What Is The Expression And Value Of six Less Than The Quotient Of A Number And Two, Increased By Ten When \[$ N = 20 \$\]?A. \[$\frac{n}{2} - 6 + 10\$\]; When \[$ N = 20 \$\], The Value Is 14.B. \[$6 - \frac{n}{2} +

Feb 26, 2025 by ADMIN 218 views

Understanding the Problem

The given problem involves an algebraic expression that requires us to find the value when a specific number, denoted as n, is equal to 20. The expression is "six less than the quotient of a number and two, increased by ten." To solve this problem, we need to break down the expression into smaller parts and evaluate each part step by step.

Breaking Down the Expression

Let's start by identifying the individual components of the expression:

The quotient of a number and two: This can be represented as n/2.
Six less than the quotient: This can be represented as (n/2) - 6.
Increased by ten: This can be represented as (n/2) - 6 + 10.

Evaluating the Expression

Now that we have broken down the expression into smaller parts, let's evaluate each part step by step:

The quotient of a number and two: When n = 20, the quotient is 20/2 = 10.
Six less than the quotient: When the quotient is 10, six less than the quotient is 10 - 6 = 4.
Increased by ten: When the result is 4, increased by ten is 4 + 10 = 14.

Conclusion

Based on the evaluation of the expression, we can conclude that the value of "six less than the quotient of a number and two, increased by ten" when n = 20 is 14.

Discussion

Step-by-Step Solution

Here's a step-by-step solution to the problem:

Identify the individual components of the expression:
- The quotient of a number and two: This can be represented as n/2.
- Six less than the quotient: This can be represented as (n/2) - 6.
- Increased by ten: This can be represented as (n/2) - 6 + 10.
Evaluate each part of the expression step by step:
- The quotient of a number and two: When n = 20, the quotient is 20/2 = 10.
- Six less than the quotient: When the quotient is 10, six less than the quotient is 10 - 6 = 4.
- Increased by ten: When the result is 4, increased by ten is 4 + 10 = 14.

Common Mistakes

When solving algebraic expressions, it's essential to follow the order of operations (PEMDAS):

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.

Real-World Applications

Algebraic expressions are used in various real-world applications, such as:

Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, the value of "six less than the quotient of a number and two, increased by ten" when n = 20 is 14. This problem requires us to break down the expression into smaller parts and evaluate each part step by step. By following the order of operations and using algebraic techniques, we can solve complex algebraic expressions and apply them to real-world problems.

Frequently Asked Questions

Q: What is the expression "six less than the quotient of a number and two, increased by ten"?

A: The expression is (n/2) - 6 + 10.

Q: What is the value of the expression when n = 20?

A: The value of the expression when n = 20 is 14.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, follow the order of operations (PEMDAS): parentheses, exponents, multiplication and division, and addition and subtraction.

Q: What are some real-world applications of algebraic expressions?

A: Algebraic expressions are used in science, engineering, and economics to model real-world phenomena and make predictions about future trends.

Q&A Article

In this article, we will address some of the most frequently asked questions about algebraic expressions. Whether you are a student, teacher, or simply someone who wants to learn more about algebraic expressions, this article is for you.

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 are the Basic Components of an Algebraic Expression?

A: The basic components of an algebraic expression are:

Variables: These are letters or symbols that represent unknown values.
Constants: These are numbers that do not change value.
Mathematical Operations: These are the operations that are performed on the variables and constants, such as addition, subtraction, multiplication, and division.

Q: How Do I Evaluate an Algebraic Expression?

A: To evaluate an algebraic expression, follow the order of operations (PEMDAS):

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: 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 algebraic expressions are equal.

Q: How Do I Simplify an Algebraic Expression?

A: To simplify an algebraic expression, combine like terms and eliminate any unnecessary parentheses or brackets.

Q: What are Some Common Algebraic Expressions?

A: Some common algebraic expressions include:

Linear expressions: These are expressions that consist of a single variable and a constant, such as 2x + 3.
Quadratic expressions: These are expressions that consist of a variable squared and a constant, such as x^2 + 4x + 4.
Polynomial expressions: These are expressions that consist of a variable raised to a power and a constant, such as x^3 + 2x^2 + 3x + 1.

Q: How Do I Use Algebraic Expressions in Real-World Applications?

A: Algebraic expressions are used in various real-world applications, such as:

Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Q: What are Some Common Mistakes to Avoid When Working with Algebraic Expressions?

A: Some common mistakes to avoid when working with algebraic expressions include:

Not following the order of operations (PEMDAS)
Not combining like terms
Not eliminating unnecessary parentheses or brackets

Q: How Do I Practice Algebraic Expressions?

A: To practice algebraic expressions, try the following:

Work on algebraic expression problems from a textbook or online resource.
Practice simplifying and evaluating algebraic expressions.
Use algebraic expressions to model real-world phenomena and make predictions about future trends.

Conclusion

In conclusion, algebraic expressions are a fundamental concept in mathematics that are used to model real-world phenomena and make predictions about future trends. By understanding the basic components of an algebraic expression, how to evaluate an algebraic expression, and how to simplify an algebraic expression, you can apply algebraic expressions to various real-world applications.