Simplify { (4x) \cdot Mn \cdot 15 \cdot 2$}$.A. ${ 120mnx\$} B. ${ 34 \times Mn\$}
Understanding the Expression
To simplify the given expression, we need to apply the rules of multiplication and combine like terms. The expression is {(4x) \cdot mn \cdot 15 \cdot 2$}$. We can start by multiplying the numbers together and then combining the variables.
Step 1: Multiply the Numbers
The numbers in the expression are 4, 15, and 2. We can multiply these numbers together to get:
${4 \cdot 15 \cdot 2 = 120\$}
So, the expression becomes {(4x) \cdot mn \cdot 120$}$.
Step 2: Multiply the Variables
The variables in the expression are x, m, and n. We can multiply these variables together to get:
{x \cdot m \cdot n = mnx$}$
So, the expression becomes ${120mnx\$}.
Step 3: Combine the Results
Now, we can combine the results of the previous steps to get the final simplified expression:
${120mnx\$}
Conclusion
The simplified expression is ${120mnx\$}. This is the final answer.
Comparison with the Options
Let's compare the simplified expression with the options given:
A. ${120mnx\$} B. ${34 \times mn\$}
The simplified expression matches option A. Therefore, the correct answer is:
The Final Answer is A. ${120mnx\$}
Why is this the Correct Answer?
The correct answer is A. ${120mnx\$} because it is the simplified form of the given expression. The expression was simplified by multiplying the numbers together and combining the variables. The final simplified expression is ${120mnx\$}, which matches option A.
What is the Importance of Simplifying Expressions?
Simplifying expressions is an important skill in mathematics because it helps to:
- Make calculations easier
- Reduce errors
- Improve understanding of mathematical concepts
- Enhance problem-solving skills
Real-World Applications of Simplifying Expressions
Simplifying expressions has many real-world applications, such as:
- Calculating costs and revenues in business
- Determining the area and perimeter of shapes in architecture and engineering
- Solving problems in physics and engineering
- Understanding complex systems in computer science
Tips for Simplifying Expressions
Here are some tips for simplifying expressions:
- Start by multiplying the numbers together
- Combine like terms
- Use the distributive property to simplify expressions
- Check your work to ensure that the expression is simplified correctly
Common Mistakes to Avoid
Here are some common mistakes to avoid when simplifying expressions:
- Failing to multiply numbers together
- Not combining like terms
- Using the distributive property incorrectly
- Not checking your work
Conclusion
Q: What is the simplified form of the expression {(4x) \cdot mn \cdot 15 \cdot 2$}$?
A: The simplified form of the expression is ${120mnx\$}.
Q: How do I simplify the expression {(4x) \cdot mn \cdot 15 \cdot 2$}$?
A: To simplify the expression, you need to multiply the numbers together and combine the variables. Start by multiplying the numbers together: $4 \cdot 15 \cdot 2 = 120\$}. Then, multiply the variables together$. Finally, combine the results to get the final simplified expression: ${120mnx\$}.
Q: What is the distributive property, and how do I use it to simplify expressions?
A: The distributive property is a rule that allows you to multiply a single term by multiple terms. To use the distributive property, multiply each term inside the parentheses by the term outside the parentheses. For example, ${3(2x + 4) = 6x + 12\$}.
Q: How do I combine like terms in an expression?
A: To combine like terms, look for terms that have the same variable and coefficient. For example, ${2x + 3x = 5x\$}. Combine the coefficients of the like terms to get the final result.
Q: What is the importance of simplifying expressions?
A: Simplifying expressions is an important skill in mathematics because it helps to:
- Make calculations easier
- Reduce errors
- Improve understanding of mathematical concepts
- Enhance problem-solving skills
Q: What are some real-world applications of simplifying expressions?
A: Simplifying expressions has many real-world applications, such as:
- Calculating costs and revenues in business
- Determining the area and perimeter of shapes in architecture and engineering
- Solving problems in physics and engineering
- Understanding complex systems in computer science
Q: How do I avoid common mistakes when simplifying expressions?
A: To avoid common mistakes when simplifying expressions, make sure to:
- Multiply numbers together correctly
- Combine like terms correctly
- Use the distributive property correctly
- Check your work to ensure that the expression is simplified correctly
Q: What are some tips for simplifying expressions?
A: Here are some tips for simplifying expressions:
- Start by multiplying numbers together
- Combine like terms
- Use the distributive property to simplify expressions
- Check your work to ensure that the expression is simplified correctly
Q: Can you provide examples of expressions that can be simplified using the distributive property?
A: Yes, here are some examples of expressions that can be simplified using the distributive property:
- ${3(2x + 4) = 6x + 12\$}
- ${4(x + 2) = 4x + 8\$}
- ${2(x - 3) = 2x - 6\$}
Q: Can you provide examples of expressions that can be simplified by combining like terms?
A: Yes, here are some examples of expressions that can be simplified by combining like terms:
- ${2x + 3x = 5x\$}
- {x + 2x = 3x$}$
- ${3x - 2x = x\$}
Conclusion
Simplifying expressions is an important skill in mathematics that has many real-world applications. By following the steps outlined in this article, you can simplify expressions and improve your understanding of mathematical concepts. Remember to start by multiplying numbers together, combine like terms, and use the distributive property to simplify expressions.