Solve 807 - 204 + 4273.25 - 26.75: Step-by-Step

by Sebastian Müller 48 views

Hey guys! Let's dive into solving this math problem together. We've got a seemingly complex equation here: 807 - 204 + 4273.25 - 26.75. Don't worry, it’s not as intimidating as it looks! We’ll break it down into manageable steps to make sure we understand each part perfectly. Math can be super fun when we tackle it methodically, and that’s exactly what we’re going to do. This guide is designed to help you not only solve this specific problem but also build your confidence in tackling similar mathematical challenges. So, grab your pencils, and let's get started! Remember, every big problem is just a series of small, easy steps. Let’s jump in and see how it’s done!

Understanding the Order of Operations

Before we even touch the numbers, it's crucial to understand the order of operations. This is the golden rule in mathematics that tells us which operations to perform first. You might have heard of the acronym PEMDAS, which is a handy way to remember the order:

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

In our equation, 807 - 204 + 4273.25 - 26.75, we only have addition and subtraction. According to PEMDAS, we perform these operations from left to right. This means we'll first subtract 204 from 807, then add 4273.25 to the result, and finally subtract 26.75. Sticking to this order is super important; otherwise, we might end up with the wrong answer. Think of it like following a recipe – if you add the ingredients in the wrong order, the final dish won’t turn out as expected. Similarly, in math, the order of operations ensures we get the correct solution. Understanding this principle is like having the key to unlocking any mathematical problem, so let's keep this in mind as we move forward. Now that we've got the order sorted, let's start crunching those numbers!

Step 1: Subtract 204 from 807

Okay, let’s kick things off with the first operation: 807 - 204. This is a straightforward subtraction problem. We need to subtract 204 from 807. When we set this up, we align the numbers vertically, making sure the ones, tens, and hundreds places are lined up correctly. This helps us avoid any confusion and keeps our calculation nice and tidy. So, we have:

  807
- 204
------

Starting from the right (the ones place), we subtract 4 from 7, which gives us 3. Moving to the tens place, we subtract 0 from 0, resulting in 0. Finally, in the hundreds place, we subtract 2 from 8, which gives us 6. Putting it all together, we get 603. So, 807 - 204 = 603. This is a pretty clean and simple subtraction, and it’s a great start to solving our larger equation. We've knocked out the first step, and now we're one step closer to the final answer. Remember, breaking down a complex problem into smaller, manageable steps makes it so much easier to handle. Now that we've got 603, let’s move on to the next operation and keep the momentum going!

Step 2: Add 4273.25 to 603

Next up, we need to add 4273.25 to the result we got in the previous step, which was 603. This is where things get a little more interesting because we're dealing with a decimal number. But don't worry, the process is still quite simple. The key here is to make sure we align the decimal points properly when we set up the addition. Since 603 is a whole number, we can think of it as 603.00 to make the alignment clear. Now, let’s set it up:

  603.00
+4273.25
--------

Now we can add column by column, starting from the rightmost column (the hundredths place). 0 + 5 is 5. In the tenths place, 0 + 2 is 2. We bring down the decimal point. Then, in the ones place, 3 + 3 is 6. In the tens place, 0 + 7 is 7. In the hundreds place, 6 + 2 is 8. And finally, we bring down the 4 from the thousands place. So, putting it all together, we get 4876.25. This means 603 + 4273.25 = 4876.25. We’re making great progress! We’ve tackled the addition, and we’re one step closer to the final solution. The alignment of the decimal points is super important in this step, so always double-check that before you start adding. Now, let's move on to the final subtraction and wrap this problem up!

Step 3: Subtract 26.75 from 4876.25

Alright, we’re on the home stretch! The final step is to subtract 26.75 from 4876.25. Just like in the previous addition step, it’s crucial to align the decimal points correctly to ensure accurate subtraction. This keeps everything in its proper place value and helps us avoid any mistakes. Let’s set it up:

  4876.25
-   26.75
---------

Now, we subtract column by column, starting from the rightmost column (the hundredths place). 5 - 5 is 0. In the tenths place, 2 - 7 requires us to borrow from the ones place. So, we borrow 1 from the 6, making it 5, and the 2 becomes 12. Now, 12 - 7 is 5. We bring down the decimal point. In the ones place, we now have 5 - 6, which again requires us to borrow. We borrow 1 from the 7 in the tens place, making it 6, and the 5 becomes 15. Now, 15 - 6 is 9. In the tens place, we have 6 - 2, which is 4. In the hundreds and thousands places, we simply bring down the 8 and the 4, respectively, since there are no digits to subtract from them. Putting it all together, we get 4849.50. So, 4876.25 - 26.75 = 4849.50. And there we have it! We’ve completed all the steps.

Final Answer: 4849.50

We’ve reached the end of our mathematical journey! After carefully working through each step, we've found that 807 - 204 + 4273.25 - 26.75 = 4849.50. Great job, guys! You tackled this problem like pros. Remember, the key to solving complex problems is to break them down into smaller, manageable steps. By following the order of operations and paying close attention to detail, you can conquer any mathematical challenge that comes your way. This problem involved subtraction, addition, and working with decimals, all important skills in mathematics. The step-by-step approach we used here can be applied to a wide range of problems, making it a valuable tool in your mathematical toolkit. Keep practicing, stay patient, and you'll continue to improve your problem-solving skills. Math is like a puzzle, and each problem you solve makes you a better puzzle solver. So, keep those pencils sharp and keep exploring the exciting world of mathematics! You've got this!