Problem 20 - Beginning and Intermediate Algebra

Question

In each term, give the numerical coefficient. \(-11 y\)

Step-by-Step Solution

Answer

-11

Step 1: Identify the numerical coefficient

The numerical coefficient is the constant factor that is multiplied by the variable(s) in a term. In this term, \(-11y\), the variable is \(y\).

Step 2: Extract the numerical part

Focus on the constant factor directly in front of the variable \(y\). This number represents the numerical coefficient.

Step 3: State the numerical coefficient

In the term \(-11y\), the numerical coefficient is \-11\.

Key Concepts

algebra terminology

Algebra can sometimes feel like learning a new language. Here are some key terms you should know:

• Term: A single mathematical expression, which can be a number, a variable, or numbers and variables multiplied together. For example, in the expression \(5x - 2\), both \(5x\) and \(-2\) are terms.
• Variable: A symbol, usually a letter, that represents a number we don't know yet. Common variables include x, y, and z.
• Constant: A value that doesn't change. In algebra, it's often a standalone number like 3 or -7.
• Coefficient: A number used to multiply a variable. In the term \(-11y\), \-11\ is the coefficient.
• Expression: A combination of numbers, variables, and operators (like + and -) that represents a value. For example, \(4x + 7\) is an expression.

Understanding these terms is crucial for solving any algebra problem. Once you know the language of algebra, it becomes much easier to decode problems and find solutions.

identifying constants

In algebra, constants are the numbers that stand alone. They don't change and are not multiplied by variables.

Here are some pointers to identify constants in an expression:

• Look for standalone numbers: These are the constants. For example, in \(6x + 3\), the number \(3\) is a constant.
• Differentiate between variables and constants: In the term \(8y\), \(8\) is not a constant because it is multiplied by the variable \(y\). Instead, it is a coefficient.
• Recognize constants in different contexts: Whether the number is positive or negative, if it stands alone, it qualifies as a constant. For example, \(-5\) in an expression is a constant.

Identifying constants is a fundamental step that helps simplify and solve algebraic expressions. By knowing which parts of an expression are constants, you can better understand the overall structure of the expression and solve it more efficiently.

variable and coefficient

Variables and coefficients work hand in hand in algebra. Knowing how to identify and manipulate them is essential. Let's break this down:

Variable:

• A variable is often represented by a letter like x, y, or z. It stands in for an unknown number.
• In \(-11y\), \(y\) is the variable. It can take any value depending on the equation or context.

Coefficient:

• The coefficient is the number multiplying the variable. It indicates how many times the variable is being added together.
• In the term \(-11y\), \-11\ is the coefficient. It tells us that \(-11\) times the value of \(y\) is our term.
• Coefficients can be positive or negative, and identifying them can help simplify equations and solve for variables.

Together, understanding variables and coefficients helps you decode algebraic expressions. Once identified, you can perform operations, solve equations, and understand the relationships between different parts of the expression more clearly.