Solving Mathematical Expressions Step By Step -8 + {-5 + [(8 – 12) + (13 + 12)] – 10}

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Hey guys! Let's dive into how to solve this mathematical expression step-by-step. Expressions like these can seem intimidating at first, but don't worry, we'll break it down into manageable parts. Our goal here is to simplify the equation: -8 + {-5 + [(8 – 12) + (13 + 12)] – 10}. We'll walk through each operation, making sure you understand why we're doing what we're doing. Math is like a puzzle, and we're going to put all the pieces together.

Understanding the Order of Operations

Before we jump in, it's super important to remember the order of operations, often remembered by the acronym PEMDAS (or BODMAS in some regions):

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

This order is our roadmap. It tells us exactly which operations to perform first to ensure we get to the correct final answer. Think of it like following a recipe – if you mix the ingredients in the wrong order, you might not get the cake you were hoping for!

So, with PEMDAS in mind, we'll start with the innermost parentheses and work our way outwards. This systematic approach is crucial for tackling more complex equations too, so getting it right here is a fantastic foundation.

Step-by-Step Solution

Okay, let's get our hands dirty and solve this expression! We'll take it one step at a time, so you can follow along easily.

1. Solve the Innermost Parentheses

We've got two sets of parentheses inside the brackets: (8 – 12) and (13 + 12). Let's tackle these first.

  • (8 – 12) = -4
  • (13 + 12) = 25

Simple enough, right? We've reduced the expression inside the brackets to just two numbers.

2. Substitute and Simplify Inside the Brackets

Now, let's put those results back into our original expression. We get:

-8 + {-5 + [(-4) + (25)] – 10}

Next, we'll simplify the expression within the brackets: [-4 + 25].

  • -4 + 25 = 21

3. Substitute and Simplify Inside the Curly Braces

Now our expression looks like this:

-8 + {-5 + 21 – 10}

Let's simplify what's inside the curly braces. We'll perform the addition and subtraction from left to right:

  • -5 + 21 = 16
  • 16 – 10 = 6

So, the expression inside the curly braces simplifies to 6.

4. Final Calculation

We're almost there! Our expression is now super simple:

-8 + {6}

This is the same as:

  • -8 + 6 = -2

And that's it! The final result of the expression is -2. See? We got there by breaking it down step-by-step. Practice makes perfect, so try some similar expressions to solidify your understanding.

Common Mistakes to Avoid

When solving mathematical expressions, it's easy to slip up if you're not careful. Here are a few common mistakes to watch out for:

  • Forgetting the Order of Operations: This is the big one! Always stick to PEMDAS (or BODMAS). If you mix up the order, you'll likely get the wrong answer.
  • Sign Errors: Pay close attention to negative signs. They can be tricky, especially when you're dealing with multiple operations. Double-check your calculations to make sure you haven't dropped a negative or made an incorrect sign change.
  • Rushing: Take your time! It's better to work methodically and get the right answer than to rush and make mistakes. Break the expression down into smaller steps, and double-check each step before moving on.
  • Incorrectly Combining Terms: Make sure you're only combining like terms. For example, you can add -5 and 21 because they are both constants, but you can't combine a constant with a variable term (like x or y).

By being aware of these common pitfalls, you'll be much better equipped to solve mathematical expressions accurately. Math is all about precision, so taking the time to avoid these mistakes will pay off in the long run.

Practice Problems

To really master solving mathematical expressions, you need to practice! Here are a few problems you can try on your own. Grab a pen and paper, and work through them step-by-step, remembering PEMDAS.

  1. 15 – 3 × (4 + 2) ÷ 2
  2. -10 + {7 – [(5 + 3) – (2 – 8)] + 1}
  3. 24 ÷ (2 × 3) + 18 – 4²

Solving these problems will help you build confidence and solidify your understanding. And remember, if you get stuck, don't be afraid to review the steps we discussed earlier or seek help from a teacher, tutor, or friend. The key is to keep practicing!

Conclusion

So, there you have it! We've successfully solved the mathematical expression -8 + {-5 + [(8 – 12) + (13 + 12)] – 10}, and we've learned a lot along the way. We've reinforced the importance of the order of operations, identified common mistakes to avoid, and even tackled some practice problems.

Remember, guys, solving mathematical expressions is all about breaking them down into smaller, manageable steps. By following the order of operations (PEMDAS) and paying close attention to detail, you can tackle even the most complex equations with confidence. Math might seem like a daunting subject at times, but with practice and a solid understanding of the fundamentals, you'll be solving problems like a pro in no time!

So, keep practicing, stay curious, and don't be afraid to challenge yourself. You've got this! And who knows, maybe you'll even start to enjoy the puzzle-solving aspect of math. Keep up the great work!