Solve The Math Problem: 48 - [240 ÷ (32 - 16 ÷ 2) + 24 ÷ 4 * 3]

by TextBrain Team 64 views

Hey guys! Today, we're diving into a fun math problem that looks a bit intimidating at first glance. But don't worry, we'll break it down step by step and solve it together. Our mission is to calculate the value of this expression: 48 - [240 ÷ (32 - 16 ÷ 2) + 24 ÷ 4 * 3]. This problem involves a mix of arithmetic operations, including division, subtraction, and multiplication, and it uses parentheses and brackets to indicate the order in which we should perform these operations.

Understanding the Order of Operations

Before we jump into the calculation, it’s super important to remember the order of operations, often remembered by the acronym PEMDAS or BODMAS:

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

This order is crucial because it tells us exactly which operations to perform first. Without following this order, we might end up with the wrong answer. Think of it like a recipe – if you add the ingredients in the wrong order, the final dish might not turn out as expected!

Step-by-Step Solution

Let's apply the order of operations to our problem:

48 - [240 ÷ (32 - 16 ÷ 2) + 24 ÷ 4 * 3]

1. Innermost Parentheses: 16 ÷ 2

First, we tackle the innermost parentheses: (32 - 16 ÷ 2). Within these parentheses, we have subtraction and division. According to PEMDAS/BODMAS, division comes before subtraction. So, we start by dividing 16 by 2:

  • 16 ÷ 2 = 8

Now our expression looks like this:

48 - [240 ÷ (32 - 8) + 24 ÷ 4 * 3]

2. Remaining Parentheses: 32 - 8

Next, we complete the operation within the parentheses:

  • 32 - 8 = 24

Our expression now simplifies to:

48 - [240 ÷ 24 + 24 ÷ 4 * 3]

3. Brackets: Division and Multiplication (Left to Right)

Now we move to the brackets: [240 ÷ 24 + 24 ÷ 4 * 3]. Inside the brackets, we have division, addition, and multiplication. We perform division and multiplication from left to right.

First, we do the division:

  • 240 ÷ 24 = 10

Our expression becomes:

48 - [10 + 24 ÷ 4 * 3]

Next up, we have another division:

  • 24 ÷ 4 = 6

Now the expression looks like:

48 - [10 + 6 * 3]

Then, we perform the multiplication:

  • 6 * 3 = 18

Our expression is now:

48 - [10 + 18]

4. Brackets: Addition

We complete the addition inside the brackets:

  • 10 + 18 = 28

Now our expression simplifies beautifully to:

48 - 28

5. Final Subtraction

Finally, we perform the subtraction:

  • 48 - 28 = 20

So, after carefully following the order of operations, we find that the answer to our problem is 20.

Why Order of Operations Matters

The order of operations isn't just some arbitrary rule – it’s a fundamental concept in mathematics that ensures everyone arrives at the same answer for a given expression. Imagine if we didn't have a standard order; we could interpret the same expression in multiple ways, leading to different results. This would make math, science, and engineering incredibly confusing! By adhering to PEMDAS/BODMAS, we maintain consistency and clarity in mathematical calculations.

For example, let’s see what would happen if we didn’t follow the order of operations in our problem. Suppose we subtracted 16 from 32 first in the innermost parentheses:

  • 32 - 16 = 16

Then, we divided 16 by 2:

  • 16 ÷ 2 = 8

Now, our expression inside the parentheses would be 8 instead of 24, and that would throw off the entire calculation, leading to a completely different (and incorrect) answer. So, you see, following the order is super important!

Practicing and Mastering Order of Operations

Like any skill, mastering the order of operations takes practice. The more you work through problems that involve multiple operations, the more comfortable and confident you’ll become. Here are a few tips for honing your skills:

  1. Start with simpler problems: Begin with expressions that have fewer operations and parentheses. As you get the hang of it, gradually move on to more complex problems.
  2. Break it down: When faced with a complicated expression, break it down into smaller, manageable steps. Focus on one set of parentheses or brackets at a time.
  3. Double-check your work: After each step, take a moment to double-check your calculations. It’s easy to make a small mistake, especially when dealing with multiple operations.
  4. Use online resources: There are tons of fantastic websites and apps that offer practice problems and tutorials on order of operations. Khan Academy, for example, is an excellent resource.
  5. Teach someone else: One of the best ways to solidify your understanding of a concept is to teach it to someone else. Try explaining the order of operations to a friend or family member.

By practicing regularly and using these tips, you’ll become a pro at handling even the trickiest expressions!

Real-World Applications of Order of Operations

You might be wondering, “When will I ever use this in real life?” Well, the order of operations isn't just some abstract math concept; it actually has practical applications in various fields and everyday situations. Here are a few examples:

  1. Computer Programming: In programming, the order of operations is crucial for writing code that performs calculations correctly. Programming languages follow specific rules for operator precedence (which is essentially the order of operations), and programmers need to understand these rules to ensure their code works as intended.
  2. Finance and Accounting: When calculating financial metrics like compound interest or return on investment, you need to follow the order of operations to get accurate results. A mistake in the order of operations could lead to significant financial miscalculations.
  3. Engineering and Physics: Engineers and physicists use mathematical equations extensively to model and solve problems. These equations often involve multiple operations, and following the correct order is essential for obtaining accurate solutions.
  4. Everyday Math: Even in everyday situations, the order of operations can come in handy. For example, if you're calculating the total cost of a purchase with discounts and taxes, you need to apply the operations in the correct order to get the right amount. Or, if you're figuring out how much time you need to complete a series of tasks, you'll use the order of operations to organize your calculations.

So, whether you're a computer scientist, a financial analyst, an engineer, or just someone trying to balance a checkbook, understanding and applying the order of operations is a valuable skill.

Conclusion: Math is Awesome!

So, there you have it! We’ve successfully tackled a complex math problem by breaking it down step by step and following the order of operations. Remember, math might seem intimidating at times, but with a systematic approach and a bit of practice, you can conquer any challenge. Keep exploring, keep learning, and most importantly, keep having fun with math!

If you have any questions or want to try out more problems, feel free to ask. Let's keep the math party going! Cheers, guys! And remember, practice makes perfect, so keep those calculations coming. Math is not just a subject; it's a way of thinking, a way of problem-solving, and a way of understanding the world around us. So embrace the challenge, sharpen your skills, and who knows, you might just discover the magic of mathematics!