Complete: Week 3 AssessmentQuestion 9 (2.5 Points)Which Verbal Expression Below Represents The Mathematical Expression: M + 2 M M + 2m M + 2 M ?A. M × 2 M M \times 2m M × 2 M B. M 2 + M \frac{m}{2+m} 2 + M M ​ C. M M M Increased By Twice M M M D. $m -

Understanding the Basics of Algebraic Expressions

In mathematics, algebraic expressions are a fundamental concept that helps us represent complex mathematical operations in a concise and organized manner. These expressions are made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will focus on simplifying verbal expressions, specifically the mathematical expression $m + 2m$.

The Importance of Verbal Expressions in Mathematics

Verbal expressions are a way to describe mathematical operations using words. They are essential in mathematics as they help us understand the meaning behind the mathematical operations and make it easier to solve problems. In the context of the given question, we need to find the verbal expression that represents the mathematical expression $m + 2m$.

Analyzing the Options

Let's analyze the options given in the question:

Option A: $m \times 2m$

This option represents the mathematical expression $m \times 2m$, which is not the same as $m + 2m$. The multiplication operation is different from the addition operation, and this option does not accurately represent the given mathematical expression.

Option B: $\frac{m}{2+m}$

This option represents the mathematical expression $\frac{m}{2+m}$, which is also not the same as $m + 2m$. The division operation is different from the addition operation, and this option does not accurately represent the given mathematical expression.

Option C: $m$ increased by twice $m$

This option represents the mathematical expression $m + 2m$, which is the same as the given mathematical expression. The phrase "increased by twice" is a common way to describe the addition operation, and this option accurately represents the given mathematical expression.

Option D: $m - 2m$

This option represents the mathematical expression $m - 2m$, which is not the same as $m + 2m$. The subtraction operation is different from the addition operation, and this option does not accurately represent the given mathematical expression.

Conclusion

In conclusion, the correct verbal expression that represents the mathematical expression $m + 2m$ is "m increased by twice m". This option accurately represents the addition operation and is the correct answer to the given question.

Tips for Simplifying Verbal Expressions

When simplifying verbal expressions, it's essential to understand the mathematical operations involved and to use the correct terminology. Here are some tips to help you simplify verbal expressions:

• Use the correct terminology: Use words that accurately describe the mathematical operations involved.
• Understand the mathematical operations: Make sure you understand the addition, subtraction, multiplication, and division operations and how they are represented in verbal expressions.
• Read the question carefully: Read the question carefully and make sure you understand what is being asked.
• Use examples: Use examples to help you understand the concept and to make it easier to simplify verbal expressions.

Common Verbal Expressions and Their Mathematical Representations

Here are some common verbal expressions and their mathematical representations:

• Increased by: This phrase is often used to describe the addition operation. For example, "m increased by twice m" represents the mathematical expression $m + 2m$.
• Decreased by: This phrase is often used to describe the subtraction operation. For example, "m decreased by twice m" represents the mathematical expression $m - 2m$.
• Multiplied by: This phrase is often used to describe the multiplication operation. For example, "m multiplied by twice m" represents the mathematical expression $m \times 2m$.
• Divided by: This phrase is often used to describe the division operation. For example, "m divided by twice m" represents the mathematical expression $\frac{m}{2m}$.

Practice Problems

Here are some practice problems to help you simplify verbal expressions:

• Which verbal expression represents the mathematical expression $m + 3m$?
• Which verbal expression represents the mathematical expression $m - 2m$?
• Which verbal expression represents the mathematical expression $m \times 2m$?
• Which verbal expression represents the mathematical expression $\frac{m}{2m}$?

Answer Key

Here are the answers to the practice problems:

• $m$ increased by three times $m$
• $m$ decreased by twice $m$
• $m$ multiplied by twice $m$
• $m$ divided by twice $m$

Conclusion

Q&A: Simplifying Verbal Expressions

Q: What is a verbal expression in mathematics?

A: A verbal expression in mathematics is a way to describe mathematical operations using words. It is a phrase or sentence that represents a mathematical operation, such as addition, subtraction, multiplication, or division.

Q: Why is it important to simplify verbal expressions?

A: Simplifying verbal expressions is important because it helps us understand the meaning behind mathematical operations. By using the correct terminology and understanding the mathematical operations involved, we can solve problems more efficiently and accurately.

Q: How do I simplify verbal expressions?

A: To simplify verbal expressions, follow these steps:

1. Read the question carefully: Read the question carefully and make sure you understand what is being asked.
2. Understand the mathematical operations: Make sure you understand the addition, subtraction, multiplication, and division operations and how they are represented in verbal expressions.
3. Use the correct terminology: Use words that accurately describe the mathematical operations involved.
4. Use examples: Use examples to help you understand the concept and to make it easier to simplify verbal expressions.

Q: What are some common verbal expressions and their mathematical representations?

A: Here are some common verbal expressions and their mathematical representations:

• Increased by: This phrase is often used to describe the addition operation. For example, "m increased by twice m" represents the mathematical expression $m + 2m$.
• Decreased by: This phrase is often used to describe the subtraction operation. For example, "m decreased by twice m" represents the mathematical expression $m - 2m$.
• Multiplied by: This phrase is often used to describe the multiplication operation. For example, "m multiplied by twice m" represents the mathematical expression $m \times 2m$.
• Divided by: This phrase is often used to describe the division operation. For example, "m divided by twice m" represents the mathematical expression $\frac{m}{2m}$.

Q: How do I practice simplifying verbal expressions?

A: Here are some practice problems to help you simplify verbal expressions:

• Which verbal expression represents the mathematical expression $m + 3m$?
• Which verbal expression represents the mathematical expression $m - 2m$?
• Which verbal expression represents the mathematical expression $m \times 2m$?
• Which verbal expression represents the mathematical expression $\frac{m}{2m}$?

Q: What are some tips for simplifying verbal expressions?

A: Here are some tips for simplifying verbal expressions:

• Use the correct terminology: Use words that accurately describe the mathematical operations involved.
• Understand the mathematical operations: Make sure you understand the addition, subtraction, multiplication, and division operations and how they are represented in verbal expressions.
• Read the question carefully: Read the question carefully and make sure you understand what is being asked.
• Use examples: Use examples to help you understand the concept and to make it easier to simplify verbal expressions.

Q: How do I know if I have simplified a verbal expression correctly?

A: To know if you have simplified a verbal expression correctly, follow these steps:

1. Check the mathematical operation: Make sure the verbal expression accurately represents the mathematical operation involved.
2. Check the terminology: Make sure the verbal expression uses the correct terminology to describe the mathematical operation.
3. Check the example: Use an example to help you understand the concept and to make it easier to simplify verbal expressions.

Conclusion

In conclusion, simplifying verbal expressions is an essential skill in mathematics that helps us understand the meaning behind mathematical operations. By using the correct terminology, understanding the mathematical operations involved, and reading the question carefully, we can simplify verbal expressions and solve problems more efficiently.