Solve 10 + 5 * 2 - 30 * 2: Order Of Operations Guide

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Hey everyone! Ever find yourself staring at a math problem with a mix of operations and feeling totally lost? You're not alone! Math can seem like a tangled mess sometimes, but I'm here to help you untangle it. Today, we're going to break down a specific problem: 10 + 5 * 2 - 30 * 2. This looks a bit intimidating at first glance, right? But don't worry, we'll tackle it together using the order of operations. Trust me; it's like having a secret code to crack any math problem!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we dive into the problem, let's quickly chat about the order of operations. This is the golden rule of math, the secret code I mentioned! It ensures that everyone solves the same problem in the same way, so we all get the same answer. Think of it as a set of instructions that tells us exactly which steps to take and when. There are two acronyms that help us remember the order: PEMDAS and BODMAS. They both mean the same thing, just with slightly different words. Let's break it down:

  • Parentheses (or Brackets): This is always the first thing you tackle! If you see any parentheses or brackets in your problem, solve what's inside them first. It's like they're little VIP sections in your equation, getting attention before everything else. Imagine them as the gatekeepers of the equation; you must deal with what's inside before moving on.
  • Exponents (or Orders): Next up are exponents (or orders, depending on the acronym you use). These are those little numbers floating up in the air, like in 2^2 (which is 2 squared). If you see any exponents, calculate them next. They are the superheroes of the equation, adding power and complexity. Think of them as the special forces; they tackle the tough stuff early on.
  • Multiplication and Division: Here's where it gets a little tricky. Multiplication and division are on the same level of importance. This means you solve them in the order they appear from left to right. It’s a common mistake to think multiplication always comes before division, but that's not true! They're like co-captains, sharing the responsibility. They are the workhorses of the equation, crunching numbers and keeping things balanced.
  • Addition and Subtraction: Just like multiplication and division, addition and subtraction are also on the same level. Solve them in the order they appear from left to right. Again, don't automatically assume addition comes before subtraction! They’re the finishers, bringing the equation home. They are the diplomats of the equation, adding and subtracting to reach the final solution.

So, remember PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Keep this order in mind, and you'll be a math whiz in no time!

Step-by-Step Solution to 10 + 5 * 2 - 30 * 2

Okay, now that we've got the order of operations down, let's apply it to our problem: 10 + 5 * 2 - 30 * 2. Ready to see how it's done? We'll break it down step-by-step, so you can follow along easily.

  1. Look for Parentheses/Brackets:

The first thing we always do is check for parentheses or brackets. In our equation, 10 + 5 * 2 - 30 * 2, there aren't any! So, we can skip this step and move on. Sometimes, the absence of something is just as important to note. It means we're on the right track and can move forward confidently. This initial check is crucial because it sets the stage for the rest of the solution. 2. Check for Exponents/Orders:

Next up, we look for exponents (or orders). Do you see any little numbers floating in the air? Nope! We don't have any exponents in this problem either. That's perfectly fine; not every problem will have them. It's like checking for a specific ingredient in a recipe – if it's not there, you simply move on to the next step. This step helps us streamline the solution process by eliminating unnecessary operations. 3. Multiplication and Division (from left to right):

Now we're getting to the meat of the problem! We need to tackle multiplication and division. Remember, we do these in the order they appear, moving from left to right. In our equation, we have two multiplication operations: 5 * 2 and 30 * 2. Let's do them one at a time.

*   First, we have `5 * 2`. What's 5 multiplied by 2? It's 10! So, we can replace `5 * 2` with `10` in our equation. This simplifies the problem a bit, making it easier to manage. It's like breaking a large task into smaller, more manageable chunks.
*   Now our equation looks like this: `10 + 10 - 30 * 2`. Next, we have `30 * 2`. What's 30 multiplied by 2? It's 60! So, we replace `30 * 2` with `60`. This further simplifies the equation, bringing us closer to the final answer.
*   Our equation is now: `10 + 10 - 60`. We've successfully handled all the multiplication in this step! This careful approach ensures we don't miss any operations and maintain accuracy.
  1. Addition and Subtraction (from left to right):

We're almost there! The last step is to handle addition and subtraction. Just like with multiplication and division, we do these in the order they appear from left to right. Our equation is now 10 + 10 - 60.

*   First, we have `10 + 10`. What's 10 plus 10? It's 20! So, we replace `10 + 10` with `20`. The equation now looks like `20 - 60`.
*   Finally, we have `20 - 60`. What's 20 minus 60? It's -40! So, our final answer is **-40**.

