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Chapter 1: Problem 23

In each term, give the numerical coefficient of the variable(s). $$ \frac{2 x}{5} $$

Short Answer

Expert verified
The numerical coefficient is \( \frac{2}{5} \).

Step by step solution

01

Identify the variable

First, locate the variable in the given term. In this term, the variable is \( x \).
02

Identify the numerical part

Look at the term \( \frac{2 x}{5} \) and separate the numerical part from the variable. Here, \( 2 \) is the coefficient attached to \( x \), and \( 5 \) is in the denominator.
03

Simplify the coefficient

To find the numerical coefficient, divide the number in the numerator by the denominator. So, the numerical coefficient of the term is \( \frac{2}{5} \).

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Key Concepts

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

Variables
In algebra, variables are symbols used to represent unknown values. They are typically written as letters such as x, y, or z.
Variables allow us to create general formulas and equations that can be solved for different values. For example, in the term \(\frac{2x}{5}\), the letter x is a variable.
It stands for some number that we may or may not know. Understanding what variables represent is the first step in tackling algebraic expressions.
Coefficients
A coefficient is a number that is multiplied by a variable in an algebraic expression. For instance, in the term \(\frac{2x}{5}\), the number 2 is the coefficient of the variable x.
Coefficients tell us how much of the variable we have. They can be whole numbers, fractions, or decimals.
In this case, we divide the numerator by the denominator \[ \frac{2}{5} \] to find the numerical coefficient, yielding \(\frac{2}{5}\).
Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operations (like addition, subtraction, multiplication, and division). An example is \(\frac{2x}{5}\).
Such expressions can be simplified, evaluated, or manipulated according to algebraic rules.
Understanding each part of the expression, like variables and coefficients, helps in simplifying and solving these expressions.
Mathematics Education
Mathematics education focuses on teaching concepts like variables, coefficients, and algebraic expressions. Learning these basics builds a strong foundation for more advanced topics.
Good mathematics education involves breaking down complex concepts into simpler steps, as seen in the detailed solution above.
It ensures that students grasp each part fully before moving on. Mastering these fundamentals aids in solving more complex problems later on.

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Most popular questions from this chapter

Perform each indicated operation. $$ \frac{-5(2)+[3(-2)-4]}{-3-(-1)} $$

Write a numerical expression for each phrase and simplify. Three-fourths of the sum of \(-8\) and 12

Simplify each expression. $$ -2(-3 k+2)-(5 k-6)-3 k-5 $$

Among entertainment expenditures, the average annual spending per U.S. household on fees and admissions was \(\$ 526\) in 2001 . This amount decreased \(\$ 32\) by 2003 and then increased \(\$ 112\) by \(2006 .\) What was the average household expenditure for fees and admissions in \(2006 ?\)

Write a numerical expression for each phrase and simplify. The quotient of \(-12\) and the sum of \(-5\) and \(-1\)
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