Solving 45 ÷ (13 - (5 + 3)): A Step-by-Step Guide

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Hey guys! Let's break down this math problem together: 45 ÷ (13 - (5 + 3)). Math can seem daunting, but when we take it step by step, it becomes much more manageable. This guide will walk you through each operation, making sure you understand why we're doing what we're doing. So, grab your pencils and let’s dive into simplifying this expression! Understanding the order of operations is key, and we'll be using the PEMDAS/BODMAS method. Let's get started and conquer this problem together!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we jump into solving the expression, it's crucial to understand the order of operations. Think of it as the golden rule of math – we need to follow it to ensure we arrive at the correct answer. The order is often remembered by the acronyms PEMDAS or BODMAS:

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

This order tells us which operations to perform first. We start with anything inside parentheses or brackets, then move on to exponents or orders (like squares and cubes), followed by multiplication and division (working from left to right), and finally, addition and subtraction (also from left to right). This ensures that everyone solving the same problem arrives at the same solution. For our problem, 45 ÷ (13 - (5 + 3)), we'll first focus on the innermost parentheses and work our way out.

Step 1: Simplify the Innermost Parentheses (5 + 3)

Our expression is 45 ÷ (13 - (5 + 3)). According to the order of operations, we need to tackle the parentheses first. Specifically, we start with the innermost parentheses, which is (5 + 3). This is a straightforward addition problem. Adding 5 and 3 gives us 8. So, we replace (5 + 3) with 8 in our expression. This simplifies our problem to 45 ÷ (13 - 8). See how we're making progress? By focusing on one step at a time, the problem becomes much less intimidating. Now, we move on to the next set of parentheses.

Step 2: Simplify the Outer Parentheses (13 - 8)

Now that we've simplified the innermost parentheses, our expression looks like this: 45 ÷ (13 - 8). We still have parentheses to deal with, so we move on to the next set. Inside the remaining parentheses, we have the subtraction problem 13 - 8. Subtracting 8 from 13 gives us 5. So, we replace (13 - 8) with 5 in our expression. This further simplifies our problem to 45 ÷ 5. We're getting closer to the final answer! We've handled all the parentheses, so now we can move on to the next operation in the order of operations.

Step 3: Perform the Division (45 ÷ 5)

After simplifying the parentheses, our expression is now 45 ÷ 5. This is a simple division problem. We need to figure out how many times 5 goes into 45. If you know your multiplication tables, you might already know the answer. Dividing 45 by 5 gives us 9. So, 45 ÷ 5 = 9. We've reached the final step and found our answer! This illustrates how following the order of operations helps us break down a complex problem into manageable steps. Isn't it satisfying when it all comes together?

Final Answer: 9

So, after following the order of operations and simplifying each step, we've found that 45 ÷ (13 - (5 + 3)) = 9. Great job! You've successfully solved this mathematical expression. Remember, the key is to take it one step at a time, following the PEMDAS/BODMAS order. Math problems like these might seem tricky at first, but with practice and a clear understanding of the rules, you can conquer them all. Keep practicing, and you'll become a math whiz in no time! And remember, guys, math is like a puzzle; each step is a piece that fits together to reveal the final picture.

Why the Order of Operations Matters

You might be wondering, why is the order of operations so important? Well, imagine if we didn't have a standard order. People could interpret the same expression in different ways and arrive at different answers. That would be chaos! The order of operations ensures that everyone gets the same result when solving a mathematical expression. It’s like a universal language that mathematicians use to communicate precisely. For instance, if we didn't follow the order of operations in our problem, 45 ÷ (13 - (5 + 3)), we might accidentally subtract before dividing, leading to a completely incorrect answer. By adhering to PEMDAS/BODMAS, we maintain consistency and accuracy in mathematical calculations. This is crucial not only in simple arithmetic but also in more advanced math and science fields. So, mastering the order of operations is a fundamental skill that pays off in many areas of study and work.

Practice Makes Perfect: Similar Problems to Try

Now that you've successfully solved 45 ÷ (13 - (5 + 3)), the best way to reinforce your understanding is to practice with similar problems. Here are a few you can try:

  1. 60 ÷ (10 - (2 + 3))
  2. 36 ÷ (9 - (4 + 1))
  3. 24 ÷ (7 - (3 + 2))

Remember to follow the same steps: simplify the innermost parentheses first, then the outer parentheses, and finally perform the division. Working through these problems will help solidify your understanding of the order of operations and build your confidence in tackling mathematical expressions. Don't be afraid to make mistakes – they're a natural part of the learning process. The more you practice, the more comfortable you'll become with these types of problems. And who knows, you might even start to enjoy them! So, grab a pen and paper, and give these a try. You've got this!

Real-World Applications of Order of Operations

The order of operations isn't just some abstract concept we learn in math class; it has practical applications in many real-world scenarios. For example, when you're calculating the total cost of items with discounts and taxes, you need to follow the order of operations to get the correct amount. Imagine you're buying a shirt that costs $30, but it's 20% off, and there's a 7% sales tax. You need to calculate the discount first, then subtract it from the original price, and finally, add the sales tax. If you don't follow the order of operations, you might end up paying the wrong amount!

In computer programming, the order of operations is crucial for writing code that performs calculations correctly. Computers follow the same rules of PEMDAS/BODMAS, so programmers need to understand this order to ensure their programs produce accurate results. In fields like engineering and finance, where precise calculations are essential, a solid grasp of the order of operations is indispensable. Whether you're balancing your checkbook, cooking a recipe, or designing a bridge, the order of operations plays a vital role in everyday life. So, mastering this concept isn't just about acing your math test; it's about developing a fundamental skill that will serve you well in countless situations.