Calculate The Following Expression: 17 − 8 + ( − 18 ) = 17 - 8 + (-18) = 17 − 8 + ( − 18 ) =

Introduction

Mathematical expressions are a fundamental part of mathematics, and solving them is an essential skill for anyone who wants to excel in the subject. In this article, we will focus on solving a simple mathematical expression: $17 - 8 + (-18) =$. We will break down the expression into smaller parts, apply the rules of arithmetic operations, and finally arrive at the solution.

Understanding the Expression

Before we start solving the expression, let's take a closer look at it. The expression is $17 - 8 + (-18) =$. It consists of three terms: $17$, $-8$, and $-18$. The first term is a positive number, the second term is a negative number, and the third term is also a negative number.

Order of Operations

When solving mathematical expressions, it's essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

In our expression, there are no parentheses, exponents, multiplication, or division operations. Therefore, we can proceed to the next step.

Solving the Expression

Now that we have a clear understanding of the expression and the order of operations, let's start solving it.

Step 1: Subtract 8 from 17

The first operation is to subtract 8 from 17. This can be written as:

$17 - 8 = 9$

So, the result of the first operation is 9.

Step 2: Add -18 to 9

The next operation is to add -18 to 9. This can be written as:

$9 + (-18) = -9$

So, the result of the second operation is -9.

Conclusion

In conclusion, the solution to the expression $17 - 8 + (-18) =$ is -9. We broke down the expression into smaller parts, applied the rules of arithmetic operations, and finally arrived at the solution.

Tips and Tricks

Here are some tips and tricks to help you solve mathematical expressions like this one:

• Always follow the order of operations (PEMDAS).
• Use parentheses to group numbers and operations together.
• Evaluate any exponential expressions next.
• Evaluate any multiplication and division operations from left to right.
• Finally, evaluate any addition and subtraction operations from left to right.

By following these tips and tricks, you will become more confident and proficient in solving mathematical expressions.

Real-World Applications

Mathematical expressions like this one have many real-world applications. For example, in finance, you may need to calculate the total cost of a project, which involves subtracting the cost of materials from the total budget and then adding the cost of labor. In science, you may need to calculate the distance between two points, which involves subtracting the initial position from the final position and then adding the velocity.

Common Mistakes

Here are some common mistakes to avoid when solving mathematical expressions like this one:

• Not following the order of operations (PEMDAS).
• Not using parentheses to group numbers and operations together.
• Evaluating exponential expressions before multiplication and division operations.
• Evaluating multiplication and division operations before addition and subtraction operations.

By avoiding these common mistakes, you will become more accurate and proficient in solving mathematical expressions.

Conclusion

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Introduction

In our previous article, we discussed how to solve a simple mathematical expression: $17 - 8 + (-18) =$. We broke down the expression into smaller parts, applied the rules of arithmetic operations, and finally arrived at the solution. In this article, we will answer some frequently asked questions (FAQs) about solving mathematical expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential to ensure that mathematical expressions are evaluated correctly. If you don't follow the order of operations, you may get incorrect results.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are two basic arithmetic operations. Addition involves combining two or more numbers to get a total, while subtraction involves finding the difference between two numbers.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the rule for evaluating negative numbers?

A: When evaluating negative numbers, remember that a negative number is the opposite of a positive number. For example, -3 is the opposite of 3.

Q: How do I simplify complex expressions?

A: To simplify complex expressions, break them down into smaller parts and evaluate each part separately. Use the order of operations (PEMDAS) to ensure that you evaluate the expression correctly.

Q: What are some common mistakes to avoid when solving mathematical expressions?

A: Some common mistakes to avoid when solving mathematical expressions include:

• Not following the order of operations (PEMDAS).
• Not using parentheses to group numbers and operations together.
• Evaluating exponential expressions before multiplication and division operations.
• Evaluating multiplication and division operations before addition and subtraction operations.

Q: How can I practice solving mathematical expressions?

A: You can practice solving mathematical expressions by working through examples and exercises. Start with simple expressions and gradually move on to more complex ones. Use online resources or math textbooks to find practice problems.

Conclusion

In conclusion, solving mathematical expressions requires a clear understanding of the expression, the order of operations, and the rules of arithmetic operations. By following the order of operations (PEMDAS) and avoiding common mistakes, you can become more confident and proficient in solving mathematical expressions.

Additional Resources

If you want to learn more about solving mathematical expressions, here are some additional resources:

• Online math textbooks and resources, such as Khan Academy and Mathway.
• Math practice problems and exercises, such as those found on IXL and Math Open Reference.
• Math videos and tutorials, such as those found on 3Blue1Brown and Crash Course.

By using these resources and practicing regularly, you can become more proficient in solving mathematical expressions and improve your math skills.