Solving Math Problems: A Step-by-Step Guide

by Tom Lembong 44 views
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Hey math enthusiasts! Ready to dive into a problem that might seem a little daunting at first glance? Today, we're going to break down the expression: -3+6+ [-2+7-(-15+18+20)]-18. Don't worry, we'll take it one step at a time, making sure everyone understands the process. This isn't just about getting the right answer; it's about understanding how to solve these types of math problems. We'll be using the order of operations, dealing with parentheses, and combining positive and negative numbers. By the end, you'll be able to tackle similar problems with confidence. Let's get started, guys!

Breaking Down the Problem: Understanding the Basics

Before we jump into the calculations, let's make sure we're all on the same page. The expression involves addition, subtraction, and parentheses. Remember the order of operations (often remembered by the acronym PEMDAS or BODMAS):

  • Parentheses / Brackets
  • Exponents / Orders
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

In our case, we'll start with the innermost parentheses and work our way outwards. This means we'll first solve the expression inside the parentheses: (-15+18+20). Then, we will tackle the brackets: [-2+7-(result of the parentheses)]. After that, we'll combine the remaining terms. This is a pretty standard approach, and it’s the key to keeping things organized and accurate. The most common mistake in these problems is forgetting the order of operations or mixing up the positive and negative signs. That's why we're going to be super careful and methodical. Think of it like building with LEGOs: you need to put the pieces together in the right order to get the final structure right. Let’s make sure we build a strong foundation for this problem, understanding each piece before we assemble them.

Now, let's get our hands dirty with the first step of the problem.

Step 1: Solving the Innermost Parentheses

Alright, guys, let’s begin with the innermost part: (-15 + 18 + 20). This is where we need to be extra careful with our signs. We have a mix of negative and positive numbers, and the trick is to combine them correctly. The goal here is to reduce this part of the equation to a single number, which will then be used in the next steps. Start by combining the first two numbers: -15 + 18. This gives us 3. The rule is that when adding numbers with different signs, you subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. Then, take that result (which is 3) and add the remaining number, which is 20. So, 3 + 20 = 23. Therefore, (-15 + 18 + 20) = 23. Great job, you guys! We've successfully simplified the innermost part, and now we can move on to the next level. Remember, even though it may seem like a small step, each one is crucial in getting to the final answer. It's like a chain; if one link is weak, the entire chain suffers. So, keep up the great work, and let's head to the next step.

Simplifying the Brackets: Working Outward

With the innermost parentheses sorted, we now turn our attention to the brackets. Remember, brackets are just another form of grouping, just like parentheses. Now we will work our way out to simplify the entire expression. The brackets contain the expression: [-2 + 7 - (-15 + 18 + 20)]. But hey, wait a second! We've already solved what's inside the parentheses in the previous step, which is 23. So, the brackets now look like this: [-2 + 7 - 23]. This simplifies our task significantly. This is all about breaking down a complex problem into smaller, more manageable parts. We're getting closer to the solution with each step, guys. Remember, the key is to stay organized and not rush. Rushing often leads to mistakes, and we want to avoid that at all costs. Now, combine the numbers step-by-step to be accurate.

Step 2: Calculating Within the Brackets

Now, let's calculate the expression inside the brackets: [-2 + 7 - 23]. Here, we have both addition and subtraction. Starting from left to right, we first solve -2 + 7, which equals 5. Now, subtract 23 from 5: 5 - 23 = -18. So, the simplified value of the brackets is -18. Fantastic work, you're doing great! We've tackled the parentheses and the brackets, and now we're one step closer to solving the entire problem. Remember, each step builds on the previous one. If you’ve followed along carefully, you're well on your way to understanding how to solve these types of expressions. Don’t forget to double-check your work along the way. That helps ensure we haven’t made any errors. Let's move on!

Final Calculation: Putting It All Together

We’ve simplified the parentheses and brackets. Now it's time to bring everything together and find the final answer. The original expression was: -3 + 6 + [-2 + 7 - (-15 + 18 + 20)] - 18. We have already solved the parentheses and brackets. We can now rewrite the problem to see what we're dealing with. Let's replace the bracket with its simplified value of -18. So, the original expression is now: -3 + 6 + (-18) - 18. See how we've reduced a complicated expression into something much easier to handle? Now it's all about combining the terms. Remember the rules for adding and subtracting positive and negative numbers, and you'll be just fine. Let’s do it!

Step 3: Combining the Remaining Terms

Here’s the expression we need to solve: -3 + 6 - 18 - 18. Let's add and subtract from left to right. First, calculate -3 + 6 = 3. Now the expression is 3 - 18 - 18. Next, calculate 3 - 18 = -15. So, now we have -15 - 18. Finally, calculate -15 - 18 = -33. And there you have it, guys! We've solved the entire expression. The answer is -33. Give yourselves a pat on the back; you’ve successfully worked through the problem step-by-step. Remember, practice makes perfect. The more problems you solve, the more comfortable you'll become with the order of operations and handling positive and negative numbers. Keep practicing, and you'll be math whizzes in no time. We went through the entire process, step by step, which is key.

Summary and Tips for Success

Alright, let’s recap what we've learned and some tips to help you in the future. We started with the expression -3 + 6 + [-2 + 7 - (-15 + 18 + 20)] - 18 and broke it down systematically using the order of operations (PEMDAS/BODMAS). First, we solved the innermost parentheses: (-15 + 18 + 20) = 23. Then, we simplified the brackets: [-2 + 7 - 23] = -18. Finally, we combined all the terms: -3 + 6 - 18 - 18 = -33. Here are a few tips to help you in your future math endeavors:

  • Always follow the order of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • Pay close attention to signs: Positive and negative signs can make or break your answer. Double-check them!
  • Break down the problem into smaller steps: This makes it less overwhelming and reduces the chances of errors.
  • Practice, practice, practice: The more you practice, the better you'll get.
  • Don't be afraid to ask for help: If you're stuck, don't hesitate to ask a teacher, friend, or use online resources.

I hope this guide has been helpful, guys. Math can be tricky, but with the right approach and practice, you can definitely master it. Keep up the great work, and happy calculating! Remember, it's all about understanding the process and staying organized. You've got this!