Step-by-Step Guide Solving (156250 + 250037) / 11 + 9

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Hey guys! Today, we're going to break down a math problem that looks a bit intimidating at first glance, but trust me, it's totally manageable once we take it step by step. We're tackling this: (156250 + 250037) / 11 + 9. Don't worry, we'll go through it together, making sure every step is crystal clear. So, let's dive in and make math a little less scary and a lot more fun!

Understanding the Order of Operations

Before we even think about adding or dividing, we need to understand the golden rule of mathematics: the order of operations. You might have heard of it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Basically, it's the sequence we need to follow to solve any mathematical expression correctly. If we don't follow this order, we might end up with a completely wrong answer, and nobody wants that!

Think of it like a recipe. If you add the ingredients in the wrong order, you might end up with a culinary disaster. The same goes for math. The order of operations ensures that we all get to the same correct answer, no matter who's solving the problem or where they are in the world. It’s like a universal language for numbers! So, let's break down what each part of PEMDAS or BODMAS means in our specific problem.

  • Parentheses/Brackets: This is always our first stop. Anything inside parentheses or brackets needs to be simplified before we do anything else. It’s like the most important part of the equation, and we need to deal with it first. In our problem, we have (156250 + 250037), so this is where we’ll start our journey.
  • Exponents/Orders: These are those little numbers that float above the main numbers, indicating powers or roots. We don't have any in our current problem, but if we did, we'd tackle them after the parentheses.
  • Multiplication and Division: These operations are like siblings; they have equal priority. We perform them from left to right in the expression. If we had both multiplication and division, we'd simply work our way across the equation from left to right, solving each as we encounter it. In our problem, we have a division operation, so it's definitely on our radar.
  • Addition and Subtraction: Just like multiplication and division, addition and subtraction are also on the same level of priority. We handle them from left to right. We have both addition operations in our problem, so we'll get to those after we've taken care of the parentheses and division.

So, with the order of operations in mind, we have a clear roadmap for solving our problem. First, we'll tackle the numbers inside the parentheses. Then, we'll divide. Finally, we'll add. Easy peasy, right? Let's get started!

Step 1: Adding Numbers Inside the Parentheses

The first thing we need to do, according to the order of operations, is to tackle what's inside the parentheses. In our equation, (156250 + 250037) / 11 + 9, the expression inside the parentheses is 156250 + 250037. This is a straightforward addition problem, but it’s crucial to get it right because it sets the stage for the rest of our calculation. So, let’s get those numbers lined up and add them together carefully.

When adding large numbers like these, it’s super important to keep everything aligned by place value. This means lining up the ones, tens, hundreds, thousands, and so on. This way, we avoid making any accidental errors. Think of it like building a tower with blocks; if the foundation isn't aligned, the whole thing could topple over!

Here’s how we set up the addition:

  156250
+ 250037
------

Now, let’s add column by column, starting from the rightmost column (the ones place):

  • Ones place: 0 + 7 = 7. We write down 7.
  • Tens place: 5 + 3 = 8. We write down 8.
  • Hundreds place: 2 + 0 = 2. We write down 2.
  • Thousands place: 6 + 0 = 6. We write down 6.
  • Ten-thousands place: 5 + 5 = 10. We write down 0 and carry over the 1 to the next column.
  • Hundred-thousands place: 1 (carried over) + 1 + 2 = 4. We write down 4.

So, when we add 156250 and 250037, we get 406287. It’s like putting together a puzzle, piece by piece, until we have the complete picture. Now we can rewrite our original equation, replacing the expression in parentheses with its sum:

(406287) / 11 + 9

We've conquered the first step! We’ve simplified the expression inside the parentheses, and we're one step closer to solving the whole problem. Now, we move on to the next operation in the order: division. Let's keep the momentum going!

Step 2: Performing the Division

Alright, we've successfully tackled the parentheses, and now it's time to move on to the next operation in our equation: (406287) / 11 + 9. According to the order of operations, division comes before addition, so we need to divide 406287 by 11 before we even think about adding 9. Division can sometimes seem a bit daunting, especially with larger numbers, but don’t worry, we’ll break it down into manageable chunks.

