Problem 14 - Algebra 1: Concepts and Skills

Question

Evaluate the variable expression when \(k=3\) $$ \frac{18}{k} $$

Step-by-Step Solution

Answer

The result of evaluating the given variable expression when \(k=3\) is \(6\).

Step 1: Substitute given value

Replace \(k\) in the expression \(\frac{18}{k}\) with \(3\). Hence, the expression becomes \(\frac{18}{3}\).

Step 2: Perform the Division Operation

The next step is to perform the division operation, giving \( \frac{18}{3} = 6\).

Key Concepts

Substitution

Substitution is a fundamental concept in math that simplifies expressions by replacing variables with known values.
The purpose is to make calculations straightforward. In the original exercise, we have a variable expression \(\frac{18}{k}\).
Whenever you hear about substitution, think of it as plugging a number into every spot where a variable is present.

• Identify the variable: Double-check which variable needs to be replaced. In our case, it's \(k\).
• Find its value: Here, we are given \(k = 3\). Make sure you know the correct value to substitute.
• Substitute effectively: Replace \(k\) with the number 3 in the expression \(\frac{18}{k}\), we transform it into the fraction \(\frac{18}{3}\).

Substitution sets the stage for further operations, making the expression easier to solve.

Division

Division is a basic arithmetic operation that tells us how many times one number is contained within another.
In our expression, we encounter the fraction \(\frac{18}{3}\).

• Understand the terms: The top number, 18, is called the numerator, while the bottom number, 3, is the denominator.
• Perform the division: Here, you see how many times 3 fits into 18. The answer is 6.
• Interpret the process: When you divide 18 by 3, you're essentially distributing 18 into 3 equal parts.

Practicing division will strengthen your mathematical skills and help you handle variable expressions confidently.

Evaluate Expressions

Evaluating expressions involves executing operations after substituting variables, ultimately arriving at a numerical outcome.
This complete process is essential for interpreting mathematical problems. Let's finish with one last look at our example.

• Start with substitution: Substituting the variable gives us \(\frac{18}{3}\).
• Proceed with division: Perform the division operation to find that \(\frac{18}{3} = 6\).
• Conclude with the result: The evaluated expression equals 6. This is our final answer.

Evaluating expressions can feel like solving a puzzle, where each step logically brings us closer to the solution.