Solving: (-9) + (+3) - (-7) + 4 - 10 + 12

Hey guys! Let's break down this math problem step by step so it's super easy to understand. We're going to solve the expression: (-9) + (+3) - (-7) + 4 - 10 + 12. Arithmetic expressions might look intimidating, but once you understand the rules, they're a piece of cake. So, grab your pencils, and let's get started!

Step 1: Understanding the Basics

Before we dive in, let's refresh some basic principles. Remember that adding a positive number is like moving to the right on the number line, and adding a negative number is like moving to the left. Subtracting a negative number is the same as adding a positive number. These simple rules are the key to solving this problem efficiently.

Adding and Subtracting Integers

• Adding a positive number: a + (+b) = a + b
• Adding a negative number: a + (-b) = a - b
• Subtracting a positive number: a - (+b) = a - b
• Subtracting a negative number: a - (-b) = a + b

These rules help simplify the expression and make it easier to calculate. Keep these in mind as we move through the steps.

Step 2: Simplifying the Expression

Our expression is: (-9) + (+3) - (-7) + 4 - 10 + 12.

Let's simplify this by removing the unnecessary parentheses and applying the rules we just discussed:

• (-9) is just -9
• (+3) is just +3
• -(-7) becomes +7

So our expression now looks like this: -9 + 3 + 7 + 4 - 10 + 12. This already looks much simpler, right?

Step 3: Combining the Numbers

Now, let's combine these numbers step by step. We'll go from left to right to keep things organized.

First Pair: -9 + 3

Start with the first two numbers: -9 + 3. Think of it as starting at -9 on the number line and moving 3 steps to the right. This gives us:

-9 + 3 = -6

Next: -6 + 7

Now add the next number, 7, to our result:

-6 + 7 = 1

Adding 4: 1 + 4

Next, we add 4:

1 + 4 = 5

Subtracting 10: 5 - 10

Now subtract 10 from our current result:

5 - 10 = -5

Finally: -5 + 12

Lastly, add 12 to -5:

-5 + 12 = 7

So, after all these steps, we find that the solution to our expression is 7.

Step 4: Writing it All Together

Let's write down the entire process so you can see it all in one place:

1. Original expression: (-9) + (+3) - (-7) + 4 - 10 + 12
2. Simplified: -9 + 3 + 7 + 4 - 10 + 12
3. Step-by-step calculation:
   • -9 + 3 = -6
   • -6 + 7 = 1
   • 1 + 4 = 5
   • 5 - 10 = -5
   • -5 + 12 = 7

Therefore, (-9) + (+3) - (-7) + 4 - 10 + 12 = 7

Common Mistakes to Avoid

When solving these types of expressions, it's easy to make mistakes if you're not careful. Here are a few common pitfalls to watch out for:

Sign Errors

One of the most common mistakes is messing up the signs. Remember, subtracting a negative is the same as adding a positive, and vice versa. Always double-check your signs to ensure you're performing the correct operation.

Order of Operations

In this particular problem, we can simply go from left to right because it only involves addition and subtraction. However, if there were multiplication or division, you'd need to follow the order of operations (PEMDAS/BODMAS).

Rushing

Rushing through the problem can lead to careless errors. Take your time, especially when you're dealing with multiple numbers and operations. Writing down each step can help you avoid mistakes.

Alternative Methods

While we solved this expression by going from left to right, there are other ways to approach it. Let's explore a couple of alternative methods.

Grouping Positives and Negatives

Another approach is to group all the positive numbers together and all the negative numbers together, and then combine them. For our expression, -9 + 3 + 7 + 4 - 10 + 12, we can do this:

• Positive numbers: 3 + 7 + 4 + 12 = 26
• Negative numbers: -9 - 10 = -19

Now, combine the sums:

26 + (-19) = 26 - 19 = 7

Using a Number Line

Visualizing the problem on a number line can also be helpful, especially for those who are more visual learners. Start at -9, then move 3 steps to the right, 7 steps to the right, 4 steps to the right, 10 steps to the left, and finally, 12 steps to the right. You'll end up at 7.

Practice Problems

To solidify your understanding, here are a few practice problems you can try:

1. (-5) + (+8) - (-2) + 3 - 7 + 11
2. 15 - (+4) + (-6) - (-9) + 2 - 8
3. (-12) + 5 - (-3) + 7 - 10 + 4

Work through these problems using the methods we've discussed. Check your answers to ensure you're on the right track.

Conclusion

So there you have it! We've successfully solved the expression (-9) + (+3) - (-7) + 4 - 10 + 12, and found that the answer is 7. By understanding the basic rules of adding and subtracting integers, avoiding common mistakes, and exploring alternative methods, you can tackle similar problems with confidence. Keep practicing, and you'll become a math whiz in no time! Remember, math isn't about being perfect; it's about understanding and improving. Keep up the great work, guys! You got this!