Solving 600+80×(-9) +1.800:25 A Step-by-Step Guide

August 12, 2025 by Scholario Team 51 views

Unraveling the Mystery: Solving 600+80×(-9) +1.800:25 with Ease

Hey guys! Ever stumbled upon a mathematical expression that looks like a tangled mess? Don't worry, we've all been there! Today, we're going to dissect one such expression and break it down step by step. Our mission? To solve 600+80×(-9) +1.800:25 with clarity and precision. This isn't just about finding the right answer; it's about understanding the process and the order of operations that govern the world of mathematics. So, grab your thinking caps, and let's dive in!

Understanding the Order of Operations: PEMDAS/BODMAS

Before we even touch the numbers, it's crucial to understand the golden rule of mathematical calculations: the order of operations. This rule, often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), dictates the sequence in which we perform operations. Think of it as the mathematical roadmap that guides us to the correct destination. Ignoring this order can lead to wildly incorrect results, so let's make sure we're on the right track from the get-go.

Parentheses/Brackets: Operations within parentheses or brackets are always tackled first. This is like dealing with the inner workings of a machine before addressing the external components.
Exponents/Orders: Next, we handle exponents or orders (powers and square roots, etc.). These represent repeated multiplication and division, so they take precedence over basic multiplication and division.
Multiplication and Division: These operations are performed from left to right. Think of them as having equal priority, so we work our way across the expression as we encounter them.
Addition and Subtraction: Finally, we tackle addition and subtraction, also from left to right. These are the final touches that bring our calculation to its conclusion.

With PEMDAS/BODMAS firmly in our minds, we're ready to approach our expression with confidence and clarity. This order ensures that everyone, no matter where they are, solves the same expression and arrives at the same answer. It's a universal language of mathematics, and understanding it unlocks the door to solving even the most complex problems.

Step-by-Step Solution: Breaking Down the Expression

Now, let's apply our knowledge of PEMDAS/BODMAS to the expression 600+80×(-9) +1.800:25. We'll break it down into manageable steps, making sure to follow the correct order of operations.

Step 1: Multiplication

According to PEMDAS/BODMAS, multiplication and division come before addition and subtraction. So, our first task is to tackle the multiplication operation: 80 × (-9). This is where we need to be careful with our signs. Multiplying a positive number by a negative number results in a negative number. Therefore, 80 multiplied by -9 equals -720. This step is crucial because it simplifies a significant portion of our expression, making it easier to manage.

Step 2: Division

Next up is the division operation: 1.800 : 25. Here, the colon (:) symbol represents division. Dividing 1.800 by 25, we get 72. This step further simplifies our expression, reducing the number of operations we need to perform. It's like trimming the branches of a tree to reveal its core structure.

Step 3: Rewriting the Expression

Now that we've handled the multiplication and division, let's rewrite the expression with our results: 600 + (-720) + 72. This revised expression looks much cleaner and less intimidating than our original problem. It's like decluttering a room to create a more organized and inviting space. We've effectively transformed a complex expression into a simple addition problem.

Step 4: Addition

Finally, we're left with addition. We'll perform the addition operations from left to right. First, we add 600 and -720. Adding a negative number is the same as subtracting its positive counterpart. So, 600 + (-720) is equivalent to 600 - 720, which equals -120. This step requires careful attention to signs, as we're dealing with both positive and negative numbers.

Step 5: Final Addition

We now have -120 + 72. Adding these two numbers, we get -48. This is our final answer! It's the culmination of all our hard work and careful calculations. We've successfully navigated the expression and arrived at the solution.

The Grand Finale: The Solution and Its Significance

So, the solution to 600+80×(-9) +1.800:25 is -48. But it's not just about the number itself; it's about the journey we took to get there. We've reinforced the importance of PEMDAS/BODMAS, practiced our multiplication, division, and addition skills, and honed our ability to work with negative numbers. These are valuable mathematical tools that will serve us well in countless situations.

