Solving 120% - 3 + 2 X 0.75 + 2 / 3 Step-by-Step
Hey guys! Math can sometimes feel like navigating a maze, but with a step-by-step approach, even the trickiest problems become manageable. Today, we're going to break down the expression 120% - 3 + 2 x 0.75 + 2 / 3 into simple, bite-sized pieces. We'll walk through each operation, explaining the reasoning behind each step so you not only get the answer but also understand the process. So, grab your calculators (or your thinking caps!) and let's dive into this math adventure together! This guide is perfect for anyone looking to brush up on their basic arithmetic skills or tackle more complex equations with confidence. Remember, math isn't about memorizing formulas; it's about understanding the logic and applying it. Let's make math less intimidating and more fun, one step at a time. Get ready to transform from math-phobes to math-whizzes! We'll cover everything from percentages to fractions, multiplication to division, ensuring you grasp every concept along the way. Our goal is to empower you with the skills and confidence to conquer any mathematical challenge that comes your way. So, let's get started and unlock the secrets of this mathematical expression together!
Understanding the Order of Operations (PEMDAS/BODMAS)
Before we even think about crunching numbers, it's super important to understand the order of operations. Think of it as the golden rule of math – it tells us exactly which order to solve the different parts of an equation. You might have heard of it as PEMDAS or BODMAS. Both acronyms stand for the same thing, just with slightly different names for the operations. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS, on the other hand, stands for Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). See? Same order, just different words! Ignoring this order can lead to wildly incorrect answers, and we definitely don't want that. So, let's break it down a little further. First up, we tackle anything inside parentheses or brackets. This is our top priority. Next, we deal with exponents or orders, like squares or cubes. After that, we handle multiplication and division. Here's a crucial point: we work from left to right. If an equation has both multiplication and division, we solve them in the order they appear. Lastly, we tackle addition and subtraction, again working from left to right. It's like reading a sentence – we move from left to right, solving as we go. This order might seem a bit rigid, but it's what ensures everyone arrives at the same answer. Think of it as a universal language of math! By following PEMDAS/BODMAS, we're speaking that language fluently. So, before we dive into our specific problem, let's keep this order in mind. It's our roadmap to success! Mastering the order of operations is like having the key to unlock any mathematical puzzle. It's the foundation upon which all other calculations are built. So, let's make sure we have this foundation solid before we move on.
Step 1: Converting the Percentage
Alright, first things first, we've got a percentage staring at us: 120%. Percentages can sometimes seem a bit daunting, but they're really just fractions in disguise! The word "percent" literally means "out of one hundred." So, 120% simply means 120 out of 100. To make this easier to work with in our equation, we need to convert it into a decimal. This is a super simple process. All we do is divide the percentage by 100. So, 120% becomes 120 / 100, which equals 1.2. See? Not so scary! Now, we've transformed our percentage into a friendly decimal that we can easily use in our calculations. This step is crucial because it allows us to apply the rules of arithmetic directly. Working with percentages directly can be confusing, but decimals play nicely with addition, subtraction, multiplication, and division. Think of it as translating from one language to another. We're taking the percentage and converting it into the language of decimals, which our mathematical operations understand perfectly. This conversion is a common trick in math, and it's one you'll use again and again. It's all about making things simpler and clearer. So, let's recap: we took our 120%, divided it by 100, and got 1.2. We've now successfully converted our percentage into a decimal, and we're ready to move on to the next step. This simple conversion is a powerful tool in your math arsenal. It allows you to handle percentages with confidence and integrate them seamlessly into your calculations. So, remember this trick, and you'll be a percentage pro in no time!
Step 2: Multiplication
Okay, let's keep the momentum going! Looking back at our equation, 1. 2 - 3 + 2 x 0.75 + 2 / 3, what's the next operation we need to tackle according to PEMDAS/BODMAS? That's right, it's multiplication. We've got 2 x 0.75 sitting right there, waiting to be solved. This is a straightforward multiplication problem. If you're comfortable with mental math, you might already know that 2 times 0.75 is 1.5. But if not, no worries! Grab your calculator or do it the long way – both are perfectly fine. The important thing is to get the right answer. So, 2 multiplied by 0.75 equals 1.5. We've now simplified another part of our equation. See how we're chipping away at it, one step at a time? This is the beauty of the order of operations – it breaks down a complex problem into smaller, more manageable pieces. By focusing on one operation at a time, we avoid confusion and ensure accuracy. Multiplication is a fundamental operation in math, and it's essential to master it. It's used in countless real-world scenarios, from calculating the cost of multiple items to determining the area of a rectangle. So, by practicing these types of multiplication problems, you're not just solving equations; you're building valuable skills that you can use every day. Now that we've conquered the multiplication, let's update our equation. We started with 120% - 3 + 2 x 0.75 + 2 / 3, and now we have 1.2 - 3 + 1.5 + 2 / 3. We're making progress! Let's keep going and see what's next on our list.
