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Chapter 1: Problem 24

In each term, give the numerical coefficient. \(p q\)

Short Answer

Expert verified
The numerical coefficient is 1.

Step by step solution

01

Identify the Terms

The given expression is a single term: \(p q\).
02

Understand the Variables

In the term \(p q\), the variables are \(p\) and \(q\). There are no numerical values explicitly shown.
03

Determine the Numerical Coefficient

When variables are multiplied without any numerical value shown, it implies a coefficient of 1. Thus, the numerical coefficient of the term \(p q\) is 1.

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Key Concepts

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

Algebraic Terms
Algebraic terms are the building blocks of algebraic expressions. Each term is a combination of numbers and variables, connected through multiplication or division.
For example, in the term \(4x^2\), \(4\) and \(x^2\) make up the algebraic term.
Terms can have coefficients, which are the numerical parts, and variables, which are the symbols representing numbers.
When working with algebraic terms, it's important to break them down into their components to understand their meaning fully.
Variables in Algebra
Variables are symbols used to represent unknown values or quantities that can change. In algebra, common variables include letters such as \(x\), \(y\), \(p\), and \(q\).
Variables can appear on their own or be part of a term. In an expression, they are often combined with numbers (coefficients) and other variables.
For example, in the term \(pq\), both \(p\) and \(q\) are variables. It means we're considering two unknown quantities multiplied together.
Understanding variables is essential, as they allow us to form equations and expressions to solve a wide range of problems.
Implied Coefficients
Implied coefficients refer to the numerical value assumed when no explicit number is shown.
Commonly, when variables are written without a numerical coefficient, it means the coefficient is 1.
For instance, in the term \(pq\), there is no number before \(p\) or \(q\), which implies that both variables have a coefficient of 1.
When simplifying or evaluating expressions, recognizing implied coefficients helps to clearly understand and work with each term efficiently. Be sure to always account for implied values to avoid mistakes.

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