Decoding Math Equation 120% - 3 + 2 X 0.75 + 2 / 3 A Step By Step Guide

Hey guys! Ever stared at a math problem that looks like it's written in another language? You're not alone! Today, we're diving headfirst into a seemingly complex equation: 120% - 3 + 2 x 0.75 + 2 / 3. Don't worry, we're going to break it down piece by piece, so by the end, you'll be a math whiz! This isn't just about getting the right answer; it's about understanding the process, the why behind each step. Think of it like building a house – you wouldn't start with the roof, right? Math is the same; there's a logical order to follow. So, grab your calculators (or your brainpower!), and let's get started!

Unraveling the Mystery: A Deep Dive into the Equation

So, you're probably looking at 120% - 3 + 2 x 0.75 + 2 / 3 and thinking, "Where do I even begin?" Well, fear not! The first step in tackling any mathematical puzzle is understanding the order of operations. Think of it as the golden rule of math – a set of instructions that tells us which operations to perform first. We're talking about the famous PEMDAS (or BODMAS, depending on where you went to school). This acronym stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (also from left to right). This order isn't some arbitrary rule; it's the foundation of mathematical consistency. Imagine if we all did calculations in different orders – math would be chaos! By following PEMDAS/BODMAS, we ensure everyone arrives at the same correct answer. It's like a universal language that keeps our mathematical conversations clear and concise. This principle ensures that regardless of who solves the equation, the result remains consistent and accurate. Let's hold that thought and dive deeper into our equation, identifying the different operations lurking within. We've got a percentage, subtraction, multiplication, addition, and division – quite the party! Now, knowing PEMDAS/BODMAS, we can start planning our attack strategy. We'll begin by converting that percentage into a more manageable form and then systematically work our way through the equation, step by calculated step. Remember, math isn't about speed; it's about accuracy and understanding. So, let's take our time, break down the problem, and conquer it together!

Step 1: Taming the Percentage Beast

Alright, let's tackle that 120% first. Percentages can seem a bit intimidating, but they're really just fractions in disguise! The word "percent" literally means "out of 100," so 120% is simply 120 out of 100. To make it easier to work with, we need to convert this percentage into a decimal. How do we do that? Easy! We divide by 100. So, 120 / 100 = 1.2. Voila! We've transformed our percentage into a decimal. Why is this important? Because decimals are much easier to use in calculations like multiplication and division. Trying to multiply with a percentage sign hanging around can get messy. Now, think about what 120% actually means. It's more than 100%, right? So, it represents a value greater than the original whole. In our case, 1.2 represents 1 and 2 tenths of the original value. This understanding is crucial in real-world applications, like calculating sales tax or understanding interest rates. Imagine you're buying something that's 20% off – you're essentially paying 80% of the original price. That's the power of understanding percentages! So, by converting 120% to 1.2, we've not only made our equation easier to solve, but we've also reinforced our understanding of what percentages represent. This foundational knowledge will serve you well in countless mathematical scenarios. Now that we've tamed the percentage beast, let's move on to the next step in our mathematical adventure!

Step 2: Multiplication and Division – The Dynamic Duo

Now that we've handled the percentage, it's time to tackle the multiplication and division lurking in our equation: 1.2 - 3 + 2 x 0.75 + 2 / 3. Remember PEMDAS/BODMAS? Multiplication and division come before addition and subtraction. But here's a crucial detail: we perform these operations from left to right. It's like reading a sentence; we work our way across the equation in the order we encounter them. So, let's start with the multiplication: 2 x 0.75. This is where knowing your basic multiplication facts comes in handy. 0.75 is the same as 3/4, so we're really calculating 2 times 3/4, which equals 1.5. Easy peasy! Now, let's move on to the division: 2 / 3. This one isn't quite as clean as the multiplication, but it's still manageable. 2 divided by 3 gives us approximately 0.6667 (we'll round to four decimal places for accuracy). Remember, in some cases, you might want to leave this as a fraction (2/3) to avoid rounding errors, especially if you're dealing with more complex calculations later on. But for our purposes, the decimal approximation works just fine. Now, why is the order of operations so important here? Imagine if we did the addition or subtraction before the multiplication and division – we'd get a completely different (and incorrect) answer! That's why PEMDAS/BODMAS is the cornerstone of accurate mathematical calculations. By prioritizing multiplication and division from left to right, we ensure we're following the correct logical sequence. So, with our multiplication and division complete, our equation is starting to look much simpler. We've transformed it from a complex string of operations into a more manageable form. Let's move on to the final step: addition and subtraction.

