Solving 8 + 2 × (3 - 1)² Correct Order Of Operations

by ADMIN 53 views

Hey guys! Ever found yourself staring at a numerical expression wondering where to even begin? It’s like having a map without a starting point, right? Well, don't worry, because we’re going to break down the correct sequence of operations you need to follow to solve expressions accurately. Let's use the expression 8 + 2 × (3 - 1)² as our example. By the end of this article, you'll be a pro at tackling these problems!

Understanding the Order of Operations

So, what’s the secret sauce to solving any numerical expression? It all boils down to following the order of operations, often remembered by the acronym PEMDAS (or BODMAS in some parts of the world). This nifty little mnemonic helps us keep track of what to do first, second, and so on. PEMDAS stands for:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division
  • Addition and Subtraction

It might sound a bit technical, but trust me, it’s super straightforward once you get the hang of it. The key thing to remember is that we perform operations inside parentheses first, then deal with exponents, followed by multiplication and division (from left to right), and finally, addition and subtraction (also from left to right). Skipping a step or doing things out of order can totally throw off your answer, so let’s make sure we’ve got this down.

Diving Deep into the First Steps Parentheses and Exponents

Okay, let's circle back to our example: 8 + 2 × (3 - 1)². According to PEMDAS, we’ve got to tackle those parentheses first. Inside the parentheses, we have (3 - 1), which is a no-brainer – it equals 2. So, we’ve simplified our expression a bit, and now it looks like this: 8 + 2 × 2². See how much cleaner it looks already?

Next up are the exponents. We’ve got 2², which means 2 squared, or 2 times 2. That’s 4, guys! So, we can replace 2² with 4 in our expression. Now we’re looking at 8 + 2 × 4. We're making progress, right? It’s like peeling an onion – layer by layer, we’re getting closer to the core (which, in this case, is the solution).

This part is crucial because messing up the order here can lead to a completely wrong answer. Imagine if we decided to add 8 + 2 before dealing with the exponent – yikes! We’d be way off track. So, remember, parentheses and exponents are your best friends in the first phase of solving any numerical expression.

Tackling Multiplication and Division

Alright, we've conquered the parentheses and exponents. Next on our PEMDAS adventure are multiplication and division. Remember, these two operations hang out together, and we tackle them in the order they appear from left to right. Looking back at our simplified expression, we’ve got 8 + 2 × 4. Spot any multiplication or division? You bet! We've got 2 × 4 sitting right there.

So, let's do the math: 2 multiplied by 4 equals 8. Now we can replace 2 × 4 with 8 in our expression. This brings us to 8 + 8. See how each step makes the expression simpler and easier to handle? It’s like decluttering your room – bit by bit, things start to look much better!

Now, here’s a little tip: if you had both multiplication and division in the same expression, you'd work from left to right. For example, if you had something like 10 ÷ 2 × 3, you’d do 10 ÷ 2 first (which is 5), and then multiply by 3 (giving you 15). Ignoring this left-to-right rule can lead to errors, so keep it in mind.

The importance of handling multiplication and division correctly can’t be overstated. They’re like the engines of our mathematical train, driving us closer to the final destination. Get this step right, and you’re in the home stretch!

Bringing It Home Addition and Subtraction

We're on the final leg of our journey, guys! We've handled the parentheses, exponents, multiplication, and division. Now, all that’s left are addition and subtraction. Just like multiplication and division, these two operations are partners in crime, and we tackle them in the order they appear from left to right. Looking at our expression, we’ve got 8 + 8 – a nice, straightforward addition problem.

What’s 8 plus 8? It’s 16, of course! So, after all those steps, we’ve finally arrived at our answer. The value of the expression 8 + 2 × (3 - 1)² is 16. How cool is that? We took a seemingly complex problem and broke it down into manageable steps, all thanks to the order of operations.

Just like with multiplication and division, if you had both addition and subtraction, you’d work from left to right. For instance, if you had 10 - 5 + 3, you’d first do 10 - 5 (which is 5), and then add 3 (giving you 8). Keeping this left-to-right rule in mind ensures you don’t stumble in the final stretch.

The beauty of following the order of operations is that it provides a clear, consistent path to the solution. It’s like following a recipe – if you follow the steps in the right order, you’re much more likely to end up with a delicious result. So, remember PEMDAS, and you’ll be solving numerical expressions like a math whiz in no time!

Applying PEMDAS to Our Problem

Let’s bring it all together and walk through our original problem, 8 + 2 × (3 - 1)², step by step, just to make sure we’ve got it nailed down. This is where we put all our knowledge into action, guys!

  1. Parentheses: First up, we tackle (3 - 1), which equals 2. Our expression now looks like 8 + 2 × 2².
  2. Exponents: Next, we deal with 2², which is 2 squared, or 2 × 2, giving us 4. So, our expression becomes 8 + 2 × 4.
  3. Multiplication: Now, we handle the multiplication: 2 × 4 equals 8. Our expression is now 8 + 8.
  4. Addition: Finally, we do the addition: 8 + 8 equals 16.

And there you have it! We’ve successfully solved the expression, and our final answer is 16. By following PEMDAS, we broke down a complex problem into a series of simple steps. Each step was like a mini-victory, leading us closer to the ultimate solution. It’s like climbing a ladder – one rung at a time, you reach the top.

This step-by-step approach is not just a way to get the right answer; it’s also a way to build confidence. When you see how each operation fits into the bigger picture, math problems become less intimidating and more like puzzles waiting to be solved. So, keep practicing, keep following PEMDAS, and you’ll be amazed at how quickly you improve!

Why the Order Matters

You might be wondering,