Understanding the order of operations is like having the key to a secret code. It allows us to decipher complex expressions and arrive at accurate solutions. Without this knowledge, we'd be lost in a sea of numbers and symbols. But with PEMDAS/BODMAS as our guide, we can confidently tackle any mathematical challenge that comes our way.

Remember, guys, mathematics isn't just about memorizing formulas and crunching numbers. It's about developing logical thinking, problem-solving skills, and a deep appreciation for the elegance and precision of the mathematical world. By breaking down complex problems into smaller, manageable steps, we can unlock their secrets and discover the beauty that lies within.

Common Mistakes to Avoid: Staying on the Right Track

Even with a solid understanding of PEMDAS/BODMAS, it's easy to make mistakes if we're not careful. Let's take a look at some common pitfalls and how to avoid them.

Ignoring the Order of Operations: This is the most common mistake, and it can lead to drastically incorrect answers. Always double-check that you're following PEMDAS/BODMAS meticulously. It's like making sure you're following the traffic rules to avoid accidents on the road.
Sign Errors: Working with negative numbers can be tricky, and it's easy to make mistakes with signs. Pay close attention to whether you're adding, subtracting, multiplying, or dividing negative numbers, as each operation has its own rules. It's like navigating a maze with multiple paths; one wrong turn can lead you astray.
Calculation Errors: Simple arithmetic mistakes can derail your entire calculation. Double-check your multiplications, divisions, additions, and subtractions to ensure accuracy. It's like proofreading an essay for typos; small errors can have a big impact.
Rushing Through the Problem: It's tempting to rush through a problem to get to the answer, but this can lead to careless mistakes. Take your time, break the problem down into steps, and double-check your work along the way. It's like building a house; a solid foundation is essential for long-term stability.

By being aware of these common mistakes and taking steps to avoid them, we can increase our accuracy and confidence in solving mathematical expressions. It's like having a checklist before a flight; ensuring that everything is in order prevents potential problems down the line.

Practice Makes Perfect: Honing Your Mathematical Skills

The best way to master any skill, including mathematics, is through practice. The more we practice, the more comfortable and confident we become in our abilities. So, let's talk about some ways to hone our mathematical skills and tackle expressions like 600+80×(-9) +1.800:25 with ease.

Work Through Practice Problems: There are countless practice problems available online and in textbooks. Start with simpler problems and gradually work your way up to more complex ones. It's like training for a marathon; you start with shorter runs and gradually increase your mileage.
Use Online Resources: Websites and apps like Khan Academy and Wolfram Alpha offer a wealth of mathematical resources, including tutorials, practice problems, and step-by-step solutions. These resources can be invaluable for reinforcing your understanding and identifying areas where you need more practice. It's like having a personal tutor available 24/7.
Seek Help When Needed: Don't be afraid to ask for help from teachers, classmates, or online forums if you're struggling with a particular concept or problem. Collaboration and discussion can often shed new light on challenging topics. It's like working on a puzzle with friends; different perspectives can help you find the missing pieces.
Make Math a Habit: Incorporate math into your daily routine, even if it's just for a few minutes each day. This could involve solving a quick math problem while waiting in line, playing a math-based game, or simply thinking about mathematical concepts in everyday situations. It's like brushing your teeth; a little bit of daily effort can have a significant impact on your long-term mathematical health.

By making practice a priority, we can build a solid foundation in mathematics and develop the skills we need to tackle any mathematical challenge. It's like learning a new language; consistent practice is key to fluency.

We've successfully unraveled the mystery of 600+80×(-9) +1.800:25 and arrived at the solution: -48. More importantly, we've reinforced our understanding of the order of operations, honed our calculation skills, and explored common mistakes to avoid. We've also discussed the importance of practice and seeking help when needed.

Mathematics is a fascinating and powerful tool that can help us understand the world around us. By embracing the challenges it presents and approaching problems with a clear and methodical approach, we can unlock its secrets and discover its beauty. So, keep practicing, keep learning, and keep exploring the wonderful world of mathematics!