’s how you can think about it:

• Write down the numbers vertically if needed and multiply as you would with whole numbers.
• Remember to account for decimal places in the final result.

Multiplying 4.2 by 4.1 gives you their product, which can be calculated using a calculator or manual multiplication. It's especially helpful to understand the role of decimal places and how they affect the placement of the decimal in your final answer.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In this context, algebra basics help you evaluate expressions and solve equations efficiently. Here are a few key points to remember in algebra:

• Variables represent numbers and can be substituted or manipulated depending on the problem.
• Arithmetic operations like addition, subtraction, multiplication, and division are solved following the rules of precedence, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• Expressions are simplified by performing the operations in a step-by-step manner.

The intrinsic beauty of algebra lies in its ability to generalize arithmetic operations. It allows us to create expressions and equations that model real-world situations, making these concepts essential for advanced mathematics and practical problem-solving. Remember that practicing these basics will build a strong foundation for more complex topics in the future.