That's it! We've solved the problem! See? It wasn't so scary after all. By following the order of operations step-by-step, we were able to break it down and find the solution. Remember, the key is to take your time and be methodical. Math is like a puzzle; each piece fits perfectly when you put it in the right place.

Common Mistakes to Avoid

Even with the order of operations in mind, it's easy to slip up! Let's chat about some common mistakes people make when solving problems like this, so you can avoid them.

  1. Forgetting PEMDAS/BODMAS:

    This is the big one! If you forget the order of operations, you're likely to solve the problem incorrectly. It's like trying to build a house without a blueprint – you might end up with something that doesn't quite work. Always keep PEMDAS/BODMAS in mind as your guiding principle. Write it down if you need to! Think of it as your math mantra, repeating it to yourself before you start. This simple act can prevent many errors.

  2. Adding/Subtracting Before Multiplying/Dividing:

    This is a classic mistake. People often see addition or subtraction first and jump right in, but remember, multiplication and division come before addition and subtraction! It’s tempting to just go from left to right, but the order of operations is crucial. Imagine you're baking a cake – you need to mix the dry ingredients before adding the wet ones, right? Math is similar; the order matters.

  3. Not Working from Left to Right (for M/D and A/S):

    Remember, multiplication and division are on the same level, and so are addition and subtraction. This means you solve them in the order they appear from left to right. Don't assume that multiplication always comes before division or that addition always comes before subtraction. They're like teammates, working together in a specific sequence. Think of it as reading a sentence – you go from left to right, not randomly jumping around.

  4. Ignoring Negative Signs:

    Negative signs can be tricky! Make sure you carry them along with the numbers they belong to. It's easy to lose track of a negative sign, especially when there are a lot of operations. Think of the negative sign as a shadow – it always follows the number it belongs to. Pay close attention to signs; they can completely change the outcome of a problem.

  5. Rushing Through the Problem:

    Math isn't a race! Take your time, write out each step, and double-check your work. Rushing can lead to careless errors. It's better to solve one problem correctly than to solve three problems incorrectly. Think of it as quality over quantity. Slow and steady wins the race, especially in math.

By being aware of these common pitfalls, you can avoid them and solve math problems with greater accuracy and confidence. Remember, practice makes perfect! The more you work with the order of operations, the more natural it will become.

Practice Problems

Alright, guys! Now that we've walked through an example and talked about common mistakes, it's time to put your knowledge to the test! Practice is the key to mastering any skill, and math is no exception. Here are a few problems for you to try on your own. Remember to use PEMDAS/BODMAS as your guide, and take your time. Don't be afraid to make mistakes – that's how we learn! Grab a pencil and paper, and let's get started!

  1. 20 - 4 * 3 + 8 / 2
  2. 15 + (10 - 5) * 2 - 1
  3. 3^2 + 12 / 4 - 2 * 3
  4. 100 / (25 - 15) + 6 * 2
  5. 8 * 4 - 36 / 9 + 7

Try solving these problems on your own, following the steps we discussed. If you get stuck, don't worry! Go back and review the order of operations, and look at the example we worked through earlier. The more you practice, the easier it will become. These problems are designed to help you solidify your understanding of PEMDAS/BODMAS and build your problem-solving skills. Treat them like a fun challenge, and enjoy the process of figuring them out.

(Answers: 1. 12, 2. 24, 3. 6, 4. 22, 5. 35)

Conclusion

So, there you have it! We've successfully tackled the problem 10 + 5 * 2 - 30 * 2 and learned all about the order of operations. Remember, PEMDAS/BODMAS is your friend! It's the secret code that unlocks the solution to any math problem with multiple operations. By following this order, you can break down complex equations into manageable steps and arrive at the correct answer every time. Math may seem daunting at times, but with a systematic approach and a little practice, you can conquer it!

We also discussed some common mistakes to avoid, like forgetting the order of operations, adding/subtracting before multiplying/dividing, and not working from left to right. By being aware of these pitfalls, you can steer clear of them and improve your accuracy. Think of these mistakes as learning opportunities – each one helps you grow and become a better problem-solver.

And finally, we put your skills to the test with some practice problems. Practice is the key to mastery, so don't shy away from challenges. The more you practice, the more confident you'll become in your math abilities. Remember, math is like a muscle – the more you exercise it, the stronger it gets!

I hope this guide has been helpful and that you now feel more confident in your ability to solve math problems with the order of operations. Keep practicing, keep learning, and most importantly, have fun with math! You've got this!