Step 3: Division
Alright, we're cruising along nicely! We've handled the percentage conversion and the multiplication, so what's next on our PEMDAS/BODMAS checklist? You guessed it – it's division time! Looking at our updated equation, 1. 2 - 3 + 1.5 + 2 / 3, we see the division operation right there: 2 / 3. Now, this involves a fraction, which might make some people a little nervous, but don't worry, it's totally manageable. 2 divided by 3 is simply the fraction 2/3. If you want to express this as a decimal, you can divide 2 by 3 using a calculator or long division. You'll find that 2 divided by 3 is approximately 0.6666... It's a repeating decimal, which means the 6s go on forever. For practical purposes, we can round this to 0.67. So, we've successfully tackled the division! We've converted the fraction 2/3 into its decimal equivalent, approximately 0.67. Division is another fundamental operation in math, and it's closely related to multiplication. In fact, they're often thought of as the inverse of each other. Just like multiplication, division has countless real-world applications, from splitting a bill among friends to calculating the speed of a moving object. By mastering division, you're expanding your mathematical toolkit and becoming a more confident problem-solver. Now that we've handled the division, let's update our equation once more. We started with 1.2 - 3 + 1.5 + 2 / 3, and now we have 1.2 - 3 + 1.5 + 0.67. We're getting closer and closer to our final answer! Let's keep the momentum going and tackle the remaining operations. We're in the home stretch now!
Step 4: Addition and Subtraction (Left to Right)
Okay, folks, we've reached the final leg of our mathematical journey! We've conquered the percentage, multiplication, and division. Now, according to PEMDAS/BODMAS, we're left with addition and subtraction. And remember the golden rule: we tackle these operations from left to right, just like reading a sentence. So, let's take a look at our equation: 1. 2 - 3 + 1.5 + 0.67. First up, we have 1.2 - 3. This is a subtraction problem. 1.2 minus 3 equals -1.8. Now, let's update our equation again. We've simplified 1.2 - 3 to -1.8, so our equation now looks like this: -1.8 + 1.5 + 0.67. Next, we have -1.8 + 1.5. This is another addition problem, but we're adding a negative number. -1.8 plus 1.5 equals -0.3. Let's update our equation one more time: -0.3 + 0.67. Finally, we have -0.3 + 0.67. This is our last operation! -0.3 plus 0.67 equals 0.37. And there you have it! We've successfully solved the equation. Our final answer is 0.37. Addition and subtraction are the building blocks of arithmetic, and they're used in countless everyday situations. From balancing your checkbook to calculating the total cost of your groceries, these operations are essential for navigating the world around us. By mastering addition and subtraction, you're empowering yourself with valuable life skills. Now that we've reached the end of our calculation, let's take a moment to appreciate the journey. We started with a seemingly complex equation, but by breaking it down step by step and following the order of operations, we were able to solve it with confidence. Remember, math is like a puzzle – each step is a piece that fits together to create the final solution. So, let's celebrate our success and move on to the next challenge!
Final Answer
Drumroll, please! After carefully navigating through each step of the equation 120% - 3 + 2 x 0.75 + 2 / 3, we've arrived at our final answer. We converted the percentage, tackled the multiplication and division, and finally, handled the addition and subtraction from left to right. And the grand result is... 0.37! Congratulations, mathletes! We did it! We successfully solved this mathematical puzzle. This journey wasn't just about getting the right answer; it was about understanding the process, learning the rules, and building confidence in our mathematical abilities. Remember, math isn't about memorizing formulas; it's about developing logical thinking and problem-solving skills. By breaking down complex problems into smaller, manageable steps, we can conquer any mathematical challenge that comes our way. This final answer is a testament to our hard work and dedication. We followed the order of operations, paid attention to detail, and persevered until we reached our goal. This is the kind of mindset that will serve us well in all areas of life, not just in math. So, let's celebrate our success and carry this confidence with us as we tackle future challenges. We've proven that we can do it! And remember, practice makes perfect. The more we practice these types of problems, the more comfortable and confident we'll become. So, keep exploring, keep learning, and keep challenging yourselves. The world of math is vast and fascinating, and there's always something new to discover. Let's continue to embrace the challenge and unlock the power of mathematics!
