Besides helping me solve the sum also please explain why my rough work is incorrect..

Let's dive into your question about solving a sum and understanding where your rough work might have gone off track. To provide a thorough explanation, I'll need to see the specific sum you're working on and the steps you took in your rough work. However, I can guide you through a general approach to solving mathematical problems and highlight common pitfalls that might lead to errors.

Breaking Down the Problem

When tackling a mathematical sum, it's essential to follow a structured approach. Here’s a step-by-step method you can use:

• Read the Problem Carefully: Ensure you understand what is being asked. Look for keywords that indicate operations, such as "sum," "difference," "product," or "quotient."
• Identify the Components: Break the problem into smaller parts. If it’s an equation, identify the variables and constants involved.
• Write Down Your Steps: As you work through the problem, write down each step clearly. This not only helps you keep track but also makes it easier to identify where you might have gone wrong.
• Check Your Work: After arriving at an answer, go back through your steps to ensure each one is correct. This is where many mistakes can be caught.

Common Mistakes to Avoid

Here are some frequent errors that can occur during calculations:

• Misreading the Problem: Sometimes, a simple misinterpretation of the question can lead to an entirely different approach.
• Arithmetic Errors: Basic addition, subtraction, multiplication, or division mistakes can easily happen, especially under time pressure.
• Incorrect Order of Operations: Remember the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to ensure you perform operations in the correct sequence.
• Neglecting Units: If your problem involves measurements, forgetting to keep track of units can lead to incorrect answers.

Example Scenario

Let’s say you were solving the sum 3 + 5 × 2. If you added 3 and 5 first, you might have gotten 8, and then multiplied by 2 to get 16. However, the correct approach is to follow the order of operations:

1. First, multiply: 5 × 2 = 10
2. Then, add: 3 + 10 = 13

So, the correct answer is 13. If your rough work led you to 16, it was likely due to not applying the order of operations correctly.

Final Thoughts

To summarize, always take your time to understand the problem, break it down into manageable parts, and carefully follow each step. If you share your specific sum and rough work, I can provide more targeted feedback on where things might have gone awry. Remember, making mistakes is a part of learning, and each error is an opportunity to improve your understanding!