Find $13.1 - 20.2 + 9 - (-38.5)$.A. 40.4 B. -40.4 C. 36.6 D. -36.6
Introduction
Arithmetic expressions can be complex and involve multiple operations, including addition, subtraction, multiplication, and division. In this article, we will focus on solving a specific arithmetic expression that involves a combination of these operations. The expression is: $13.1 - 20.2 + 9 - (-38.5)$. Our goal is to simplify this expression and find the final result.
Understanding the Order of Operations
Before we start solving the expression, it's essential to understand the order of operations. The order of operations is a set of rules that dictates the order in which we perform mathematical operations. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Breaking Down the Expression
Now that we understand the order of operations, let's break down the expression into smaller parts. The expression is: $13.1 - 20.2 + 9 - (-38.5)$. We can start by evaluating the expressions inside the parentheses.
Evaluating the Expression Inside the Parentheses
The expression inside the parentheses is: $-(-38.5)$. To evaluate this expression, we need to remember that a negative sign in front of a negative number becomes a positive number. Therefore, $-(-38.5) = 38.5$.
Substituting the Value Back into the Original Expression
Now that we have evaluated the expression inside the parentheses, we can substitute the value back into the original expression. The expression becomes: $13.1 - 20.2 + 9 + 38.5$.
Evaluating the Expression from Left to Right
Now that we have simplified the expression, we can start evaluating it from left to right. We will start by evaluating the first two operations: $13.1 - 20.2$.
Evaluating the First Two Operations
To evaluate the first two operations, we need to subtract 20.2 from 13.1. This gives us: $13.1 - 20.2 = -7.1$.
Substituting the Value Back into the Expression
Now that we have evaluated the first two operations, we can substitute the value back into the expression. The expression becomes: $-7.1 + 9 + 38.5$.
Evaluating the Next Operation
The next operation is to add 9 to -7.1. This gives us: $-7.1 + 9 = 1.9$.
Substituting the Value Back into the Expression
Now that we have evaluated the next operation, we can substitute the value back into the expression. The expression becomes: $1.9 + 38.5$.
Evaluating the Final Operation
The final operation is to add 38.5 to 1.9. This gives us: $1.9 + 38.5 = 40.4$.
Conclusion
In this article, we have solved a complex arithmetic expression that involved a combination of addition, subtraction, and negation. We have followed the order of operations and broken down the expression into smaller parts to simplify it. The final result is: $40.4$.
Answer
The correct answer is: A. 40.4
Discussion
Introduction
In our previous article, we solved a complex arithmetic expression that involved a combination of addition, subtraction, and negation. We followed the order of operations and broke down the expression into smaller parts to simplify it. In this article, we will provide a Q&A guide to help you understand the concepts and solve similar problems.
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which we perform mathematical operations. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate expressions inside parentheses?
A: To evaluate expressions inside parentheses, you need to follow the order of operations. If there are no parentheses, you can ignore this step. If there are parentheses, you need to evaluate the expression inside the parentheses first.
Q: What is the difference between a negative sign and a positive sign?
A: A negative sign in front of a number makes it negative, while a positive sign in front of a number makes it positive. For example, -5 is negative, while +5 is positive.
Q: How do I evaluate expressions with multiple operations?
A: To evaluate expressions with multiple operations, you need to follow the order of operations. You need to evaluate the expressions inside parentheses first, then evaluate any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.
Q: What is the final result of the expression 13.1 - 20.2 + 9 - (-38.5)?
A: The final result of the expression 13.1 - 20.2 + 9 - (-38.5) is 40.4.
Q: How do I simplify complex expressions?
A: To simplify complex expressions, you need to follow the order of operations and break down the expression into smaller parts. You need to evaluate the expressions inside parentheses first, then evaluate any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.
Q: What are some common mistakes to avoid when solving complex arithmetic expressions?
A: Some common mistakes to avoid when solving complex arithmetic expressions include:
- Not following the order of operations
- Not evaluating expressions inside parentheses first
- Not evaluating exponential expressions before multiplication and division operations
- Not evaluating multiplication and division operations from left to right
- Not evaluating addition and subtraction operations from left to right
Conclusion
In this article, we have provided a Q&A guide to help you understand the concepts and solve similar problems. We have covered the order of operations, evaluating expressions inside parentheses, the difference between a negative sign and a positive sign, evaluating expressions with multiple operations, and simplifying complex expressions. We have also covered some common mistakes to avoid when solving complex arithmetic expressions. If you have any questions or need further clarification, please don't hesitate to ask.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Practice Problems
- Solve the expression 2 + 3 - 4 + 5
- Solve the expression 10 - 2 + 3 - 4
- Solve the expression 5 + 2 - 3 + 4
Answer Key
- 2 + 3 - 4 + 5 = 6
- 10 - 2 + 3 - 4 = 7
- 5 + 2 - 3 + 4 = 8