Definition of Numerical Coefficient

The numerical coefficient of a term in an algebraic expression is the number that is multiplied by the variable(s) in that term. It represents the magnitude or size of the term and is independent of any variables or exponents involved. In other words, it is the constant factor that appears in front of the variables.

Example: -7pq

Let's consider the term -7pq as an example to understand its numerical coefficient.

Identification of Variables

In this term, we have two variables: p and q. These variables represent unknown values or quantities.

Identification of Numerical Coefficient

To identify the numerical coefficient, we need to look at the constant factor that is multiplied by the variables. In this case, the constant factor is -7. Therefore, the numerical coefficient of the term -7pq is -7.

Explanation of Numerical Coefficient

The numerical coefficient provides information about the magnitude or size of the term. In this case, the coefficient -7 indicates that the term -7pq is relatively larger or smaller compared to other terms in the expression, depending on the context.

Visual Representation of the Term

The term -7pq can be visually represented as follows:

-7pq

Here, the negative sign (-) indicates a negative coefficient. The variables p and q are multiplied by the coefficient -7.

Importance of Numerical Coefficient

The numerical coefficient plays a crucial role in simplifying algebraic expressions, solving equations, and performing various algebraic operations. It helps in understanding the relative size or scale of different terms within an expression.

Conclusion

The numerical coefficient of a term in an algebraic expression represents the constant factor that is multiplied by the variables in that term. In the case of the term -7pq, the numerical coefficient is -7. It provides information about the magnitude or size of the term and is essential in algebraic manipulations.