Write And Evaluate The Following Algebraic Expression When $n=4.8$: The Product Of 24 And A Number.Which Is The Correct Expression And Product?A. 24 N \frac{24}{n} N 24 ​ ; When N = 4.8 N=4.8 N = 4.8 , The Value Is 115.2.B. N 24 \frac{n}{24} 24 N ​ ;

Understanding the Problem

In this article, we will explore the concept of algebraic expressions and how to evaluate them when given a specific value for the variable. We will focus on the problem of finding the product of 24 and a number, and then evaluate the expression when the value of the variable is 4.8.

What is an Algebraic Expression?

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants. Algebraic expressions can be used to solve equations, inequalities, and other mathematical problems.

The Product of 24 and a Number

The problem asks us to find the product of 24 and a number. This can be represented algebraically as:

$$24 \times n$$

where $n$ is the unknown number.

Evaluating the Expression

To evaluate the expression, we need to substitute the value of $n$ into the expression. In this case, we are given that $n=4.8$. Substituting this value into the expression, we get:

$$24 \times 4.8$$

To evaluate this expression, we can multiply 24 by 4.8.

Multiplying 24 by 4.8

To multiply 24 by 4.8, we can use the multiplication algorithm. We can multiply 24 by 4 and then multiply the result by 0.8.

$$24 \times 4 = 96$$

$$96 \times 0.8 = 76.8$$

Therefore, the product of 24 and 4.8 is 76.8.

Evaluating the Algebraic Expression

Now that we have evaluated the expression, we can write the correct algebraic expression and product.

The correct algebraic expression is:

$$24 \times n$$

When $n=4.8$, the value of the expression is:

$$24 \times 4.8 = 76.8$$

Conclusion

In this article, we have explored the concept of algebraic expressions and how to evaluate them when given a specific value for the variable. We have focused on the problem of finding the product of 24 and a number, and then evaluated the expression when the value of the variable is 4.8. We have shown that the correct algebraic expression is $24 \times n$, and when $n=4.8$, the value of the expression is 76.8.

Common Mistakes

When evaluating algebraic expressions, it is easy to make mistakes. Here are some common mistakes to avoid:

• Not substituting the value of the variable: Make sure to substitute the value of the variable into the expression.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when evaluating the expression.
• Not simplifying the expression: Make sure to simplify the expression before evaluating it.

Real-World Applications

Algebraic expressions have many real-world applications. Here are a few examples:

• Science: Algebraic expressions are used to model scientific phenomena, such as the motion of objects and the behavior of populations.
• Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and electronic circuits.
• Finance: Algebraic expressions are used to model financial systems, such as investments and loans.

Final Thoughts

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about evaluating 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 of representing a mathematical relationship between variables and constants.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the value of the variable into the expression and then follow the order of operations (PEMDAS).

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

• P: Parentheses (evaluate expressions inside parentheses first)
• E: Exponents (evaluate any exponential expressions next)
• M: Multiplication and Division (evaluate any multiplication and division operations from left to right)
• A: Addition and Subtraction (finally, evaluate any addition and subtraction operations from left to right)

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the same exponent (1).

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, 2x + 4x = 6x.

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. An equation is a statement that says two expressions are equal. For example, 2x + 3 = 5 is an equation because it says that the expression 2x + 3 is equal to the expression 5.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What are some common mistakes to avoid when evaluating algebraic expressions?

A: Some common mistakes to avoid when evaluating algebraic expressions include:

• Not substituting the value of the variable: Make sure to substitute the value of the variable into the expression.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when evaluating the expression.
• Not simplifying the expression: Make sure to simplify the expression before evaluating it.

Q: How can I practice evaluating algebraic expressions?

A: You can practice evaluating algebraic expressions by working through practice problems and exercises. You can also use online resources, such as algebraic expression evaluators and practice tests, to help you improve your skills.

Conclusion

In conclusion, evaluating algebraic expressions is an important skill that is used in a wide range of mathematical and real-world applications. By understanding how to evaluate algebraic expressions, you can solve complex mathematical problems and make informed decisions in your personal and professional life. Remember to always follow the order of operations and simplify the expression before evaluating it. With practice and patience, you will become proficient in evaluating algebraic expressions and solving complex mathematical problems.