Simplify The Following Algebraic Expression:$ \frac{1}{9} M - 5 + \frac{2}{3} M }$Choose The Correct Simplification A. { \frac{7 {9} M - 5$}$B. { \frac{1}{4} M - 5$}$C. { -\frac{5}{9} M - 5$}$D.

by ADMIN 196 views

Understanding the Problem

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying a given algebraic expression, which involves combining like terms and performing arithmetic operations.

The Algebraic Expression

The given algebraic expression is:

19m−5+23m{ \frac{1}{9} m - 5 + \frac{2}{3} m }

Our goal is to simplify this expression by combining like terms and performing arithmetic operations.

Step 1: Identify Like Terms

To simplify the expression, we need to identify like terms, which are terms that have the same variable raised to the same power. In this case, the like terms are the terms involving the variable mm. The expression contains two terms involving mm: 19m\frac{1}{9} m and 23m\frac{2}{3} m.

Step 2: Combine Like Terms

To combine like terms, we need to add or subtract the coefficients of the like terms. In this case, we need to add the coefficients of the two terms involving mm. To do this, we need to find a common denominator for the fractions. The least common multiple of 9 and 3 is 9, so we can rewrite the second term as:

23m=69m{ \frac{2}{3} m = \frac{6}{9} m }

Now we can combine the two terms:

19m+69m=79m{ \frac{1}{9} m + \frac{6}{9} m = \frac{7}{9} m }

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by performing arithmetic operations. In this case, we need to subtract 5 from the combined term:

79m−5{ \frac{7}{9} m - 5 }

Conclusion

In conclusion, the simplified algebraic expression is:

79m−5{ \frac{7}{9} m - 5 }

This is the correct answer among the given options.

Discussion

The discussion category for this problem is mathematics, specifically algebra. The problem requires the application of algebraic techniques, such as combining like terms and performing arithmetic operations.

Answer Options

The answer options are:

A. ${ \frac{7}{9} m - 5 }$

B. ${ \frac{1}{4} m - 5 }$

C. ${ -\frac{5}{9} m - 5 }$

D. (Not provided)

Final Answer

The final answer is A. ${ \frac{7}{9} m - 5 }$

Additional Tips and Tricks

  • When simplifying algebraic expressions, it's essential to identify like terms and combine them.
  • To combine like terms, find a common denominator and add or subtract the coefficients.
  • Perform arithmetic operations, such as subtraction, to simplify the expression.
  • Check your answer by plugging in values for the variable to ensure that the expression is simplified correctly.

Common Mistakes to Avoid

  • Failing to identify like terms and combine them.
  • Not finding a common denominator when combining like terms.
  • Not performing arithmetic operations to simplify the expression.
  • Not checking the answer by plugging in values for the variable.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications, such as:

  • Physics: Simplifying algebraic expressions is essential in physics, where equations often involve complex variables and operations.
  • Engineering: Engineers use algebraic expressions to model and analyze complex systems, and simplifying these expressions is crucial for making accurate predictions.
  • Computer Science: Simplifying algebraic expressions is a fundamental concept in computer science, where algorithms often involve complex mathematical operations.

Conclusion

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants.

Q: What is the purpose of simplifying algebraic expressions?

A: The purpose of simplifying algebraic expressions is to make them easier to work with and understand. Simplifying expressions can help us to:

  • Identify patterns and relationships between variables and constants
  • Make predictions and calculations more accurate
  • Solve equations and inequalities more efficiently

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

  1. Identify like terms and combine them
  2. Perform arithmetic operations, such as addition and subtraction
  3. Simplify fractions and decimals
  4. Check your answer by plugging in values for the variable

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, follow these steps:

  1. Find a common denominator for the fractions
  2. Add or subtract the coefficients of the like terms
  3. Simplify the resulting expression

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I simplify fractions and decimals?

A: To simplify fractions and decimals, follow these steps:

  1. Simplify the numerator and denominator of the fraction
  2. Reduce the fraction to its simplest form
  3. Convert the decimal to a fraction or vice versa

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

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

  • Failing to identify like terms and combine them
  • Not finding a common denominator when combining like terms
  • Not performing arithmetic operations to simplify the expression
  • Not checking the answer by plugging in values for the variable

Q: How do I check my answer when simplifying an algebraic expression?

A: To check your answer when simplifying an algebraic expression, follow these steps:

  1. Plug in values for the variable
  2. Evaluate the expression using the given values
  3. Check that the result is correct

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

A: Some real-world applications of simplifying algebraic expressions include:

  • Physics: Simplifying algebraic expressions is essential in physics, where equations often involve complex variables and operations.
  • Engineering: Engineers use algebraic expressions to model and analyze complex systems, and simplifying these expressions is crucial for making accurate predictions.
  • Computer Science: Simplifying algebraic expressions is a fundamental concept in computer science, where algorithms often involve complex mathematical operations.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By following the steps outlined in this article, you can simplify complex expressions and make accurate predictions in various fields.