Problem 2
Question
Fill in the blanks. The _____ of the term \(-8 c\) is \(-8\)
Step-by-Step Solution
Verified Answer
The coefficient of the term \(-8c\) is \(-8\).
1Step 1: Understanding the Components of a Term
A term in an algebraic expression consists of a constant multiplied by a variable. In the term \(-8c\), \(-8\) is the constant while \(c\) is the variable.
2Step 2: Identify the Coefficient
In an algebraic term, the coefficient is the numerical part that is multiplied by the variable. Therefore, for the term \(-8c\), the coefficient is \(-8\).
3Step 3: Complete the Sentence
Based on the identified coefficient, we can now fill in the blank: The coefficient of the term \(-8c\) is \(-8\).
Key Concepts
Understanding Term ComponentsCoefficients in AlgebraVariables in Terms
Understanding Term Components
In algebra, a term is a single mathematical expression. It can be a number, a variable, or a combination of both. A term is a building block for algebraic expressions. Each term consists of several components, which can include:
A simple term like \(-8c\) has just two components: \(-8\) and \(c\). The \(-8\) is the numerical coefficient, and \(c\) is the variable. No exponent is explicitly shown, so the variable is understood to be to the power of 1.
This basic knowledge of term components lays the foundation for algebraic operations.
- Numerical coefficients
- Variables
- Constants
- Exponents (in some cases)
A simple term like \(-8c\) has just two components: \(-8\) and \(c\). The \(-8\) is the numerical coefficient, and \(c\) is the variable. No exponent is explicitly shown, so the variable is understood to be to the power of 1.
This basic knowledge of term components lays the foundation for algebraic operations.
Coefficients in Algebra
The coefficient in algebra is the number that is multiplied by the variable in an algebraic term. It represents the quantity of the variable in the term.
Coefficients can be positive or negative, integers or fractions. They play a vital role in operations such as addition and subtraction of algebraic expressions. For instance, if you have two terms like \(3x\) and \(-8x\), their coefficients (3 and \(-8\) respectively) can be added by first adding the coefficients: \((3 + (-8)) = -5\). Therefore, the expression becomes \(-5x\).
In the term \(-8c\), the coefficient is \(-8\), signifying how much of the variable \(c\) is present.
Coefficients can be positive or negative, integers or fractions. They play a vital role in operations such as addition and subtraction of algebraic expressions. For instance, if you have two terms like \(3x\) and \(-8x\), their coefficients (3 and \(-8\) respectively) can be added by first adding the coefficients: \((3 + (-8)) = -5\). Therefore, the expression becomes \(-5x\).
In the term \(-8c\), the coefficient is \(-8\), signifying how much of the variable \(c\) is present.
Variables in Terms
Variables are symbols, often letters, that stand in for numbers in algebraic expressions. They are essential to formulating and solving algebra problems, representing unknowns or varying values.
Commonly, variables are denoted by letters like \(x\), \(y\), or \(z\), but any letter can serve as a variable. In the term \(-8c\), \(c\) is the variable, representing an unknown number.
The role of a variable is to facilitate formulating equations that represent real-world problems or abstract equations in algebra. By manipulating variables, you can simplify complex expressions and solve equations to find the value of the unknown variable. This is why understanding variables in terms is so crucial in algebra.
Commonly, variables are denoted by letters like \(x\), \(y\), or \(z\), but any letter can serve as a variable. In the term \(-8c\), \(c\) is the variable, representing an unknown number.
The role of a variable is to facilitate formulating equations that represent real-world problems or abstract equations in algebra. By manipulating variables, you can simplify complex expressions and solve equations to find the value of the unknown variable. This is why understanding variables in terms is so crucial in algebra.
Other exercises in this chapter
Problem 2
Fill in the blanks. When we multiply two numbers, the result is called the _____. When we divide two numbers, the result is called the _____.
View solution Problem 2
When all the members of one set are members of a second set, we say the first set is a _____ of the second set.
View solution Problem 2
Variables and/or numbers can be combined with mathematical operations to create algebraic _______.
View solution Problem 3
Fill in the blanks. When the regular price of an item is reduced, the amount of reduction is called the _____.
View solution