Problem 15 - Algebra 1: Concepts and Skills

Question

Evaluate the variable expression when \(k=3\) $$ 18 \cdot k $$

Step-by-Step Solution

Answer

The value of the expression when \(k=3\) is 54.

Step 1: Identify the value of the variable

The problem gives the specific value for 'k'; it is 3.

Step 2: Substitute variable into the expression

Replace 'k' in the expression 18 \cdot k with the number 3. This turns the expression into 18 \cdot 3.

Step 3: Simplify the expression

Multiply 18 by 3 to simplify the expression into a single numerical value.

Key Concepts

Substitution in Algebra

In algebra, 'substitution' refers to the process of replacing variables with their corresponding values. This is an essential technique for evaluating variable expressions, like the one you're working with. When you are given a variable expression and the value of that variable, such as evaluating the expression when \(k=3\), your first step is to replace every instance of \(k\) with 3.

For example, if you have the expression \(18 \cdot k\), the substitution process involves replacing \(k\) with 3 to obtain \(18 \cdot 3\). Substitution is a straightforward process, but it's crucial to be accurate to avoid any mistakes in the following steps.

Simplifying Expressions

Simplifying expressions in algebra means turning a complex or compound expression into a simpler one that has the same value. This often involves carrying out the arithmetic operations indicated in the expression.

After substituting the variables with their values, you'll often end up with an arithmetic expression. In our example, substituting \(k\) with 3 gives us the expression \(18 \cdot 3\), which we then simplify by multiplying 18 by 3. Simplification doesn't change the value of the expression; it makes it easier to understand and work with.

It is crucial to follow the correct order of operations when simplifying, usually denoted by the acronym PEMDAS—Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). In our case, only multiplication is involved, making the process simple.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. These are the basic building blocks of math and are essential when simplifying algebraic expressions.

Once you have substituted values into a variable expression and have an arithmetic expression to simplify, you'll perform the necessary operations to find the answer. Our given expression \(18 \cdot k\) becomes \(18 \cdot 3\), and here, multiplication is the operation we use.

• Addition combines numbers together.
• Subtraction removes one number from another.
• Multiplication finds the total when adding a number to itself multiple times.
• Division splits a number into several equal parts.

In the example provided, the solution is the product of 18 and 3, which is 54. Understanding how to perform these operations swiftly and correctly is fundamental to building solid mathematical skills.