Long division is our trusty tool here. It allows us to divide large numbers methodically, making sure we don't miss any steps. Think of it like taking a long journey; we break it down into smaller segments, making the overall trip less overwhelming. Let's set up our long division problem:

11 | 406287

Now, we’ll go through the process step by step:

  1. Divide: How many times does 11 go into 4? It doesn't, so we look at the next digit. How many times does 11 go into 40? It goes 3 times (3 x 11 = 33).
  2. Multiply: We write the 3 above the 0 in 406287 and multiply 3 by 11, which gives us 33.
  3. Subtract: We subtract 33 from 40, which leaves us with 7.
  4. Bring down: We bring down the next digit, which is 6, making our new number 76.

Now, we repeat the process with 76:

  1. Divide: How many times does 11 go into 76? It goes 6 times (6 x 11 = 66).
  2. Multiply: We write the 6 next to the 3 above 406287 and multiply 6 by 11, which gives us 66.
  3. Subtract: We subtract 66 from 76, which leaves us with 10.
  4. Bring down: We bring down the next digit, which is 2, making our new number 102.

Let's keep going:

  1. Divide: How many times does 11 go into 102? It goes 9 times (9 x 11 = 99).
  2. Multiply: We write the 9 next to the 6 above 406287 and multiply 9 by 11, which gives us 99.
  3. Subtract: We subtract 99 from 102, which leaves us with 3.
  4. Bring down: We bring down the next digit, which is 8, making our new number 38.

Almost there!

  1. Divide: How many times does 11 go into 38? It goes 3 times (3 x 11 = 33).
  2. Multiply: We write the 3 next to the 9 above 406287 and multiply 3 by 11, which gives us 33.
  3. Subtract: We subtract 33 from 38, which leaves us with 5.
  4. Bring down: We bring down the last digit, which is 7, making our new number 57.

Finally:

  1. Divide: How many times does 11 go into 57? It goes 5 times (5 x 11 = 55).
  2. Multiply: We write the 5 next to the 3 above 406287 and multiply 5 by 11, which gives us 55.
  3. Subtract: We subtract 55 from 57, which leaves us with 2.

So, 406287 divided by 11 is 36935 with a remainder of 2. For our purposes, we'll focus on the whole number part, which is 36935. Now, we can update our equation:

36935 + 9

We’ve conquered division! We're in the home stretch now, with just one more operation to go. Let’s finish strong with addition!

Step 3: Final Addition

We've made it to the final step, guys! After tackling the parentheses and conquering the division, we're left with a simple addition problem: 36935 + 9. This is the last piece of the puzzle, and it's going to bring us to the final answer. Addition is like the grand finale of our mathematical journey, and it's always satisfying to see the result of our hard work.

To add 36935 and 9, we simply need to add the numbers together. It might seem straightforward, but it’s still important to be careful and make sure we don't make any silly mistakes at the last moment. Let’s line up the numbers and add them:

  36935
+     9
------

Starting from the rightmost column (the ones place):

  • Ones place: 5 + 9 = 14. We write down 4 and carry over the 1 to the next column (the tens place).
  • Tens place: 1 (carried over) + 3 = 4. We write down 4.
  • Hundreds place: 9 + 0 = 9. We write down 9.
  • Thousands place: 6 + 0 = 6. We write down 6.
  • Ten-thousands place: 3 + 0 = 3. We write down 3.

So, when we add 36935 and 9, we get 36944. That’s it! We’ve reached the end of our mathematical adventure.

Conclusion: The Final Answer

Wow, we did it! We successfully solved the equation (156250 + 250037) / 11 + 9 by breaking it down step by step. We started by adding the numbers inside the parentheses, then we performed the division, and finally, we completed the equation with the last addition. It’s like climbing a mountain; we took it one step at a time, and now we're at the summit, enjoying the view of our accomplishment.

Our final answer is 36944. Give yourselves a pat on the back, guys! You've shown that even seemingly complex problems can be solved if we approach them methodically and follow the rules of the order of operations. Remember, math is like a puzzle, and every step we take brings us closer to the solution. Keep practicing, keep exploring, and most importantly, keep having fun with math! You've got this!