Solving The Mathematical Expression (5 - 2) * 3 - (2 + 5) / 3 Step By Step

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Hey guys! Today, let's break down this mathematical expression: (5 - 2) * 3 - (2 + 5) / 3. I know, it might look a bit intimidating at first glance, but trust me, we'll get through it together, step by step. Think of it like solving a puzzle – we just need to follow the right order of operations to get to the solution. So, grab your imaginary pencils and paper (or maybe your real ones!) and let’s dive in!

Understanding the Order of Operations

Before we even touch the numbers, it’s super important to understand the order of operations. This is the golden rule of mathematics that tells us what to do first, second, and so on. Remember the acronym PEMDAS? It stands for:

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

Following PEMDAS ensures we all get the same answer, no matter who's solving the problem. It's like having a universal language for math! So, with our PEMDAS goggles on, let’s get back to our expression: (5 - 2) * 3 - (2 + 5) / 3.

Step 1: Tackling the Parentheses

Alright, first up are the parentheses. We’ve got two sets of them in our expression: (5 - 2) and (2 + 5). According to PEMDAS, we need to resolve these before anything else. It's like they're little mini-problems hiding inside the bigger problem, and we need to crack them open first!

Let's start with the first set: (5 - 2). This is a simple subtraction. 5 minus 2 equals 3. Easy peasy! So, we can replace (5 - 2) with 3.

Now, let’s move on to the second set: (2 + 5). This is an addition. 2 plus 5 equals 7. Another one down! We can replace (2 + 5) with 7.

Our expression now looks like this: 3 * 3 - 7 / 3. See? It’s already looking less intimidating. We’ve conquered the parentheses, and that’s a big win! We're making progress, guys! Just keep breaking it down step by step, and you'll see how manageable even complex-looking problems can become.

Remember, the key is to take it one chunk at a time. Don't try to do everything at once, or you might get lost in the numbers. Focus on the task at hand, and celebrate each small victory along the way. Math is like building with Lego bricks – you start with the individual pieces and gradually assemble them into a beautiful structure.

Step 2: Multiplication and Division

Okay, now that we've handled the parentheses, it's time to move on to the next step in our PEMDAS journey: Multiplication and Division. Remember, PEMDAS tells us to perform these operations from left to right. It's like reading a sentence – we go from the beginning to the end, addressing each multiplication or division as we encounter it.

Looking at our expression, which is now 3 * 3 - 7 / 3, we see a multiplication first: 3 * 3. This is straightforward. 3 multiplied by 3 equals 9. So, we can replace 3 * 3 with 9. Our expression now looks like 9 - 7 / 3.

Next up, we have a division: 7 / 3. 7 divided by 3 is not a whole number; it’s a fraction or a decimal. We can express it as 7/3 (a fraction) or approximately 2.33 (a decimal). For the sake of this example, let's keep it as the fraction 7/3 for now. This will give us a more precise answer in the end. So, we replace 7 / 3 with 7/3, and our expression becomes 9 - 7/3.

We've successfully tackled the multiplication and division, following the left-to-right rule. You see, PEMDAS is like a roadmap, guiding us through the maze of operations. Without it, we might end up taking the wrong turns and getting lost! But with PEMDAS as our guide, we're on the right track to solving this problem.

It's also important to remember that multiplication and division are like two sides of the same coin. They're inverse operations, meaning they undo each other. Similarly, addition and subtraction are inverse operations. Understanding this relationship can help you simplify expressions and solve equations more efficiently. So, keep that in mind as we move on to the final step!

Step 3: Addition and Subtraction

We're on the home stretch, guys! We've conquered the parentheses, tackled the multiplication and division, and now we're left with the final step in our PEMDAS adventure: Addition and Subtraction. Just like with multiplication and division, we perform these operations from left to right. It’s all about maintaining that order and keeping things nice and tidy.

Our expression is currently 9 - 7/3. We have a subtraction operation here. To subtract a fraction from a whole number, we need to express the whole number as a fraction with the same denominator as the fraction we're subtracting. In this case, our fraction has a denominator of 3, so we need to express 9 as a fraction with a denominator of 3.

To do this, we multiply 9 by 3/3 (which is equal to 1, so we're not changing the value of the number). 9 * (3/3) = 27/3. Now we can rewrite our expression as 27/3 - 7/3.

Now that we have two fractions with the same denominator, we can simply subtract the numerators. 27 minus 7 equals 20. So, 27/3 - 7/3 = 20/3. Our final answer is 20/3.

We can also express this as a mixed number. 20 divided by 3 is 6 with a remainder of 2. So, 20/3 is equal to 6 and 2/3. If we want a decimal approximation, 20 divided by 3 is approximately 6.67.

So, there you have it! We’ve successfully navigated through the entire expression, step by step, following the sacred order of PEMDAS. It might have seemed daunting at first, but by breaking it down into smaller, manageable chunks, we were able to reach the solution. Remember, math is not about memorizing formulas or performing calculations blindly; it's about understanding the underlying principles and applying them logically. And you guys just rocked it!

Final Answer and Takeaways

So, after all that hard work, what's our final answer? The solution to the expression (5 - 2) * 3 - (2 + 5) / 3 is 20/3, which is also equal to 6 and 2/3 or approximately 6.67. Woohoo! Give yourselves a pat on the back – you've earned it!

But more than just getting the right answer, what's really important are the takeaways from this exercise. We’ve not only solved a math problem, but we’ve also reinforced some crucial problem-solving skills that can be applied in all areas of life. Here are a few key things to remember:

  • The Power of Order: PEMDAS is not just a set of rules; it’s a testament to the power of order and structure. In math, as in life, following a systematic approach can help you tackle complex challenges with confidence.
  • Break It Down: Big problems often seem less daunting when we break them down into smaller, more manageable steps. This is a strategy you can use not only in math but also in project management, goal setting, and even everyday tasks.
  • Embrace the Process: Math is not always about finding the quick solution; it's about understanding the process. The journey of solving a problem can be just as valuable as the destination.
  • Practice Makes Perfect: The more you practice, the more comfortable you’ll become with mathematical concepts and operations. So, keep challenging yourself, keep exploring, and keep having fun with math!

So, guys, I hope this step-by-step breakdown has been helpful and has made the expression a little less scary. Remember, math is just another language, and with a little practice, you can become fluent in it. Keep practicing, keep exploring, and never stop questioning! You've got this!