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Chapter 1: Problem 20

Fill in the blanks. Terms that have no variables are called __________.

Short Answer

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Constants

Step by step solution

01

Identifying the Concept

The exercise is based on the basic terminology of algebra. We are looking for the term that describes elements in mathematical expressions that have no variables. This can be remembered or found in any introductory material on algebraic expressions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Constant Terms
In algebra, constant terms play an important role. These are numbers in an equation or expression that do not have any variables attached to them. Think of them as fixed values that do not change, regardless of how the variables in the algebraic expression change. For example, in the expression \(3x + 4\), the number 4 is a constant term. It remains 4 no matter what value \(x\) takes. Constant terms are crucial because they provide stability and predictability to algebraic equations.
Breaking Down Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operations that represent values. They are like sentences in mathematics, constructed with numbers as the nouns and operations as the verbs. In expressions such as \(5x + 3y - 7\), each part separated by a plus or minus sign is called a 'term.' Each term can include numbers, variables, or a combination of both. This makes algebraic expressions a little like recipes, where each term represents an ingredient that contributes to the final dish.
Exploring Introductory Algebra
Introductory algebra is often your first step into the world of abstract mathematics. It introduces basic concepts such as variables, constants, and algebraic expressions. These concepts are the building blocks of algebra. When you start learning algebra, you explore how to manipulate numbers and variables in expressions, which sets the foundation for solving equations and understanding more advanced mathematical ideas. Familiarizing yourself with these basics can make advanced topics easier to tackle later on. Studies and exercises at this level focus on understanding terminology and learning how to recognize different components of algebraic expressions.

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Most popular questions from this chapter

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$6-2<10-4$$

Suppose there were no numbers other than the odd integers. \(\cdot\) Would the closure property for addition still be true? \(\cdot\) Would the closure property for multiplication still be true? \(\cdot\) Would there still be an identity for addition? \(\cdot\) Would there still be an identity for multiplication?

When would it be better to change an improper-fraction answer into a mixed number?

Explain why zero is an even integer.

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