Solving 18×5-27÷9+1 A Step-by-Step Guide

Hey guys! Let's dive into this intriguing math problem: 18×5-27÷9+1. It might look a bit intimidating at first glance, but trust me, with a dash of PEMDAS magic and a sprinkle of patience, we'll crack it open in no time. This isn't just about getting the right answer; it's about understanding the fundamental principles of mathematical operations. So, buckle up, grab your calculators (or not, if you're feeling brave!), and let's embark on this mathematical journey together. We'll break down each step, explain the logic behind it, and by the end, you'll be a math whiz, ready to tackle any similar problem that comes your way. Think of it as a fun puzzle where each operation is a piece, and our goal is to fit them together perfectly to reveal the final answer. Let's get started!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we even think about multiplying, dividing, adding, or subtracting, we need to understand the golden rule of math problems like this: PEMDAS. Or, if you grew up in a different part of the world, you might know it as BODMAS. But don't worry, they're the same thing! It's an acronym that tells us the order in which we should perform mathematical operations:

• Parentheses (or Brackets)
• Exponents (or Orders)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order is crucial. Imagine trying to build a house by putting the roof on before the walls – it just wouldn't work! PEMDAS ensures that we solve the problem in a way that makes mathematical sense, leading us to the correct answer. Without this order, we'd be lost in a sea of numbers, getting different results each time. So, let's keep PEMDAS in our minds as we tackle this problem. It's our guiding star, ensuring we stay on the right path. Remember, PEMDAS is your friend, not your foe! Understanding this order is the key to unlocking not just this problem, but countless others in the world of mathematics. Think of it as the grammar of math – without it, the sentences (or equations) just don't make sense. So, with PEMDAS firmly in our grasp, let's move on to the next step and start applying it to our equation.

Step 1: Multiplication (18 × 5)

The first operation we encounter in our problem, 18×5-27÷9+1, that fits the PEMDAS criteria is multiplication. According to the order of operations, we need to handle multiplication and division before we even think about addition or subtraction. So, let's focus on this part: 18 multiplied by 5. You can use a calculator, do it in your head if you're feeling confident, or even break it down on paper using long multiplication. The important thing is to get this step right because it forms the foundation for the rest of the solution. Multiplication is like the engine of our equation, driving us forward to the next stage. So, what's the answer? 18 multiplied by 5 equals 90. Now we can replace 18 × 5 in our original equation with 90, making it look a little less intimidating: 90-27÷9+1. See? We're already making progress! We've taken the first step, conquered the multiplication, and now we're ready to move on to the next challenge. Each step we take is like climbing a rung on a ladder, bringing us closer and closer to the final answer. And with PEMDAS as our guide, we know we're heading in the right direction. So, let's keep the momentum going and tackle the next operation.

Step 2: Division (27 ÷ 9)

Now that we've successfully handled the multiplication, let's turn our attention to the next operation in our equation: 90-27÷9+1. According to PEMDAS, division and multiplication have the same priority, but we perform them from left to right. In this case, division comes next. So, let's tackle 27 divided by 9. This is a straightforward division problem, and if you know your times tables, you'll know the answer right away. Division is like sharing equally, we're figuring out how many times 9 fits into 27. And the answer is… 3! So, 27 divided by 9 equals 3. We can now replace 27 ÷ 9 in our equation with 3, simplifying it even further: 90-3+1. We're making great progress, guys! The equation is becoming more and more manageable with each step. We've successfully navigated the multiplication and division, and now we're left with just addition and subtraction. Remember, the key to solving these problems is to break them down into smaller, more manageable steps. And with PEMDAS as our guide, we know exactly which step to take next. So, let's keep going and conquer the remaining operations!

Step 3: Subtraction (90 - 3)

Our equation is now looking much simpler: 90-3+1. We've tackled the multiplication and division, and now we're left with subtraction and addition. According to PEMDAS, subtraction and addition have the same priority, so we perform them from left to right. That means we'll handle the subtraction first. Let's focus on 90 minus 3. This is a simple subtraction problem, and you can probably do it in your head. Subtraction is like taking away, we're removing 3 from 90. So, what's the answer? 90 minus 3 equals 87. We can now replace 90 - 3 in our equation with 87, making it even simpler: 87+1. We're almost there, guys! We've successfully navigated the subtraction, and now we have just one operation left: addition. Each step we take is like peeling away a layer of an onion, revealing the core – the final answer. And with each operation we complete, we gain confidence and momentum. So, let's finish strong and tackle the final step: addition.

Step 4: Addition (87 + 1)

We've reached the final step of our mathematical adventure! Our equation has been simplified to 87+1. This is a straightforward addition problem, and it's the last piece of the puzzle. Addition is like putting things together, we're combining 87 and 1. So, what's 87 plus 1? It's 88! And that's it! We've solved the problem. We started with a seemingly complex equation, 18×5-27÷9+1, and by following the order of operations (PEMDAS) and breaking it down step by step, we arrived at the final answer: 88. Congratulations, you've done it! This wasn't just about getting the right answer; it was about understanding the process and the logic behind it. You've learned how to apply PEMDAS, how to break down complex problems, and how to tackle each operation with confidence. Now, you can take this knowledge and apply it to other math problems, knowing that you have the tools and the skills to succeed. So, let's celebrate our mathematical victory and remember that math can be fun and engaging when we approach it with a positive attitude and a willingness to learn.

The Final Answer: 88

So, after carefully navigating through the world of PEMDAS, we've arrived at our final destination: the answer to the equation 18×5-27÷9+1 is 88. Yay! We did it! But this isn't just about getting the right number; it's about the journey we took to get there. We've learned the importance of the order of operations, the power of breaking down complex problems, and the satisfaction of solving a mathematical puzzle. Think of this answer as the treasure we found at the end of a challenging quest. It's not just a number; it's a symbol of our perseverance, our understanding, and our mathematical prowess. So, let's take a moment to appreciate the journey and the skills we've gained along the way. We've not only solved a math problem, but we've also strengthened our problem-solving abilities, which are valuable in all aspects of life. So, the next time you encounter a challenging problem, remember this journey and the steps we took to conquer it. You have the power to break it down, apply the right tools, and arrive at the solution. And remember, math isn't just about numbers; it's about logic, reasoning, and the joy of discovery. So, keep exploring, keep learning, and keep challenging yourself. The world of mathematics is vast and full of exciting possibilities. And with your newfound skills and confidence, you're ready to explore it all!