upgrade

➕pre-algebra review

Numerical Expression

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

A numerical expression is a mathematical phrase that represents a value or quantity using numbers, variables, and operations. It is a fundamental concept in algebra and pre-algebra, as it forms the basis for evaluating, simplifying, and translating expressions.

5 Must Know Facts For Your Next Test

  1. Numerical expressions can be evaluated by applying the order of operations (PEMDAS) to calculate the final value.
  2. Simplifying a numerical expression involves reducing it to its simplest form by performing the necessary operations.
  3. Translating a verbal description into a numerical expression requires identifying the relevant numbers, variables, and operations.
  4. Numerical expressions can contain both constants (fixed values) and variables (unknown or changeable values).
  5. The complexity of a numerical expression can range from simple arithmetic operations to more advanced expressions involving exponents, roots, and functions.

Review Questions

  • Explain the process of evaluating a numerical expression, including the importance of the order of operations.
    • Evaluating a numerical expression involves applying the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), to calculate the final value. This order ensures that the operations are performed in the correct sequence, as the result can vary depending on the order in which the operations are carried out. By following PEMDAS, the numerical expression is simplified step-by-step, leading to the correct solution.
  • Describe the difference between simplifying and translating a numerical expression, and provide examples of each.
    • Simplifying a numerical expression involves reducing it to its most basic form by performing the necessary operations. For example, the expression $3 + 4 \times 2$ can be simplified to $11$ by first multiplying $4 \times 2$ and then adding $3$. Translating a verbal description into a numerical expression, on the other hand, requires identifying the relevant numbers, variables, and operations, and then representing them in a mathematical form. For instance, the verbal description 'the sum of a number and its square' can be translated into the numerical expression $x + x^2$, where $x$ represents the unknown number.
  • Analyze how the presence of variables in a numerical expression affects the process of evaluating and simplifying the expression, and explain the importance of understanding the role of variables in this context.
    • The presence of variables in a numerical expression adds an additional layer of complexity to the processes of evaluating and simplifying. When variables are involved, the expression cannot be reduced to a single numerical value, as the value of the expression will depend on the specific value assigned to the variable(s). Instead, the expression must be simplified as much as possible, leaving the variable(s) in the final result. Understanding the role of variables is crucial in this context, as it allows you to manipulate and work with expressions that contain unknown quantities, which is a fundamental skill in algebra and pre-algebra. By mastering the handling of variables within numerical expressions, you can solve a wide range of problems and equations that involve unknown values.