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Chapter 1: Problem 21

In each term, give the numerical coefficient of the variable(s). $$ \frac{x}{2} $$

Short Answer

Expert verified
The numerical coefficient is \(\frac{1}{2}\).

Step by step solution

01

Identify the Variable

The term given is \(\frac{x}{2}\). Identify the variable in the term, which is \(x\) in this case.
02

Understand the Format of the Term

Observe the format of the term, \(\frac{x}{2}\). This can be rewritten as \(\frac{1}{2} x\).
03

Extract the Numerical Coefficient

The numerical coefficient is the number that multiplies the variable \(x\). In the rewritten form \(\frac{1}{2} x\), the coefficient is \(\frac{1}{2}\).

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Key Concepts

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

Variable Identification
Variables are symbols, usually letters, that represent unknown values in mathematical expressions. Identifying the variable is a crucial first step in algebra. In the term \(\frac{x}{2}\), the variable is clearly noted as \ x \. Recognizing variables helps understand the structure of the term and how different operations affect the expression. Always remember to look for letters or symbols that are not numbers to spot the variables easily.
Format of Algebraic Terms
Algebraic terms come in different formats, but understanding how they are structured makes manipulation easier. The term \(\frac{x}{2}\) can be tricky to interpret at first glance. To simplify, it helps to rewrite this format. For example, \(\frac{x}{2}\) is the same as saying \(\frac{1}{2}x\). Here, \ \frac{1}{2} \ serves as the numerical part, while \ x \ remains the variable. Rewriting terms in a more recognizable format ensures you correctly identify each part, aiding your calculations and interpretations.
Rewriting Algebraic Expressions
Rewriting algebraic expressions is a valuable skill in simplifying and solving equations. In algebra, expressions might initially appear complex. Taking \(\frac{x}{2}\) again, this can be refactored for clarity. Rewritten, it appears as \(\frac{1}{2} x \). This transformation makes it evident that the numerical coefficient is \ \frac{1}{2}\. Rewriting helps in several ways:
  • Clarifying the structure of the term.
  • Making it easier to identify the variable and numerical parts.
  • Providing a standardized form for further operations.
Utilize rewriting techniques to simplify algebraic terms and enhance your understanding.

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