Step 3: Addition and Subtraction – The Final Countdown

We're in the home stretch! Our equation now looks like this: 1.2 - 3 + 1.5 + 0.6667. We've conquered the percentage, tamed the multiplication and division, and now we're left with addition and subtraction. Just like with multiplication and division, we perform these operations from left to right. This is key to getting the correct answer. So, let's start at the beginning: 1.2 - 3. This gives us -1.8. Remember your rules for adding and subtracting negative numbers! It's like having $1.20 and owing $3 – you're still in the hole by $1.80. Now, we add 1.5: -1.8 + 1.5. This brings us to -0.3. We're getting closer! Finally, we add 0.6667: -0.3 + 0.6667. This gives us our final answer: 0.3667. And there you have it! We've successfully navigated the equation and arrived at our solution. But hold on a second – let's not just focus on the answer. The journey is just as important as the destination. Think about all the steps we took, the rules we followed, and the concepts we applied. We didn't just blindly punch numbers into a calculator; we understood why we were doing each operation. This understanding is what truly makes you a math master! So, whether you're balancing your budget, calculating a tip at a restaurant, or tackling a complex engineering problem, the skills you've honed by understanding the order of operations will serve you well. Now, go forth and conquer those math challenges!

The Grand Finale: Our Solution Unveiled

After our epic mathematical journey, we've finally arrived at the solution to the equation 120% - 3 + 2 x 0.75 + 2 / 3. Drumroll, please... The answer is 0.3667 (rounded to four decimal places). But remember, the final answer is just one piece of the puzzle. The real victory lies in understanding the process we used to get there. We started by decoding the order of operations (PEMDAS/BODMAS), then we tamed the percentage, conquered multiplication and division, and finally, navigated addition and subtraction. Each step built upon the previous one, leading us to our final destination. Now, take a moment to appreciate the power of math! It's not just about numbers and symbols; it's about logical thinking, problem-solving, and breaking down complex challenges into manageable steps. These are skills that will serve you well in all aspects of life, from personal finance to career success. So, the next time you encounter a seemingly daunting math problem, remember our adventure. Remember the steps we took, the rules we followed, and the satisfaction of cracking the code. You've got this! And who knows, maybe you'll even start to enjoy the thrill of the mathematical chase. Math isn't just a subject; it's a superpower. Now, go out there and use it!

Why This Matters: Real-World Applications

Okay, so we've conquered this equation, but you might be thinking, "When am I ever going to use this in real life?" Great question! The truth is, the principles behind solving 120% - 3 + 2 x 0.75 + 2 / 3 are applicable in countless everyday scenarios. It's not just about this specific equation; it's about the underlying skills you've developed. Think about budgeting, for example. You need to calculate expenses, income, and savings, often involving percentages, multiplication, division, addition, and subtraction. Understanding the order of operations is crucial for accurately tracking your finances and making informed decisions. Or what about cooking? Recipes often require you to adjust quantities based on the number of servings you need. This involves multiplying and dividing ingredient amounts, and if you mess up the order, you might end up with a culinary disaster! Let's not forget about shopping. Calculating discounts, sales tax, and comparing prices requires a solid grasp of percentages and basic arithmetic. Imagine trying to figure out which deal is better – 30% off or a buy-one-get-one-free offer – without understanding these concepts. Even in fields like science and engineering, the order of operations is fundamental. Scientists use mathematical equations to model the world around us, and engineers rely on these principles to design and build everything from bridges to smartphones. So, while you might not encounter this exact equation in your daily life, the skills you've gained by solving it – logical thinking, problem-solving, and attention to detail – are invaluable. Math isn't just an abstract subject; it's a tool that empowers you to navigate the world more effectively. By mastering these fundamental concepts, you're setting yourself up for success in all areas of life. Keep practicing, keep exploring, and keep applying your mathematical superpowers!

Practice Makes Perfect: Similar Problems to Try

So, you've successfully cracked the code of 120% - 3 + 2 x 0.75 + 2 / 3! Awesome! But like any skill, math requires practice to truly master. Think of it like learning a musical instrument or playing a sport – the more you practice, the better you get. To help you solidify your understanding of the order of operations, let's try a few similar problems. These will give you the opportunity to apply the concepts we've discussed and build your confidence. Remember, the key is to break down each problem step by step, following PEMDAS/BODMAS. Don't be afraid to make mistakes – that's how we learn! And if you get stuck, review the steps we took in this article or seek out additional resources. There are tons of great websites and videos that can help you hone your math skills. Here are a few problems to get you started:

1. 150% + 4 - 3 x 0.5 + 4 / 2
2. 8 - 2 + 5 x 1.2 - 100% / 4
3. 25% x 8 + 6 / 3 - 1 + 2.75

Try working through these problems on your own, showing your steps along the way. This will help you identify any areas where you might need extra practice. And remember, math isn't a spectator sport – it's something you have to actively engage with to truly understand. So, grab a pencil and paper, put on your thinking cap, and dive in! The more you practice, the more comfortable and confident you'll become with these concepts. And who knows, you might even start to enjoy the challenge of solving math problems. Happy calculating!