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Chapter 5: Problem 8

Give the numerical coefficient and the degree of each term. $$ \frac{m}{4} $$

Short Answer

Expert verified
Numerical coefficient: \[ \frac{1}{4} \], Degree: 1

Step by step solution

01

Identify the Term

The given term is \[ \frac{m}{4} \]. This can be written as \[ \frac{1}{4} m \].
02

Determine the Numerical Coefficient

The numerical coefficient is the number multiplying the variable. In \[ \frac{1}{4} m \], the numerical coefficient is \[ \frac{1}{4} \].
03

Determine the Degree of the Term

The degree of a term is the exponent of the variable. Since \[ m \] is to the power of 1, the degree is 1.

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Key Concepts

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

Numerical Coefficient
In algebra, the numerical coefficient is a fundamental concept. This term describes the number that multiplies a variable in an algebraic expression. For instance, in the expression \(\frac{1}{4} m\), the numerical coefficient is \(\frac{1}{4}\). This concept helps identify the specific impact of the variable's multiplication. Always look at the number directly attached to the variable to find the numerical coefficient.
Algebraic Terms
Algebraic terms are the building blocks of algebraic expressions. They consist of numbers, variables, and sometimes exponents. Every algebraic term combines these elements in a particular format. For example, in the term \(\frac{1}{4} m\), \(\frac{1}{4}\) is the numerical coefficient, and \(m\) is the variable. Multiple algebraic terms can be added or subtracted to form a complete expression, like in the equation \(3x + 2y - 7\).
Degree of a Term
The degree of a term is determined by the exponent of its variable. It tells you the power to which the variable is raised. For example, in the term \(m\), the variable \(m\) is to the power of 1, so the degree is 1. In a term like \(3x^2\), the exponent is 2, making the degree 2. Knowing the degree helps understand the term's complexity and its role in polynomial functions.
Variables and Exponents
Variables and exponents are key elements of algebraic expressions. A variable represents an unknown value, like \(m\) or \(x\). An exponent indicates how many times the variable is multiplied by itself. For example, in \(x^2\), the variable \(x\) is squared, meaning \(x\) is multiplied by itself. Understanding these components helps in simplifying and solving algebraic equations.

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Most popular questions from this chapter

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ 4^{4} \cdot 4^{-6} $$

Evaluate. Express answers in standard notation. $$ \frac{12 \times 10^{4}}{2 \times 10^{6}} $$

Simplify each expression. Assume that all variables represent nonzero real numbers. $$ \left(\frac{-2 a^{4}}{b^{5}}\right)^{6} $$

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Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \frac{12 k^{-2}\left(k^{-3}\right)^{-4}}{6 k^{5}} $$
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