Problem 50 - Prealgebra

Question

Evaluate each expression for the given value. (lesson \(1-3\) ) $$12 p ; p=11$$

Step-by-Step Solution

Answer

The result is 132.

Step 1: Understand the expression

The given expression is \(12p\), and you have to evaluate it for \(p=11\). This means you'll substitute \(11\) for \(p\) in the expression.

Step 2: Substitute the value of p

Replace \(p\) in the expression \(12p\) with \(11\). So it becomes \(12(11)\).

Step 3: Calculate the product

Multiply the constant \(12\) by \(11\) to find the result of the expression. Calculate \(12 \times 11\).

Step 4: Final Calculation

Perform the multiplication: \(12 \times 11 = 132\).

Key Concepts

Understanding Substitution in Algebraic Expressions

Substitution in algebra is a fundamental concept that involves replacing a variable with a given number to simplify or evaluate an expression. This is particularly useful when you're given a specific value for the variable. Let's consider the expression \(12p\). Here, \(p\) is a variable that we need to substitute with a number to simplify the expression.

In our problem, the given value is \(p = 11\). So, substitution means we replace \(p\) with \(11\) in the expression \(12p\). This turns our expression into \(12(11)\).

Practicing substitution helps you in solving algebraic equations efficiently and is a stepping stone for more complex topics in algebra. Always ensure to substitute carefully and check that all instances of the variable have been replaced before proceeding to the next steps.

Mastering Multiplication in Algebra

Once substitution is completed, multiplication becomes the main focus. In algebra, multiplication is used to simplify expressions or solve equations after substitution. In our example, after substituting \(p\) with \(11\), we have the expression \(12(11)\).

This is where our multiplication skills come in. You now multiply \(12\), which is a constant, by \(11\) to find the product. This is a straightforward arithmetic operation, but it helps to break it down into steps:

• First, calculate \(12 \times 11\).
• A simple way is to break it into smaller multiplication parts such as \(12 \times 10 = 120\) and then \(12 \times 1 = 12\).
• Sum these results to get the total: \(120 + 12 = 132\).

Breaking down multiplication like this can simplify the process and help avoid mistakes in calculations.

Evaluating Expressions: Arriving at the Final Answer

Evaluation of expressions is the process of finding the value of an expression by carrying out all necessary operations, such as substitution and arithmetic calculations. We've substituted \(p\) and done the multiplication for our expression \(12p\), where \(p = 11\).

After performing the multiplication \(12 \times 11\), we've arrived at \(132\). This is the value of the expression \(12p\) after substituting \(p\) with \(11\).

Evaluation is critical in algebra because it verifies that all mathematical operations have been correctly executed, ensuring the result is accurate. Always double-check your substitutions and calculations to make sure the evaluation is correct. This practice will not only enhance your accuracy but also build confidence in dealing with algebraic expressions.