Solving The Math Expression: $5-{6-2-(1-8)-3+6}+5$

Hey guys! Ever stumbled upon a mathematical expression that looks like it belongs in a complex code rather than a textbook? Well, let's break down one such expression today: $5-{6-2-(1-8)-3+6}+5$. It might seem daunting at first, but trust me, with a little step-by-step approach, we can solve it together. This is not just about finding the right answer; it's about understanding the process, which is super important in mathematics. So, grab your imaginary calculators, and let's dive in!

Understanding the Order of Operations

Before we even think about the numbers, let's talk about the golden rule of math: order of operations. You might have heard of the acronym PEMDAS (or BODMAS in some parts of the world), which stands for:

• Parentheses (or Brackets)
• Exponents (or Orders)
• Multiplication and Division
• Addition and Subtraction

This order tells us exactly which operations to perform first. In our expression, we have parentheses, so that's where we'll start. Remember, math is like a precise recipe; you gotta follow the instructions in the right order to get the perfect result! So, let's get this mathematical recipe cooking!

Diving Deep into Parentheses

Okay, so the first thing we need to tackle are the parentheses. Inside our main expression, we've got a set of parentheses: (1-8). This is our initial target. It's a small, manageable part of the problem, and that's how we should approach it – one step at a time. Think of it as decluttering your room; you don't do it all at once, right? You start with a drawer or a shelf. Similarly, we're starting with this little expression inside the parentheses.

Now, let's calculate 1-8. This is a simple subtraction, but be careful with the signs! When you subtract a larger number from a smaller one, you end up with a negative number. In this case, 1-8 equals -7. So, we've simplified our first part. Feels good, doesn't it? We've taken the first step in unraveling this mathematical puzzle. It's like finding the first clue in a treasure hunt – exciting!

Simplifying the Inner Brackets

With the parentheses (1-8) simplified to -7, our expression now looks like this: $5-{6-2-(-7)-3+6}+5$. Notice how we replaced (1-8) with -7. It's like swapping out a complicated ingredient in a recipe for a simpler one. Now, we need to focus on the curly braces, or what we can call the inner brackets: {6-2-(-7)-3+6}. Remember PEMDAS? We're still working within the parentheses/brackets part, just a level deeper.

Inside these brackets, we have a series of additions and subtractions. The cool thing about addition and subtraction is that they have equal priority, so we can perform them from left to right. It's like reading a sentence; you go from the beginning to the end. So, let's start crunching these numbers one by one.

Crunching the Numbers Inside the Brackets

Let's take it step-by-step:

1. First, we have 6-2, which equals 4. So, our expression inside the brackets becomes 4-(-7)-3+6.
2. Next, we have 4-(-7). Remember that subtracting a negative number is the same as adding its positive counterpart. So, 4-(-7) becomes 4+7, which equals 11. Now our bracketed expression is 11-3+6. See how we're making progress? It's like peeling an onion, layer by layer.
3. Now, we have 11-3, which equals 8. The expression simplifies to 8+6.
4. Finally, 8+6 equals 14. So, the entire expression inside the brackets {6-2-(-7)-3+6} simplifies to 14. Woohoo! We've conquered the brackets! It’s like completing a level in a game – a real sense of accomplishment!

Final Calculation: The Home Stretch

Now that we've simplified the expression inside the brackets to 14, our original expression becomes much simpler: $5-14+5$. We're in the home stretch now! This is like the final lap in a race, so let's give it our all. We just have a couple of additions and subtractions to take care of, and remember, we do them from left to right.

First, we have 5-14. This is another subtraction where we're taking a larger number away from a smaller one, so we'll end up with a negative number. 5-14 equals -9. Our expression now looks like -9+5. We’re almost there; you can practically taste the mathematical victory!

The Grand Finale

Finally, we have -9+5. When you add a positive number to a negative number, you're essentially moving closer to zero on the number line. In this case, -9+5 equals -4. And there you have it! The solution to our mathematical puzzle is -4. We did it! It’s like reaching the summit of a mountain after a long climb – the view is amazing!

The Final Answer

So, after all that mathematical maneuvering, we've arrived at our final answer: $5-{6-2-(1-8)-3+6}+5 = -4$. It might have seemed complex at the beginning, but by breaking it down step-by-step and following the order of operations, we solved it like pros. Remember, the key to tackling any mathematical problem is to take it one step at a time, stay organized, and don't be afraid to make mistakes. Mistakes are just learning opportunities in disguise! So, keep practicing, keep exploring, and most importantly, keep enjoying the fascinating world of mathematics! You guys are awesome!