Solving (6 ÷ 3 + 5) × (11 - 4): A Step-by-Step Guide

Hey guys! Let's dive into this mathematical expression together and break it down step by step. We've got $(6 iv 3 + 5) imes (11 - 4)$, and it might look a bit intimidating at first, but trust me, it's totally manageable. Math can be fun, especially when we approach it like solving a puzzle. So, grab your thinking caps, and let's get started!

Understanding the Order of Operations

Before we jump into the nitty-gritty, it’s super important to understand the order of operations. Think of it as the golden rule of math – if you don't follow it, you might end up with the wrong answer. We often use the acronym PEMDAS or BODMAS to help us remember the order. It stands for:

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

This order tells us which operations to perform first. So, in our expression, we'll first tackle anything inside parentheses, then move on to division and multiplication, and finally handle addition and subtraction.

Breaking Down the Expression Step-by-Step

Okay, let's apply PEMDAS/BODMAS to our expression: $(6 iv 3 + 5) imes (11 - 4)$.

1. Parentheses First: We have two sets of parentheses, so let's start with the first one: $(6 iv 3 + 5)$.
   • Inside this parenthesis, we have division and addition. According to PEMDAS/BODMAS, we do division first.
   • $6 iv 3 = 2$. So, now our expression inside the first parenthesis looks like this: $(2 + 5)$.
   • Next, we do the addition: $2 + 5 = 7$. So, the first parenthesis simplifies to 7.
2. Now, let's tackle the second set of parentheses: $(11 - 4)$.
   • This one is straightforward: $11 - 4 = 7$. So, the second parenthesis also simplifies to 7.
3. Rewriting the Expression: Now that we've simplified the parentheses, our expression looks much simpler: $7 imes 7$.
4. Multiplication: Finally, we perform the multiplication: $7 imes 7 = 49$.

So, the answer to the expression $(6 iv 3 + 5) imes (11 - 4)$ is 49. Ta-da! We did it!

Why the Order of Operations Matters So Much

You might be wondering, “Why all the fuss about the order of operations?” Well, if we didn't follow this order, we could end up with a completely different result. Imagine if we decided to add before dividing in the first parenthesis. We'd get a different answer, and that's why PEMDAS/BODMAS is so crucial for consistency in math.

Think of it like following a recipe. If you add the ingredients in the wrong order, you might not get the cake you were hoping for. Math is the same way – the order matters!

Real-World Applications of Order of Operations

This isn't just some abstract math concept, guys. The order of operations is used everywhere in real-world calculations. From balancing your checkbook to calculating the tip at a restaurant, from computer programming to engineering, understanding PEMDAS/BODMAS is essential. Whenever you're dealing with formulas or complex calculations, you'll need to know which steps to take in what order.

For example, imagine you're calculating the total cost of some items you bought online. You might have the price of each item, sales tax, and a discount code. To get the correct total, you'll need to apply the discount, calculate the tax, and then add it all up in the correct order. Without the order of operations, you could easily overpay or underpay!

Diving Deeper: Practice Problems and Tips

Now that we've conquered this expression, let's talk about how you can become even more confident in your math skills. Practice makes perfect, as they say! The more you work through different problems, the more natural the order of operations will become.

Practice Problems

Here are a few practice problems you can try on your own:

1. $(10 + 2) iv 4 - 1$
2. $5 imes (8 - 3) + 6$
3. $18 iv (2 + 4) imes 3$

Work through these problems step-by-step, remembering PEMDAS/BODMAS, and see if you can get the correct answers. Don't be afraid to make mistakes – that's how we learn! You can even check your answers with a calculator to make sure you're on the right track.

Tips for Mastering the Order of Operations

• Write it out: When you're working through a problem, write out each step clearly. This will help you keep track of where you are and avoid making careless errors.
• Use parentheses: If you're creating your own expressions or trying to clarify a calculation, don't hesitate to use parentheses to group operations together. This can make your intentions crystal clear and prevent confusion.
• Check your work: Always double-check your work, especially if you're dealing with complex expressions. It's easy to make a small mistake, so taking the time to review your steps can save you from getting the wrong answer.
• Break it down: If a problem seems overwhelming, break it down into smaller, more manageable steps. This can make the whole process feel less daunting and help you focus on each individual operation.

Common Mistakes to Watch Out For

Even with a solid understanding of the order of operations, it's easy to slip up sometimes. Here are a few common mistakes to watch out for:

• Forgetting PEMDAS/BODMAS: This is the biggest one! Always keep the order of operations in mind, and refer back to it if you're not sure what to do next.
• Mixing up multiplication and division (or addition and subtraction): Remember that multiplication and division have equal priority, so you perform them from left to right. The same goes for addition and subtraction. Don't automatically assume that multiplication always comes before division, or that addition always comes before subtraction.
• Skipping steps: It's tempting to try to do everything in your head, but skipping steps can lead to errors. Write out each step clearly, especially when you're first learning.
• Not distributing correctly: If you have a number multiplying a set of parentheses, make sure you distribute it to every term inside the parentheses. For example, $2 imes (x + 3)$ is $2x + 6$, not $2x + 3$.

By being aware of these common mistakes, you can avoid them and improve your accuracy.

Let's Recap: The Key Takeaways

Okay, guys, let's recap what we've learned today. We've tackled the expression $(6 iv 3 + 5) imes (11 - 4)$ and discovered that the answer is 49. More importantly, we've reinforced the importance of the order of operations (PEMDAS/BODMAS) and how it helps us solve mathematical expressions correctly. Remember:

• PEMDAS/BODMAS is your friend: It's the roadmap for solving mathematical expressions.
• Practice makes perfect: The more you practice, the more confident you'll become.
• Break down complex problems: Divide and conquer – tackle one step at a time.
• Watch out for common mistakes: Awareness is half the battle.

Conclusion: You've Got This!

So, there you have it! We've successfully navigated the world of mathematical expressions and the order of operations. Math might seem challenging at times, but with a little bit of knowledge and a lot of practice, you can conquer any problem that comes your way. Keep practicing, keep learning, and most importantly, keep having fun with math! You've got this!