Solving (-2) + (+9) - (+1) - (-4) A Step-by-Step Guide

Hey guys! Math can sometimes feel like navigating a maze, right? But don't worry, we're here to break down even the trickiest problems into easy-to-understand steps. Today, we're tackling the question: what is the result of (-2) + (+9) - (+1) - (-4)? This might look intimidating at first glance, but trust me, by the end of this guide, you'll be solving similar problems like a pro!

Understanding the Basics: A Quick Refresher

Before we dive into the problem, let's quickly review some fundamental concepts. Think of numbers as existing on a number line. Positive numbers are to the right of zero, and negative numbers are to the left. Adding a positive number means moving to the right on the number line, while adding a negative number means moving to the left. Subtraction can be thought of as adding the opposite. So, subtracting a positive number is the same as adding a negative number, and subtracting a negative number is the same as adding a positive number. Remember this key concept: subtracting a negative is like adding a positive. This is crucial for solving our problem.

To further clarify, let’s consider some simple examples. Imagine you have $5 and you add $3. This is represented as 5 + 3, which equals 8. You now have $8. Now, imagine you have $5 and you lose $2. This is represented as 5 - 2, which equals 3. You now have $3. What if you owe $2 (represented as -2) and you get $5? This is represented as -2 + 5, which equals 3. You can pay off your debt and have $3 left over. Lastly, what if you owe $2 (represented as -2) and you lose another $3? This is represented as -2 - 3, which equals -5. You now owe $5. These basic examples illustrate how positive and negative numbers interact with addition and subtraction. Keeping these concepts in mind will make solving more complex problems, like the one we are addressing today, much easier.

Another important aspect to understand is the concept of additive inverses. The additive inverse of a number is the number that, when added to the original number, results in zero. For example, the additive inverse of 5 is -5, because 5 + (-5) = 0. Similarly, the additive inverse of -3 is 3, because -3 + 3 = 0. Recognizing additive inverses can simplify calculations, especially when dealing with multiple positive and negative numbers. In our problem, we'll see how understanding additive inverses can help us group numbers and make the arithmetic easier.

Finally, let's briefly touch on the order of operations. While this problem doesn't involve multiplication or division, it's always a good practice to remember the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This acronym tells us the order in which we should perform operations in a mathematical expression. In our case, we only have addition and subtraction, so we'll simply work from left to right. This consistent approach will ensure we arrive at the correct solution.

Breaking Down the Problem: Step-by-Step Solution

Okay, now that we've refreshed our memory on the basics, let's tackle our problem: (-2) + (+9) - (+1) - (-4). To make things super clear, we'll go through each step meticulously.

Step 1: Simplify the signs.

First, let's simplify the expression by removing the extra plus signs. Remember that adding a positive number is the same as just adding the number. So, (+9) is the same as 9, and (+1) is the same as 1. Our expression now looks like this: -2 + 9 - 1 - (-4).

Step 2: Deal with the double negative.

This is the most crucial part! Remember our rule: subtracting a negative is the same as adding a positive. So, - (-4) becomes + 4. Our expression now becomes: -2 + 9 - 1 + 4.

Step 3: Perform the addition and subtraction from left to right.

Now we just work our way through the expression, performing the operations in order.

• -2 + 9 = 7 (Think of it as having a debt of $2 and gaining $9. You pay off the debt and have $7 left.)
• So now our expression is: 7 - 1 + 4
• 7 - 1 = 6 (You have $7 and spend $1, leaving you with $6.)
• Our expression now looks like this: 6 + 4
• 6 + 4 = 10 (Simple addition!) So, the final result is 10.

Therefore, (-2) + (+9) - (+1) - (-4) = 10

Alternative Method: Grouping Positive and Negative Numbers

There's another way to solve this problem that some people find easier. It involves grouping the positive and negative numbers together. Let's try it out!

Starting with our simplified expression: -2 + 9 - 1 + 4

Step 1: Group the positive and negative numbers.

We can rearrange the expression (remember, addition is commutative, meaning the order doesn't matter) to group the negative numbers together and the positive numbers together: 9 + 4 - 2 - 1

Step 2: Add the positive numbers and the negative numbers separately.

• Positive numbers: 9 + 4 = 13
• Negative numbers: -2 - 1 = -3

Step 3: Combine the results.

Now we have: 13 - 3

Step 4: Perform the final subtraction.

13 - 3 = 10

As you can see, we arrive at the same answer: 10. This method can be helpful if you find it easier to visualize the positive and negative numbers separately.

Common Mistakes to Avoid

When dealing with positive and negative numbers, it's easy to make small mistakes that can lead to the wrong answer. Let's go over some common pitfalls to avoid:

• Forgetting the rule of subtracting a negative: This is the most common mistake. Always remember that subtracting a negative number is the same as adding a positive number. Don't let those double negatives trip you up!
• Incorrectly combining signs: Make sure you understand how positive and negative signs interact. For example, a positive plus a negative can be confusing for some, but always remember to consider their absolute value and the sign with the larger absolute value determines the result sign. Similarly, a negative plus a negative is going to give a negative result.
• Not following the order of operations: While our problem only involves addition and subtraction, it's crucial to remember PEMDAS in more complex expressions. If you have multiplication, division, or parentheses, make sure you perform those operations in the correct order.
• Rushing through the steps: It's tempting to try and do the calculations in your head, but it's always best to write out each step clearly, especially when you're first learning. This will help you avoid careless errors.
• Mixing up addition and subtraction: Pay close attention to the signs in front of each number. A plus sign means you're adding, and a minus sign means you're subtracting. Don't let them blur together!

By being aware of these common mistakes, you can significantly improve your accuracy when solving problems involving positive and negative numbers.

Practice Makes Perfect: Try These Problems!

Now that we've thoroughly dissected our problem and covered some helpful strategies, it's time to put your knowledge to the test! Here are a few practice problems for you to try:

1. (-5) + (+12) - (+3) - (-2)
2. 10 - (-8) + (-4) - 6
3. -7 + 15 - 9 + (-1)

Work through these problems using the methods we discussed. Remember to simplify the signs, deal with the double negatives, and perform the operations from left to right. You can also try grouping the positive and negative numbers separately.

Don't worry if you don't get the answers right away. The key is to practice and learn from your mistakes. If you're struggling, go back and review the steps we outlined earlier in this guide. And remember, there are tons of resources available online and in textbooks to help you further develop your math skills.

Conclusion: You've Got This!

So, guys, we've successfully navigated the question: what is the result of (-2) + (+9) - (+1) - (-4)? We've broken down the problem step-by-step, explored different methods, and discussed common mistakes to avoid. Remember, the key to mastering math is understanding the fundamental concepts and practicing consistently.

Whether you prefer solving problems step-by-step from left to right or grouping positive and negative numbers, the most important thing is to find a method that works for you. Keep practicing, stay patient, and don't be afraid to ask for help when you need it. You've got this! Math might seem like a maze sometimes, but with the right tools and approach, you can conquer any problem that comes your way. Keep up the great work, and happy calculating!