Solve (9+4) * 5 - 18 - 6: Step-by-Step Guide

by Natalie Brooks 45 views

Hey guys! Let's dive into a fun mathematical problem today. We're going to break down how to solve the expression (9+4) * 5 - 18 - 6 step-by-step. It might look a bit intimidating at first, but trust me, it’s super manageable when we tackle it using the right order of operations. So, grab your thinking caps, and let's get started!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we even touch the numbers, it’s crucial to understand the golden rule of math problems like this: the order of operations. You might have heard of it as PEMDAS or BODMAS. Either way, it's your best friend in solving complex expressions. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS, on the other hand, stands for Brackets, Orders, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). See? Same concept, just different names!

Why is this order so important? Imagine if we just went from left to right without any rules. We'd end up with a totally different answer, and math would be chaos! By following PEMDAS/BODMAS, we ensure that everyone gets the same correct answer, no matter who's solving the problem. Think of it as the grammar of mathematics – it gives structure and clarity.

Let's break down each part of PEMDAS/BODMAS a little further:

  • Parentheses/Brackets: Anything inside parentheses or brackets gets top priority. We solve these first, no matter what operations are inside.
  • Exponents/Orders: Next up are exponents (like 2 squared or 3 cubed) or orders (like square roots). We tackle these after the parentheses.
  • Multiplication and Division: These guys have equal priority. We work from left to right, performing any multiplication or division we encounter.
  • Addition and Subtraction: Last but not least, we have addition and subtraction. Just like multiplication and division, we work from left to right.

Knowing this order is half the battle. Now that we've got it down, let’s apply it to our problem!

Step-by-Step Solution of (9+4) * 5 - 18 - 6

Okay, let’s get our hands dirty and solve this expression! Remember, our goal is to break it down into smaller, manageable chunks using PEMDAS/BODMAS. This way, we avoid any confusion and ensure we get the right answer.

Step 1: Parentheses/Brackets

The first thing we spot is (9+4). According to PEMDAS/BODMAS, we need to solve this first. So, 9 + 4 equals 13. We can rewrite our expression as:

13 * 5 - 18 - 6

See how much simpler it looks already? By tackling the parentheses first, we've reduced the complexity and made it easier to see the next steps.

Step 2: Multiplication

Now that we’ve handled the parentheses, we move on to the next operation in our order: multiplication. We have 13 * 5 in our expression. So, let’s multiply those numbers:

13 * 5 = 65

Our expression now looks like this:

65 - 18 - 6

We’re getting closer! Notice how each step simplifies the problem, making it less daunting. This is the power of following the order of operations.

Step 3: Subtraction

Finally, we’re left with subtraction. Remember, when we have multiple additions or subtractions, we work from left to right. So, first, we subtract 18 from 65:

65 - 18 = 47

Now our expression is even simpler:

47 - 6

One last subtraction to go!

Step 4: Final Subtraction

Let’s finish this off! We subtract 6 from 47:

47 - 6 = 41

And there we have it! The solution to our expression (9+4) * 5 - 18 - 6 is 41. 🎉

Common Mistakes and How to Avoid Them

Now that we’ve solved the problem, let’s talk about some common pitfalls that people often encounter when dealing with mathematical expressions. Knowing these mistakes can help you avoid them and boost your math confidence!

1. Ignoring the Order of Operations:

This is the biggest culprit! As we’ve stressed, PEMDAS/BODMAS is crucial. Many errors occur when people perform operations in the wrong order. For example, someone might try to subtract 18 from 5 before multiplying by 13, which would lead to an incorrect answer.

  • How to Avoid It: Always write down PEMDAS/BODMAS at the top of your paper as a reminder. Before you start solving, identify which operations you need to do in which order. Take it one step at a time!

2. Calculation Errors:

Sometimes, the mistake isn’t about the process but simply making a mistake in the arithmetic. A small addition or subtraction error can throw off the entire result.

  • How to Avoid It: Double-check your calculations! If you’re doing it by hand, take your time and be careful. If you’re using a calculator, make sure you’ve entered the numbers correctly. It’s always a good idea to do a quick mental check to see if your answer seems reasonable.

3. Forgetting the Negative Sign:

Negative signs can be tricky. It’s easy to overlook them, especially when there are multiple operations involved.

  • How to Avoid It: Pay close attention to signs. When you rewrite an expression, make sure you carry the correct sign with each number. If it helps, circle the sign with the number so you don’t lose track of it.

4. Not Breaking Down the Problem:

Complex expressions can be overwhelming if you try to do everything at once. It’s like trying to eat a whole pizza in one bite – not a good idea!

  • How to Avoid It: Break the problem down into smaller, manageable steps. Solve the parentheses first, then multiplication/division, and finally addition/subtraction. This makes the problem much less intimidating and reduces the chance of errors.

5. Skipping Steps:

It might be tempting to rush through the problem and skip steps, especially if you feel confident. However, skipping steps increases the likelihood of making a mistake.

  • How to Avoid It: Show your work! Writing out each step not only helps you keep track of what you’re doing but also makes it easier to spot any errors. Plus, if you do make a mistake, you can go back and see where you went wrong.

Practice Problems to Sharpen Your Skills

Alright, guys, now that we've tackled a problem together and discussed common mistakes, it’s time for you to put your skills to the test! Practice makes perfect, and the more you work with mathematical expressions, the more comfortable and confident you’ll become. So, let’s dive into some practice problems.

Here are a few expressions for you to solve:

  1. (12 - 5) * 3 + 8 / 2
  2. 25 + (16 / 4) - 2 * 7
  3. (7 + 3) * (15 - 10) - 5
  4. 48 / (6 + 2) + 3 * 4
  5. 100 - (9 * 6) + 14 / 7

Take your time, follow the order of operations (PEMDAS/BODMAS), and show your work step-by-step. Don’t worry if you make a mistake – that’s how we learn! The important thing is to practice and understand the process.

After you’ve solved these problems, you can check your answers. If you get stuck on any of them, go back to the step-by-step solution we worked through earlier and see if you can identify where you might have gone wrong. Remember, it’s all about understanding the process, not just getting the right answer.

Conclusion

So, there you have it! We’ve successfully solved the mathematical expression (9+4) * 5 - 18 - 6, discussed the importance of the order of operations, and looked at common mistakes to avoid. Remember, math might seem tricky at times, but with a clear understanding of the rules and plenty of practice, you can conquer any expression that comes your way!

The key takeaways are:

  • Always follow the order of operations (PEMDAS/BODMAS).
  • Break down complex problems into smaller, manageable steps.
  • Double-check your calculations.
  • Practice regularly to build your skills and confidence.

Keep practicing, keep learning, and most importantly, keep having fun with math! You’ve got this! 😉