Problem 82 - Algebra 1: Concepts and Skills

Question

Identify the terms of the expression. \(31-15 n\)

Step-by-Step Solution

Answer

The terms of the expression \(31-15 n\) are \(31\) and \(-15 n\).

Step 1: Identify the First Term

In the expression \(31-15 n\), the first term present is \(31\). It's a constant term, meaning a term with only a number and no variable.

Step 2: Identify the Second term

Following the subtraction sign, the next term is \(-15 n\). This term is a variable term, including a variable \(n\).

Step 3: List the Terms

After identifying, list the terms of the expression. Here, we have two terms: \(31\) and \(-15 n\). Usually, positive terms are listed first, but it's also appropriate to list them as they appear in the original expression.

Key Concepts

Terms of an Expression

Algebraic expressions are like mathematical sentences formed by combining numbers, variables, and operators. Understanding the terms of an expression is a crucial step in grasping algebraic concepts. Terms are individual components separated by addition or subtraction signs in an expression. For instance, in the expression \(31 - 15n\), there are two distinct terms:

• 31: A simple numeric value.
• -15n: A product of a number and a variable.

Each term can be a single number, a single variable, or a product of numbers and variables. They are building blocks that make up the entire expression.
Paying attention to the signs (+/-) is crucial, as they indicate whether you are adding or subtracting the terms. It's not unlike separating a complex sentence into understandable parts, where each term plays its unique role.

Constant Term

A constant term in an algebraic expression is a term that contains only a number, with no variable attached. These terms stand alone numerically, like isolated pieces unaffected by any changes in the value of a variable. They are easy to spot since they appear as plain numbers.In our example expression \(31 - 15n\), \(31\) is the constant term. It remains unchanged regardless of the values that variables in the expression might take. Think of it as a fixed point in a dynamic system. Constant terms act like fixed foundations upon which the rest of the expression builds. They make calculations more straightforward by providing known values to work with. Identifying the constant terms in any given expression is a basic yet critical skill in algebra.

Variable Term

The other component of algebraic expressions is the variable term. Unlike constant terms, variable terms contain variables and coefficients. They represent parts of the expression that can change depending on the variable's value. Variable terms encapsulate the essence of algebra, bringing flexibility and dynamic computation into play.In the expression \(31 - 15n\), \(-15n\) is a variable term. Here:

• -15: The coefficient, which is the number multiplying the variable.
• n: The variable, an unknown that represents different values.

Variable terms are important because they express how things might change. They are adaptable and can represent real-world problems where some quantities are likely to vary.
Grasping the nature of variable terms is vital for solving and manipulating algebraic expressions and equations.