Solving (5,500 + 6,780) ÷ 2: A Step-by-Step Guide

Hey guys! Let's break down this math problem together. It looks a bit intimidating at first, but I promise it's totally manageable once we go through it step by step. We're tackling the expression (5,500 + 6,780) ÷ 2, which involves both addition and division. The key here is to remember the order of operations – often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This tells us which operations to perform first to get the correct answer.

First things first, let's talk about why understanding the order of operations is super important. Imagine if we just went from left to right without following any rules. We might end up with a completely different answer, and that's not what we want! PEMDAS ensures that everyone solves the problem in the same way, so we all get the same correct result. In our case, the parentheses tell us to handle the addition part first. This is crucial because we need the sum of 5,500 and 6,780 before we can divide by 2. Jumping straight to division would throw everything off, so let's stick to the plan and follow PEMDAS!

Now, let's dive into the first step: the addition within the parentheses. This is where we combine 5,500 and 6,780. You can do this manually by lining up the numbers and adding each column, or you can use a calculator if you prefer. Either way, the goal is to find the total of these two numbers. Addition is a fundamental operation in math, and it's something we use every day, whether we realize it or not. Think about adding up your grocery bill, calculating the distance you've traveled, or even just figuring out how many hours you've worked in a week. It's all addition! So, mastering this step is not just about solving this specific problem; it's about building a solid foundation for all sorts of math challenges.

Step 1: Adding the Numbers Inside the Parentheses

Okay, guys, let's get started! Our first task is to add the numbers inside the parentheses: 5,500 + 6,780. This is where we combine these two values to get a single sum. You can approach this in a couple of ways. If you're comfortable with manual addition, grab a piece of paper and line up the numbers vertically, making sure the ones, tens, hundreds, and thousands places are aligned. Then, add each column from right to left, carrying over any extra digits as needed. If you prefer, you can also use a calculator to quickly find the sum. No shame in using tools to make things easier!

Let's break down the manual addition method a bit further. Start with the ones column: 0 + 0 = 0. Then, move to the tens column: 0 + 8 = 8. Next, the hundreds column: 5 + 7 = 12. We write down the 2 and carry over the 1 to the thousands column. Finally, in the thousands column, we have 5 + 6 + 1 (the carried-over digit) = 12. So, the sum is 12,280. Alternatively, if you're using a calculator, just punch in 5,500 + 6,780, and you'll get the same result: 12,280. See? Math can be super straightforward when you take it step by step.

Now that we've added the numbers inside the parentheses, we've simplified our expression a bit. We've gone from (5,500 + 6,780) ÷ 2 to 12,280 ÷ 2. This is progress! We've tackled the first part of the problem, and we're ready to move on to the next operation. Remember, PEMDAS is our guide, and we're following it closely. Parentheses are done, so what's next? Division! This is where we'll split the sum we just calculated into two equal parts. Get ready, because we're about to make this number even more manageable.

Step 2: Dividing the Sum by 2

Alright, team, we've reached the second part of our problem: dividing the sum we just calculated (12,280) by 2. This is where we split that total into two equal groups. Just like with addition, you can tackle this division manually or with a calculator – whichever method you find more comfortable. Division is a key operation in math, helping us share things equally, figure out how many groups we can make, and much more. Think about splitting a pizza with friends, calculating how many miles you can drive on a tank of gas, or even figuring out the average score on a test. Division is all around us!

If you're going the manual route, you might use long division. This involves breaking down the dividend (12,280) and dividing it digit by digit by the divisor (2). It might seem a bit daunting at first, but it's a really valuable skill to have. You start by dividing the first digit (1) by 2. Since 1 is less than 2, you move on to the first two digits (12). 12 divided by 2 is 6, so you write down 6. Then, you bring down the next digit (2) and divide 2 by 2, which is 1. Write down the 1. Bring down the next digit (8) and divide 8 by 2, which is 4. Write down the 4. Finally, bring down the last digit (0) and divide 0 by 2, which is 0. Write down the 0. So, 12,280 divided by 2 is 6,140.

If calculators are your jam, simply enter 12,280 ÷ 2, and bam! The answer pops up: 6,140. Whether you went manual or used a calculator, we've arrived at the same destination. And that, my friends, is the solution to our problem. We've successfully divided the sum by 2, and we're ready to wrap things up and celebrate our math victory!

The Final Answer

Drumroll, please! After adding 5,500 and 6,780 and then dividing the result by 2, we've arrived at our final answer. We went through the steps carefully, following the order of operations (PEMDAS), and we tackled both addition and division. So, what's the magic number? The final answer is 6,140.

Congratulations! We've solved the problem (5,500 + 6,780) ÷ 2. You guys did an awesome job sticking with it and working through each step. Remember, math might seem tricky sometimes, but breaking it down into smaller parts makes it much easier to handle. And understanding the order of operations is like having a secret weapon that helps you conquer any math challenge. Keep practicing, keep exploring, and keep those math skills sharp!

So, to recap, we started with a slightly intimidating expression, but we didn't let that scare us. We remembered PEMDAS, tackled the addition inside the parentheses first, and then divided the sum by 2. We used either manual methods or a calculator, whichever made us feel more comfortable. And in the end, we nailed it! Remember, every math problem is just a puzzle waiting to be solved. And with a little bit of patience and the right tools, you can crack any code.