Solve 5 X (13 - 7) ÷ 2: A Step-by-Step Guide
Hey guys! Ever stumbled upon a math problem that looks like a jumbled mess of numbers and operations? Don't worry, we've all been there. Today, we're going to break down the expression 5 x (13 - 7) ÷ 2 and solve it together, step by step. Think of it as cracking a secret code – each step is a clue that leads us closer to the final answer.
The Order of Operations: Our Mathematical Compass
Before we dive into the nitty-gritty, let's talk about the order of operations. This is the golden rule of math, the compass that guides us through the maze of calculations. It ensures we all arrive at the same answer, no matter how complex the problem might seem. Remember the acronym PEMDAS (or BODMAS, depending on where you went to school)? 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 exactly which operations to tackle first. Ignoring it would be like trying to build a house without a blueprint – things could get messy real fast!
Parentheses First: Unveiling the Inner Circle
Looking at our expression, 5 x (13 - 7) ÷ 2, the first thing that catches our eye are the parentheses. According to PEMDAS, we need to solve what's inside them before anything else. It's like dealing with a VIP – their needs come first! Inside the parentheses, we have 13 - 7. This is a simple subtraction problem, and the answer is 6. So, we can rewrite our expression as 5 x 6 ÷ 2.
Multiplication and Division: The Dynamic Duo
Now that we've conquered the parentheses, we move on to multiplication and division. Here's a crucial point: these two operations have equal priority. This means we tackle them in the order they appear from left to right. In our expression, 5 x 6 ÷ 2, multiplication comes first. So, we multiply 5 by 6, which gives us 30. Our expression now looks like 30 ÷ 2.
The Final Showdown: Division Takes the Stage
We're in the home stretch now! All that's left is the division operation. We divide 30 by 2, and the answer is a satisfying 15. We've cracked the code!
Therefore, 5 x (13 - 7) ÷ 2 = 15.
Breaking Down the Problem: A Deeper Dive
Let's recap the steps we took, but this time, we'll dig a little deeper into why we did what we did. Understanding the 'why' is just as important as knowing the 'how'.
Step 1: The Power of Parentheses
Parentheses are like mathematical force fields. They group numbers and operations together, telling us, "Hey, deal with this first!" In our problem, (13 - 7) was enclosed in parentheses, so we knew we had to subtract 7 from 13 before doing anything else. This ensures that the subtraction directly impacts the subsequent multiplication and division.
Imagine if we ignored the parentheses and performed the operations in a different order. We might end up with a completely different (and incorrect) answer. That's why parentheses are so crucial – they dictate the flow of the calculation.
Step 2: Multiplication and Division: A Left-to-Right Dance
The rule of performing multiplication and division from left to right might seem arbitrary at first, but it's essential for consistency. Think of it as a mathematical dance – you need to follow the steps in the right order to avoid stepping on anyone's toes (or in this case, messing up the calculation!).
In our example, we had 5 x 6 ÷ 2. We multiplied 5 by 6 first because it came before the division. If we had divided 6 by 2 first, we would have gotten a different result, highlighting the importance of this left-to-right rule.
Step 3: The Grand Finale: Division Unveiled
After the multiplication, we were left with a simple division problem: 30 ÷ 2. This was the final step in our journey, the last piece of the puzzle. Dividing 30 by 2 gave us our final answer, 15.
Real-World Applications: Math in Action
Now that we've mastered this problem, you might be wondering, "Where would I ever use this in real life?" Well, mathematical expressions like this pop up in all sorts of situations!
Cooking and Baking:
Imagine you're doubling a recipe. The original recipe calls for (1/2) x (4 + 2) cups of flour. To double it, you need to calculate 2 x (1/2) x (4 + 2). Understanding the order of operations helps you get the measurements right, ensuring your cake turns out perfectly.
Budgeting and Finance:
Let's say you earn $50 per day and spend $(20 + $5) on expenses. Your daily savings can be calculated as $50 - ($20 + $5). Again, parentheses are crucial here to correctly calculate your total expenses before subtracting them from your earnings.
Travel Planning:
If you're planning a road trip, you might need to calculate the total distance you'll travel. If you drive for 3 hours at 60 miles per hour and then 2 hours at 70 miles per hour, the total distance is (3 x 60) + (2 x 70). The order of operations ensures you calculate each segment of the trip correctly before adding them together.
Computer Programming:
Mathematical expressions are the backbone of computer programming. From calculating game scores to processing financial data, computers rely on the order of operations to execute code accurately. Understanding PEMDAS is a fundamental skill for any aspiring programmer.
Practice Makes Perfect: Sharpening Your Skills
The best way to become a math whiz is to practice! Here are a few more problems you can try on your own:
- 10 + (5 x 3) - 8 ÷ 2
- (12 - 4) ÷ 2 + 3 x 5
- 2 x (8 + 2) - 15 ÷ 3
Remember to follow the order of operations (PEMDAS/BODMAS) and break down each problem into smaller, manageable steps. Don't be afraid to make mistakes – they're a natural part of the learning process. The more you practice, the more confident you'll become in your math skills.
Conclusion: Math is Your Superpower
So, there you have it! We've successfully tackled the expression 5 x (13 - 7) ÷ 2, and along the way, we've learned about the importance of the order of operations, real-world applications of math, and the power of practice. Math isn't just a subject you learn in school – it's a superpower that helps you navigate the world around you.
Keep practicing, keep exploring, and keep unlocking the mysteries of mathematics. You've got this!
