Simplifying Mathematical Expressions 5 - [7(4 - 6 * 9)]

Hey guys! Let's dive into simplifying this mathematical expression together. We've got: 5 - [7(4 - 6 * 9)]. Don't worry, it looks a bit intimidating at first, but we'll break it down step by step. We're going to use the good old order of operations (PEMDAS/BODMAS) to make sure we get this right. So, grab your thinking caps, and let's get started!

Understanding the Order of Operations

Before we jump into the actual calculation, let’s quickly recap the order of operations. You might know it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Either way, it's the golden rule for solving mathematical expressions. It tells us the sequence in which we should perform operations to get the correct answer. Ignoring this order can lead to a completely wrong result, and we definitely don't want that!

Think of it like a recipe – you need to follow the steps in the right order to bake a perfect cake. In math, PEMDAS/BODMAS is our recipe for solving expressions. First up are parentheses (or brackets), then exponents (or orders), followed by multiplication and division (from left to right), and finally addition and subtraction (also from left to right). Keeping this in mind will make simplifying expressions a breeze.

Diving into Parentheses/Brackets

Our expression has a set of brackets, (4 - 6 * 9), which means this is where we need to focus first. Inside these brackets, we have subtraction and multiplication. According to PEMDAS/BODMAS, multiplication comes before subtraction. So, we need to tackle 6 * 9 before we can subtract anything. Multiplication is key here, and we can't move on until we've handled it. It's like laying the foundation of a house – you can't build the walls until the foundation is solid. So, let's multiply 6 and 9 and see what we get. This step is crucial because it sets the stage for the rest of the calculation. If we mess this up, the whole expression goes haywire!

Performing the Multiplication

Okay, so let's multiply 6 * 9. Most of us probably know this one off the top of our heads, but it's always good to double-check. Six times nine is indeed 54. So, we can replace 6 * 9 in our expression with 54. This might seem like a small step, but it's a significant one. We've now simplified a part of the expression, making it less complex and easier to manage. It's like decluttering your desk – once you've cleared away some of the mess, you can see things more clearly.

Our expression now looks like this: 5 - [7(4 - 54)]. Notice how we've replaced the multiplication with its result. This is the power of following the order of operations – it allows us to break down complex problems into smaller, more manageable chunks. Now that we've handled the multiplication, we can move on to the next operation within the brackets.

Tackling the Subtraction within Parentheses

Now that we've taken care of the multiplication inside the parentheses, we're left with the subtraction: 4 - 54. This might look a little tricky because we're subtracting a larger number from a smaller one, but don't worry, we've got this! When you subtract a larger number from a smaller one, the result will be negative. Think of it like owing someone money – if you have $4 and you owe $54, you're going to end up in the red.

So, what's 4 - 54? It's -50. We've now simplified the expression inside the parentheses to a single number. This is a big win! We've gone from having multiple operations inside the brackets to just one value. Our expression now looks much cleaner: 5 - [7(-50)]. We're getting closer and closer to the final answer. Remember, math is like a puzzle – each step we complete brings us closer to the solution.

Moving Outside the Parentheses: Multiplication

With the parentheses simplified, our expression now reads: 5 - [7(-50)]. The next thing we need to handle is the multiplication outside the parentheses. We have 7 multiplied by -50. Remember, a positive number multiplied by a negative number gives a negative result. So, we know our answer is going to be negative. Let's do the math: 7 * 50. If you're not sure off the top of your head, you can think of it as 7 * 5 * 10. Seven times five is 35, and then multiplying by 10 gives us 350. So, 7 * 50 is 350. But since we're multiplying by -50, our result is -350.

Now we can replace 7(-50) with -350 in our expression. This gives us 5 - [-350]. Notice the double negative here – this is a key detail that we'll need to address in the next step. We're making great progress, guys! We've handled the parentheses and the multiplication, and we're down to the final operation.

Addressing the Double Negative

Okay, so we've arrived at 5 - [-350]. See that double negative? This is a classic math situation, and it's super important to handle it correctly. Remember, subtracting a negative number is the same as adding a positive number. It's like saying you're taking away a debt – which is a good thing! So, 5 - [-350] is the same as 5 + 350. This little trick can make a big difference in avoiding errors. Double negatives can be tricky, but once you understand the rule, they become much less daunting.

Our expression is now simplified to a simple addition problem. We've transformed a seemingly complex expression into something super manageable. This is the beauty of breaking things down step by step and following the order of operations. Now, let's do the final addition and get our answer!

The Final Step: Addition

We've reached the home stretch! Our expression is now 5 + 350. This is a straightforward addition problem. Five plus 350 is, of course, 355. So, we've finally arrived at our answer! After carefully following the order of operations and breaking down the expression step by step, we've successfully simplified 5 - [7(4 - 6 * 9)].

The final simplified answer is 355.

Wrapping It Up

So, there you have it! We've taken a seemingly complex expression and simplified it down to a single number. Remember, the key to solving these types of problems is to follow the order of operations (PEMDAS/BODMAS) and break the problem down into smaller, more manageable steps. Each operation is like a piece of the puzzle, and when you put them together in the right order, you get the complete picture.

I hope this explanation was helpful and clear. Math might seem intimidating at times, but with a little practice and a systematic approach, you can conquer any expression. Keep practicing, keep exploring, and most importantly, keep having fun with math!