Solving The Mathematical Expression 4x (33) - 5 X 2 + (42) - 6 ÷ 2

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Hey guys! Let's dive into solving this mathematical expression together. It looks a bit intimidating at first, but we'll break it down step by step to make it super clear. This guide will walk you through each operation, ensuring you understand the order and the logic behind it. By the end, you’ll be able to tackle similar problems with confidence. So, grab your calculators and let's get started!

Understanding the Order of Operations

Before we jump into the problem, it’s super important to understand the order of operations. Think of it as the golden rule of math! We use the acronym PEMDAS (or BODMAS, depending on where you’re from) to remember the order:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division
  • Addition and Subtraction

This means we tackle parentheses first, then exponents, followed by multiplication and division (from left to right), and finally, addition and subtraction (also from left to right). Keeping this order in mind is crucial for getting the correct answer. Ignoring it can lead to some seriously wrong results, and we definitely don’t want that!

Why is Order of Operations Important?

The order of operations ensures that everyone solves a mathematical expression in the same way. Without a standard order, we'd end up with different answers for the same problem, which would be chaos! Imagine trying to build a bridge if the engineers didn't agree on the order of calculations – yikes! So, PEMDAS (or BODMAS) is our trusty guide to consistent and accurate math.

Now that we've got the order of operations down, let's look at our specific problem and see how we can apply these rules. Remember, we'll take it one step at a time, so don't worry if it seems complicated right now. We've got this!

Breaking Down the Expression

Okay, let’s take a close look at the expression we’re dealing with: 4x (33) - 5 x 2 + (42) - 6 ÷ 2. It might seem like a jumble of numbers and symbols, but don't worry, we’ll untangle it together. The key here is to identify each operation and then tackle them in the correct order according to PEMDAS.

First, let's rewrite the expression to make it a bit clearer. When we see “4x (33),” it means 4 multiplied by 33. So, we can rewrite the expression as: 4 * 33 - 5 * 2 + 42 - 6 ÷ 2. Ah, that looks a bit less scary already, doesn't it?

Now, let's identify the operations we have here: we've got multiplication, subtraction, addition, and division. According to PEMDAS, we need to handle multiplication and division before we touch addition and subtraction. This means we'll be focusing on those parts of the expression first.

Identifying Key Operations

To make things even clearer, let's highlight the multiplication and division operations: 4 * 33, 5 * 2, and 6 ÷ 2. These are the parts we'll be working on in the next step. We'll leave the subtraction and addition for later, making sure we follow the correct order every step of the way. This methodical approach is what will help us nail this problem.

By breaking the expression down like this, we make it much easier to manage. We're not trying to solve everything at once; instead, we're focusing on smaller, more digestible chunks. This is a great strategy for tackling any complex math problem, so keep it in mind!

Performing Multiplication and Division

Alright, let's get down to the nitty-gritty and perform the multiplication and division operations we identified earlier. Remember, according to PEMDAS, these come before addition and subtraction, so we're right on track. We've got three operations to handle in this step: 4 * 33, 5 * 2, and 6 ÷ 2.

Let's start with 4 * 33. If you're doing this by hand, you can think of it as 4 times 30, which is 120, plus 4 times 3, which is 12. Add those together, and you get 132. So, 4 * 33 equals 132. If you've got a calculator handy, you can just punch it in and get the same result. Easy peasy!

Next up is 5 * 2. This one's a classic – 5 multiplied by 2 is 10. No sweat there!

Finally, let's tackle 6 ÷ 2. This means 6 divided by 2, which equals 3. Simple as that.

Rewriting the Expression

Now that we've completed the multiplication and division, let's rewrite our expression with the results we just calculated. Our original expression was 4 * 33 - 5 * 2 + 42 - 6 ÷ 2. After performing the multiplication and division, it becomes: 132 - 10 + 42 - 3. See how much simpler it looks already? We've knocked out the tougher operations, and now we're left with just addition and subtraction.

This is a great example of how breaking down a problem into smaller steps can make it much more manageable. By focusing on one type of operation at a time, we reduce the chance of making mistakes and keep things nice and clear.

Handling Addition and Subtraction

Okay, guys, we’re in the home stretch now! We’ve taken care of the multiplication and division, and we’re left with just addition and subtraction. Remember, with addition and subtraction, we work from left to right. This is super important to keep in mind, so we don't accidentally switch the order and mess up our final answer.

Our expression now looks like this: 132 - 10 + 42 - 3. Let's start from the left. First up, we have 132 - 10. That's a straightforward subtraction, and it gives us 122.

Now, we rewrite the expression with our result: 122 + 42 - 3. Next, we add 122 and 42. If you add those together, you get 164.

So, our expression now looks like this: 164 - 3. Finally, we subtract 3 from 164, which leaves us with 161.

Final Result

And there you have it! After following all the steps and carefully working through the order of operations, we've arrived at our final answer. The solution to the expression 4x (33) - 5 x 2 + (42) - 6 ÷ 2 is 161. Woo-hoo! We did it!

Conclusion and Final Answer

So, guys, we’ve successfully solved the mathematical expression 4x (33) - 5 x 2 + (42) - 6 ÷ 2. The final answer is 161. By breaking down the problem step by step and following the order of operations (PEMDAS), we made sure we tackled each operation in the correct sequence. This methodical approach is what allows us to solve even complex expressions accurately.

Key Takeaways

  • Order of Operations: Remember PEMDAS (or BODMAS) – Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. This is your golden rule for solving mathematical expressions.
  • Break It Down: Complex expressions can be intimidating, but breaking them down into smaller, manageable steps makes the whole process much easier.
  • Left to Right: When dealing with addition and subtraction, work from left to right to avoid errors.

By keeping these key takeaways in mind, you'll be well-equipped to tackle any mathematical expression that comes your way. Practice makes perfect, so keep at it, and you'll become a math whiz in no time! Great job, everyone!