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Chapter 1: Problem 13

In each term, give the numerical coefficient of the variable(s). $$ -12 k $$

Short Answer

Expert verified
-12

Step by step solution

01

Identify the variable

First, identify the variable present in the term. In this case, the variable is \( k \).
02

Identify the numerical coefficient

Next, look at the term to find the number that is multiplying the variable. Here, the term is \(-12k\), so the numerical coefficient is the number \(-12\).
03

State the numerical coefficient

Finally, state the numerical coefficient of the term \(-12k\). The coefficient is \(-12\).

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Key Concepts

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

variables in algebra
In algebra, variables are symbols that represent unknown quantities. They are usually denoted by letters such as \(x\), \(y\), or \(k\). Variables are fundamental because they can take on different values, making it possible to generalize mathematical expressions and equations.
For example, in the term \(-12k\), the letter \(k\) is the variable. This means that \(k\) can have any value, and the term \(-12k\) will change depending on the value of \(k\). Understanding variables is key to solving algebraic problems, as they help to formulate and manipulate expressions.
coefficients in algebra
Coefficients are the numerical parts of terms in algebraic expressions that multiply the variables. They give us information about how much the variable is being scaled or multiplied.
For example, in the term \(-12k\), the coefficient is \(-12\). This means that whatever value \(k\) takes, it gets multiplied by \(-12\). Coefficients can be positive, negative, fractions, and even irrational numbers. They are essential for defining the magnitude and sign of the term they accompany.
The role of coefficients is to provide a scalar value that needs to be applied to the variable. Recognizing and understanding coefficients is crucial for simplifying and solving algebraic expressions.
identifying coefficients
Identifying coefficients in algebra is a straightforward but vital skill. Here are the steps to identify the coefficient in any term:
  • **Locate the variable:** Determine which symbol in the term represents the variable.
  • **Find the number attached to the variable:** Look for the numerical part of the term that multiplies the variable. This number is the coefficient.
For instance, let's identify the coefficient in the term \(-12k\):
  • First, we identify the variable. In this case, it is \(k\).
  • Next, we look at the number attached to \(k\), which is \(-12\). This is the coefficient.
So the coefficient of \(-12k\) is \(-12\). By mastering these steps, you can easily identify coefficients in more complex algebraic expressions.

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