Problem 67 - Intermediate Algebra

Question

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Five less than a number

Step-by-Step Solution

Answer

The expression is \( n - 5 \).

Step 1: Identify the Phrase

The English phrase 'five less than a number' needs to be translated into an algebraic expression. It suggests subtracting 5 from an unknown number.

Step 2: Assign a Variable for the Unknown Number

Let the unknown number be represented by the variable \( n \). This is a common choice in algebra for unknowns.

Step 3: Translate the Phrase

The phrase 'five less than a number \( n \)' means we need to subtract 5 from \( n \). So, the algebraic expression becomes \( n - 5 \).

Key Concepts

English Phrase Translation

When working with algebraic expressions, it is crucial to understand how to translate English phrases into mathematical equations. This involves interpreting the language of words into the precise language of math. Let's take the English phrase "five less than a number" as our example.

This specific phrase indicates a subtraction operation, but with a twist. Unlike simply subtracting 5 from an unidentified number, the words "less than" imply that 5 should be subtracted from the number itself. So, our translation focuses on reversing the order because the phrase tells us to take an unknown number first and then subtract 5.

This translation process allows us to convert word problems into algebraic operations that you can then solve. Remember, different phrases in English might result in different algebraic operations, so it's important to pay close attention to the wording.

Variable Representation

In algebra, unknown quantities are often represented by variables, which are typically denoted by letters such as \( n \), \( x \), or \( y \). Systematically representing numbers with variables is both a powerful and flexible tool.

For this exercise, we represent the unknown number by \( n \). Using \( n \) as our variable helps create a universal solution that can be applied to any number that fits the conditions of the problem. This method of representation makes solving equations more straightforward because it gives us a concrete symbol to work with.

Variable representation is not merely about choosing a letter. It also involves understanding the underlying problem and knowing what the variable stands for. This skill helps in setting up and solving equations where the value of the variable is unknown but needs to be determined.

Basic Algebra

Basic algebra involves the manipulation and solving of algebraic expressions and equations. One key concept in this area is translating phrases into mathematical expressions and performing operations such as addition, subtraction, multiplication, and division.

In this exercise, the objective is to construct an algebraic expression from the phrase "five less than a number." We fulfill this by writing the expression as \( n - 5 \). The crucial step involves understanding that "less than" directly translates to subtraction, and the natural order in English is reversed in mathematical operations.

This exercise is a fundamental example of the types of operations and thought processes you will frequently encounter in algebra. Mastering these basic concepts sets the groundwork for more advanced topics in mathematics, as they're often built upon understanding expressions, assignments, and simplifications at this basic level.