Solve 113+(25-(-26)×(-8):12): A Step-by-Step Guide

Aug 13, 2025 by Axel Sørensen 51 views

Decoding the Math Puzzle: 113 + (25 - (-26) × (-8) : 12)

Hey guys! Ever stumbled upon a math problem that looks like it belongs in a cryptic crossword puzzle? Well, you're not alone! Today, we're diving deep into one such mathematical enigma: 113 + (25 - (-26) × (-8) : 12). Sounds intimidating, right? But fear not! We're going to break it down step by step, making sure everyone, from math wizards to those who break out in a cold sweat at the sight of numbers, can follow along. So, grab your calculators (or your mental math muscles) and let's get started!

Unraveling the Order of Operations

Before we even think about punching numbers into a calculator, we need to talk about the golden rule of math: the order of operations. Think of it as the traffic laws of the mathematical world. If you don't follow them, you're going to cause a wreck! The order of operations is often remembered by the acronym PEMDAS, which stands for:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

This acronym is our roadmap for solving the problem. First, we tackle anything inside parentheses. Then, we deal with exponents (if there are any). Next up, we handle multiplication and division, working our way from left to right. Finally, we finish off with addition and subtraction, again moving from left to right. Ignoring this order is like trying to read a book backwards – you might get some of the words, but you'll miss the whole story!

In our particular problem, 113 + (25 - (-26) × (-8) : 12), we see parentheses right away. That's our first stop. Within the parentheses, we have a mix of subtraction, multiplication, and division. According to PEMDAS, multiplication and division come before subtraction, so we'll tackle those first. This is where things can get a little tricky with the negative signs, so we'll need to pay close attention. Math can be like a detective story, you know? Every sign, every number is a clue. And just like a good detective, we need to follow the clues carefully to crack the case!

Step-by-Step Breakdown: Conquering the Parentheses

Let's zoom in on the part inside the parentheses: (25 - (-26) × (-8) : 12). Remember, we need to follow PEMDAS within the parentheses as well. So, multiplication and division take precedence over subtraction. First up, we have (-26) × (-8). A negative times a negative… what's the rule? Ah, yes! A negative number multiplied by another negative number gives us a positive result. So, (-26) × (-8) = 208.

Now our expression inside the parentheses looks like this: (25 - 208 : 12). Next, we handle the division: 208 : 12. This might not divide perfectly, and that's okay! We can either express it as a fraction or find a decimal approximation. If we perform the division, we get approximately 17.33. So, our expression now becomes (25 - 17.33). See how we're chipping away at the problem, making it less intimidating with each step? It's like unwrapping a present, layer by layer!

Finally, we can perform the subtraction within the parentheses: 25 - 17.33. This gives us 7.67. So, the entire expression inside the parentheses simplifies to 7.67. We've conquered the parentheses! Give yourself a pat on the back. We've taken a big, scary chunk of the problem and turned it into a manageable number. Now, we're ready to move on to the final stage.

The Grand Finale: Addition and the Final Answer

Now that we've simplified the expression inside the parentheses, our original problem, 113 + (25 - (-26) × (-8) : 12), has transformed into something much simpler: 113 + 7.67. See? Doesn't that look a whole lot less daunting? We're in the home stretch now!

All that's left to do is perform the addition. This is the easy part! We simply add 113 and 7.67 together. And the result is… 120.67! Ta-da! We've solved the puzzle! We've taken a complex-looking mathematical expression and, by carefully following the order of operations and paying attention to the signs, we've arrived at the final answer.

So, the solution to 113 + (25 - (-26) × (-8) : 12) is 120.67. Not so scary after all, right? Remember, the key to tackling these kinds of problems is to break them down into smaller, more manageable steps. And always, always follow PEMDAS! Math is like building with LEGOs – you need to put the pieces together in the right order to create something amazing.

Key Takeaways and Practice Problems

Okay, guys, let's recap what we've learned today. The big takeaway is the importance of the order of operations (PEMDAS). It's the foundation for solving any mathematical expression. We also saw how to handle negative numbers in multiplication and division – remember, a negative times a negative is a positive! And we practiced breaking down a complex problem into smaller, easier-to-solve steps. This strategy is super useful not just in math, but in all sorts of problem-solving situations in life.

To really solidify your understanding, why not try a few practice problems? Here are a couple to get you started:

50 - (10 + 5 × 2) : 3
25 + (-4 × 6 - 10) : 2

Work through them step by step, remembering PEMDAS. Don't be afraid to make mistakes – that's how we learn! And if you get stuck, go back and review the steps we took in solving the original problem. With a little practice, you'll be a master of order of operations in no time!

Remember, math isn't just about memorizing formulas and rules. It's about developing problem-solving skills, logical thinking, and the ability to break down complex challenges into manageable pieces. These are skills that will serve you well in all aspects of life, from balancing your budget to planning a road trip. So, embrace the challenge, keep practicing, and have fun with it! You got this!

Real-World Applications of Order of Operations

You might be thinking, “Okay, this is cool and all, but when am I ever going to use this in the real world?” Great question! The order of operations isn't just some abstract mathematical concept; it's actually used all the time in various fields. Think about it: any time you're working with formulas, whether it's in science, engineering, finance, or even cooking, you need to follow a specific order to get the correct result.

For example, in computer programming, the order of operations is crucial for writing code that performs calculations correctly. Computers follow a very strict set of rules when evaluating expressions, and if you don't use the correct order, your program might produce unexpected (and often incorrect) results. It's like telling a computer to add before it multiplies – it just won't work!

In finance, calculating interest, returns on investment, or even the total cost of a loan involves multiple operations that need to be performed in the correct order. Imagine trying to figure out your mortgage payment without knowing PEMDAS! You might end up paying way more (or way less) than you're supposed to. That's a scenario we definitely want to avoid!

Even in everyday situations, we use the principles of order of operations without even realizing it. Let's say you're buying ingredients for a recipe. You need 2 pounds of flour at $3 per pound and a carton of eggs for $4. To calculate the total cost, you need to multiply the price of the flour by the quantity (2 × $3) and then add the cost of the eggs ($4). This is essentially following the order of operations: multiplication before addition.

So, the next time you're faced with a complex calculation, remember that PEMDAS is your friend. It's a powerful tool that can help you break down even the most intimidating problems into manageable steps. And who knows, mastering the order of operations might just help you ace your next math test, build a killer app, or even save some money on your next big purchase!

Conclusion: Math is an Adventure!

We've reached the end of our mathematical adventure for today, and I hope you've enjoyed the journey! We started with a seemingly complex problem, 113 + (25 - (-26) × (-8) : 12), and by breaking it down step by step, we conquered it with confidence. We learned about the crucial role of the order of operations (PEMDAS), the importance of paying attention to negative signs, and the power of simplifying problems into smaller parts.

But more than that, I hope you've discovered that math isn't just a collection of rules and formulas. It's a way of thinking, a way of solving problems, and a way of understanding the world around us. It's like a giant puzzle, and each problem is a piece waiting to be solved. And just like any good puzzle, it can be challenging, frustrating, and sometimes even a little bit scary. But it's also incredibly rewarding when you finally see the pieces come together.

So, keep exploring the world of math, keep asking questions, and keep challenging yourself. Don't be afraid to make mistakes – they're just learning opportunities in disguise. And remember, the most important thing is to have fun! Math can be an adventure, and I hope you're excited to see where it takes you next.