Select The Expressions That Are Equivalent To $9n + 4n$.A. $14n$B. $ 10 N + 4 N 10n + 4n 10 N + 4 N [/tex]C. $n + 13$D. $4n + 5n + 4n$
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying the expression $9n + 4n$ and explore the different options provided in the multiple-choice question. We will break down the steps involved in simplifying the expression and analyze each option to determine which one is equivalent to the given expression.
Understanding the Expression
The given expression is $9n + 4n$. This is an algebraic expression that consists of two terms: $9n$ and $4n$. The variable $n$ is the common factor in both terms.
Simplifying the Expression
To simplify the expression, we need to combine the two terms by adding their coefficients. The coefficient of a term is the numerical value that multiplies the variable. In this case, the coefficients are 9 and 4.
# Define the coefficients
coefficient_1 = 9
coefficient_2 = 4
sum_of_coefficients = coefficient_1 + coefficient_2
By adding the coefficients, we get $13$. This means that the simplified expression is $13n$.
Analyzing the Options
Now that we have simplified the expression, let's analyze each option to determine which one is equivalent to the given expression.
Option A: $14n$
This option is not equivalent to the given expression because the coefficient is different. The coefficient in the given expression is $13$, but in this option, it is $14$.
Option B: $10n + 4n$
This option is not equivalent to the given expression because it is not simplified. The expression $10n + 4n$ can be simplified by combining the coefficients, just like we did earlier.
# Define the coefficients
coefficient_1 = 10
coefficient_2 = 4
sum_of_coefficients = coefficient_1 + coefficient_2
By adding the coefficients, we get $14$. This means that the simplified expression is $14n$, which is not equivalent to the given expression.
Option C: $n + 13$
This option is not equivalent to the given expression because the variable $n$ is not multiplied by the coefficient. In the given expression, $n$ is multiplied by $13$, but in this option, it is not.
Option D: $4n + 5n + 4n$
This option is not equivalent to the given expression because it is not simplified. The expression $4n + 5n + 4n$ can be simplified by combining the coefficients.
# Define the coefficients
coefficient_1 = 4
coefficient_2 = 5
coefficient_3 = 4
sum_of_coefficients = coefficient_1 + coefficient_2 + coefficient_3
By adding the coefficients, we get $13$. This means that the simplified expression is $13n$, which is equivalent to the given expression.
Conclusion
In conclusion, the correct answer is Option D: $4n + 5n + 4n$. This option is equivalent to the given expression $9n + 4n$ because both expressions can be simplified to $13n$.
Final Answer
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In our previous article, we explored the expression $9n + 4n$ and simplified it to $13n$. In this article, we will provide a Q&A guide to help you understand the concept of simplifying algebraic expressions.
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.
Q: What is simplifying an algebraic expression?
A: Simplifying an algebraic expression means combining like terms to reduce the expression to its simplest form. This involves adding or subtracting coefficients of like terms to get a single term.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, follow these steps:
- Identify the like terms in the expression.
- Add or subtract the coefficients of the like terms.
- Combine the like terms to get a single term.
Q: What is the order of operations when simplifying algebraic expressions?
A: The order of operations when simplifying algebraic expressions is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: Can I simplify an algebraic expression by combining unlike terms?
A: No, you cannot simplify an algebraic expression by combining unlike terms. Unlike terms are terms that have different variables or variables raised to different powers. Combining unlike terms will result in an incorrect expression.
Q: What is the difference between combining like terms and simplifying an algebraic expression?
A: Combining like terms is a step in simplifying an algebraic expression. Simplifying an algebraic expression involves combining like terms and reducing the expression to its simplest form.
Q: Can I simplify an algebraic expression with variables raised to different powers?
A: Yes, you can simplify an algebraic expression with variables raised to different powers. However, you cannot combine like terms with variables raised to different powers.
Q: What is the importance of simplifying algebraic expressions?
A: Simplifying algebraic expressions is important because it helps to:
- Reduce the complexity of the expression
- Make it easier to solve equations and inequalities
- Improve the accuracy of calculations
- Enhance problem-solving skills
Conclusion
In conclusion, simplifying algebraic expressions is a crucial skill to master in mathematics. By understanding the concept of like terms, combining like terms, and following the order of operations, you can simplify algebraic expressions and improve your problem-solving skills.
Final Answer
The final answer is that simplifying algebraic expressions is a fundamental concept in mathematics that involves combining like terms and reducing the expression to its simplest form.