Why Do You Saying That The Final Answer Is 108(4/3)4/(2/9)2
Understanding the Problem
When dealing with complex mathematical expressions, it's essential to break them down into manageable parts and follow the order of operations. In this case, the expression 108(4/3)4/(2/9)2 appears to be a mix of arithmetic operations and fractions. To determine the final answer, we need to carefully evaluate each part of the expression.
Breaking Down the Expression
Let's start by simplifying the fractions within the expression:
- 4/3
- 2/9
To simplify these fractions, we can find their decimal equivalents:
- 4/3 ≈ 1.33
- 2/9 ≈ 0.22
Now, let's substitute these decimal values back into the original expression:
108(1.33)4/(0.22)2
Evaluating the Expression
Next, we need to follow the order of operations (PEMDAS):
- Evaluate the expressions inside the parentheses:
- 108(1.33) = 143.64
- 4/(0.22) = 18.18
- Raise the results to the power of 2:
- 143.64^2 ≈ 20651.41
- 18.18^2 ≈ 329.59
- Divide the results:
- 20651.41 ÷ 329.59 ≈ 62.83
The Final Answer
Based on the step-by-step evaluation of the expression, the final answer is approximately 62.83. However, the original expression contains fractions, which may lead to a different result. Let's re-evaluate the expression using the original fractions:
108(4/3)4/(2/9)2
To simplify this expression, we can multiply the fractions:
(108 × 4) / (3 × 4) × (4 × 9) / (2 × 9) × (2 × 2)
This simplifies to:
(432) / (12) × (36) / (18) × (4)
Now, let's evaluate the expression:
432 ÷ 12 = 36 36 × 36 = 1296 1296 ÷ 18 = 72 72 × 4 = 288
The Correct Final Answer
Based on the correct evaluation of the expression, the final answer is 288.
Conclusion
In conclusion, the original expression 108(4/3)4/(2/9)2 appears to be a complex mathematical expression that requires careful evaluation. By breaking down the expression into manageable parts and following the order of operations, we can determine the final answer. However, the original expression contains fractions, which may lead to a different result. By re-evaluating the expression using the original fractions, we can arrive at the correct final answer of 288.
Common Mistakes to Avoid
When dealing with complex mathematical expressions, it's essential to avoid common mistakes such as:
- Not following the order of operations
- Not simplifying fractions
- Not evaluating expressions inside parentheses correctly
By avoiding these common mistakes, we can ensure that our calculations are accurate and reliable.
Real-World Applications
The concept of evaluating complex mathematical expressions is essential in various real-world applications, such as:
- Engineering: When designing complex systems, engineers need to evaluate mathematical expressions to ensure that their designs are accurate and reliable.
- Science: Scientists use mathematical expressions to model complex phenomena and make predictions about future events.
- Finance: Financial analysts use mathematical expressions to evaluate investment opportunities and make informed decisions.
By understanding how to evaluate complex mathematical expressions, we can apply this knowledge to real-world problems and make informed decisions.
Final Thoughts
Frequently Asked Questions
Q: What is the final answer to the expression 108(4/3)4/(2/9)2?
A: The final answer to the expression 108(4/3)4/(2/9)2 is 288.
Q: Why is the final answer different from the original calculation?
A: The original calculation used decimal equivalents of the fractions, which led to an incorrect result. By re-evaluating the expression using the original fractions, we can arrive at the correct final answer.
Q: What is the correct order of operations for evaluating the expression?
A: The correct order of operations is:
- Evaluate the expressions inside the parentheses
- Raise the results to the power of 2
- Divide the results
Q: How do I simplify fractions in a mathematical expression?
A: To simplify fractions, you can find their decimal equivalents or multiply the numerator and denominator by the same value to eliminate the fraction.
Q: What are some common mistakes to avoid when evaluating complex mathematical expressions?
A: Some common mistakes to avoid include:
- Not following the order of operations
- Not simplifying fractions
- Not evaluating expressions inside parentheses correctly
Q: How do I apply the concept of evaluating complex mathematical expressions to real-world problems?
A: You can apply the concept of evaluating complex mathematical expressions to real-world problems by:
- Breaking down complex systems into manageable parts
- Following the order of operations
- Simplifying fractions and evaluating expressions correctly
Q: What are some real-world applications of evaluating complex mathematical expressions?
A: Some real-world applications of evaluating complex mathematical expressions include:
- Engineering: Designing complex systems and ensuring that they are accurate and reliable
- Science: Modeling complex phenomena and making predictions about future events
- Finance: Evaluating investment opportunities and making informed decisions
Q: How do I ensure that my calculations are accurate and reliable?
A: To ensure that your calculations are accurate and reliable, you should:
- Follow the order of operations
- Simplify fractions and evaluate expressions correctly
- Double-check your work for errors
Q: What are some resources for learning more about evaluating complex mathematical expressions?
A: Some resources for learning more about evaluating complex mathematical expressions include:
- Online tutorials and videos
- Math textbooks and workbooks
- Online communities and forums
Q: How do I practice evaluating complex mathematical expressions?
A: You can practice evaluating complex mathematical expressions by:
- Working on sample problems and exercises
- Using online resources and tools
- Joining a study group or working with a tutor
Q: What are some tips for evaluating complex mathematical expressions quickly and accurately?
A: Some tips for evaluating complex mathematical expressions quickly and accurately include:
- Breaking down complex expressions into manageable parts
- Following the order of operations
- Simplifying fractions and evaluating expressions correctly
Q: How do I apply the concept of evaluating complex mathematical expressions to my career or personal life?
A: You can apply the concept of evaluating complex mathematical expressions to your career or personal life by:
- Using mathematical expressions to model complex systems and make predictions
- Evaluating investment opportunities and making informed decisions
- Designing complex systems and ensuring that they are accurate and reliable
Q: What are some common challenges when evaluating complex mathematical expressions?
A: Some common challenges when evaluating complex mathematical expressions include:
- Following the order of operations
- Simplifying fractions and evaluating expressions correctly
- Dealing with complex and unfamiliar mathematical concepts
Q: How do I overcome common challenges when evaluating complex mathematical expressions?
A: You can overcome common challenges when evaluating complex mathematical expressions by:
- Breaking down complex expressions into manageable parts
- Following the order of operations
- Simplifying fractions and evaluating expressions correctly
Q: What are some resources for learning more about overcoming common challenges when evaluating complex mathematical expressions?
A: Some resources for learning more about overcoming common challenges when evaluating complex mathematical expressions include:
- Online tutorials and videos
- Math textbooks and workbooks
- Online communities and forums
Q: How do I practice overcoming common challenges when evaluating complex mathematical expressions?
A: You can practice overcoming common challenges when evaluating complex mathematical expressions by:
- Working on sample problems and exercises
- Using online resources and tools
- Joining a study group or working with a tutor