Problem 19 - Beginning and Intermediate Algebra

Question

In each term, give the numerical coefficient. \(-12 k\)

Step-by-Step Solution

Answer

-12

Step 1: Identify the term

First, take a look at the given term which is \(-12 k\).

Step 2: Separate the components

Recognize that the term \(-12 k\) has two parts: the numerical part \(-12\) and the variable part \k\.

Step 3: Identify the numerical coefficient

The numerical coefficient is the number that is multiplying the variable. In this case, it is \(-12\).

Key Concepts

terms in algebra

In algebra, a term is a combination of numbers, variables, and sometimes exponents, all multiplied together. For example, in the term \( -12k \), we have one number \( -12 \) and one variable \( k \). Terms are the building blocks of algebraic expressions.

Terms can either be constants, like the number \( 5 \), or they can include variables, like \( -12k \).

• A constant term has only a number without any variable.
• A variable term includes at least one variable and is often accompanied by a coefficient.

variables

A variable is a symbol, usually a letter, that represents an unknown value in an algebraic expression.

In our example, the term \( -12k \) has the variable \( k \). Variables are essential in algebra because they allow us to write general formulas and solve equations.

Key points to remember about variables:

• Variables can represent different values at different times.
• Common variable letters include \( x \), \( y \), and \( z \), but any letter can be used.
• Variables are typically paired with coefficients that indicate how many times the variable is being multiplied.

coefficients

The coefficient in algebra is the numerical factor that is multiplied by the variable in a term.

In the term \( -12k \), \( -12 \) is the coefficient. Coefficients tell us how many times the variable is being taken.

Important points about coefficients:

• A coefficient can be positive or negative, indicating the direction of multiplication.
• If no number is written before a variable, the coefficient is \( 1 \). For example, in the term \( x \), the coefficient is understood to be \( 1 \).
• Coefficients are critical for comparing and simplifying algebraic expressions.

Understanding coefficients helps in solving algebraic problems and understanding the structure of terms better. In the given exercise, identifying \( -12 \) as the coefficient is essential to comprehend the term \( -12k \) completely.