Solving The Mathematical Expression 76×789 + 90799 - 5475 × 6578 A Step-by-Step Guide
Hey guys! Today, we're diving into a mathematical problem that looks a bit intimidating at first glance. We've got a mix of multiplication, addition, and subtraction, and we need to figure out the correct order of operations to get to the right answer. Don't worry, though! We'll break it down step by step, so it's super easy to follow. So, let's jump right into solving the expression: 76×789 + 90799 - 5475 × 6578.
Understanding the Order of Operations
Before we even think about punching numbers into a calculator, let's quickly refresh our memory on the order of operations. You might have heard of the acronym PEMDAS, which stands for:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Basically, PEMDAS tells us the sequence we need to follow when we're faced with a complex math problem. It ensures that everyone arrives at the same answer, no matter who's doing the calculations. In our case, we don't have any parentheses or exponents, so we'll be focusing on multiplication, addition, and subtraction. The key thing here is that we tackle multiplication first, working from left to right, and then we handle addition and subtraction, also from left to right.
Why is this so crucial, you ask? Well, imagine if we just went straight from left to right without considering the order. We'd end up with a completely different answer, and that's not what we want! It's like trying to build a house without laying the foundation first—things are going to get messy and unstable pretty quickly. By sticking to the rules of PEMDAS, we're ensuring that our mathematical journey is smooth, logical, and, most importantly, accurate. So, let's keep this in mind as we move forward and start crunching those numbers!
Breaking Down the Expression
Now that we've got our PEMDAS goggles on, let's dissect our expression: 76×789 + 90799 - 5475 × 6578. Remember, multiplication comes first, so we need to identify those parts of the equation before anything else. Looking closely, we can see that we have two multiplication operations to handle: 76 multiplied by 789, and 5475 multiplied by 6578. These are the two powerhouses we need to calculate before we even think about adding or subtracting.
Think of it like this: multiplication is the engine of our mathematical machine. It's what gets things moving and sets the stage for the rest of the calculations. If we don't get these multiplication parts right, the entire equation will be off balance. So, we'll take each multiplication operation one at a time, making sure we're precise and accurate. We'll treat them like separate mini-problems, solve them individually, and then bring those results back into the main equation. This approach helps us keep things organized and prevents us from getting overwhelmed by the sheer size of the numbers involved. Trust me, when you're dealing with numbers this big, a little bit of organization goes a long way! So, let's roll up our sleeves and start with the first multiplication operation. We're on our way to conquering this mathematical beast!
Performing the First Multiplication: 76 × 789
Alright, let's dive into our first multiplication problem: 76 multiplied by 789. This might seem like a big calculation, but don't worry, we'll break it down into manageable steps. You can grab a calculator if you want to speed things up, but it's also super helpful to understand the manual multiplication process. It's like knowing how to cook from scratch versus just microwaving a ready meal – both get you food, but one gives you a deeper understanding and appreciation!
When you multiply 76 by 789, you're essentially figuring out what you'd get if you added 789 to itself 76 times. That's a lot of adding! But thankfully, multiplication is just a shortcut for repeated addition. If you do the math either manually or with a calculator, you will find that 76 multiplied by 789 equals 60,084. That's a hefty number, but we're not intimidated, right? We've just conquered the first major hurdle in our equation.
Now, let's take a moment to appreciate what we've done. We've taken a seemingly complex part of the equation and simplified it down to a single number. This is the magic of breaking down problems into smaller steps – it makes the whole thing feel much less daunting. We've transformed 76 × 789 into 60,084, and that's progress we can celebrate! But we're not done yet. We've still got another multiplication to tackle, and then we can finally move on to the addition and subtraction. So, let's keep our momentum going and jump into the next challenge. We're on a roll, guys!
Tackling the Second Multiplication: 5475 × 6578
Okay, guys, we've successfully navigated our first multiplication, and now it's time to face the second one: 5475 multiplied by 6578. This one looks even bigger, doesn't it? But remember, we're not scared of big numbers – we're mathematical problem-solvers! Just like before, we'll approach this methodically and break it down into smaller, more manageable steps. This is where having a calculator handy can really save you some time, but understanding the process is still super important.
When you multiply 5475 by 6578, you're essentially asking, "What's the total if I add 5475 to itself 6578 times?" That's a massive amount of addition, which is why multiplication is such a handy tool! If you crunch the numbers, either manually or with a calculator, you'll find that 5475 multiplied by 6578 equals 36,016,650. Whoa, that's a huge number! But we've conquered it. We've successfully tackled the second multiplication in our equation.
Take a moment to let that sink in. We've just multiplied two four-digit numbers together and arrived at a result over 36 million! That's pretty impressive, if I do say so myself. But more importantly, we've simplified another significant chunk of our original equation. We've transformed 5475 × 6578 into 36,016,650. This is exactly what we need to do to make the problem more manageable. Now that we've handled both multiplications, we're ready to move on to the next stage: addition and subtraction. We're getting closer and closer to the final answer, so let's keep up the great work!
Rewriting the Expression
Alright, awesome work, everyone! We've powered through both multiplication operations, and now it's time to rewrite our expression with the results we've calculated. This is a crucial step because it helps us see the simplified form of the problem and sets us up perfectly for the next operations. Remember our original expression? It was 76×789 + 90799 - 5475 × 6578. Now, let's replace those multiplication parts with the answers we found.
We calculated that 76 multiplied by 789 equals 60,084, and 5475 multiplied by 6578 equals 36,016,650. So, we can rewrite our expression as: 60,084 + 90799 - 36,016,650. See how much simpler that looks? We've gone from a complex mix of operations to a straightforward addition and subtraction problem. This is the power of following the order of operations and breaking things down step by step.
By rewriting the expression, we've also made it much easier to spot the next steps we need to take. We've eliminated the multiplication, and now we're left with addition and subtraction. According to PEMDAS, we handle these operations from left to right. So, we'll start by adding 60,084 and 90799 together. This will give us a new number that we can then subtract from 36,016,650. It's like we're building a bridge, one step at a time, to reach the final answer on the other side. So, let's keep moving forward and tackle that addition next!
Performing Addition: 60,084 + 90799
Okay, team, let's tackle the addition part of our equation. We need to add 60,084 and 90799 together. This is a pretty standard addition problem, and you can definitely use a calculator if you want to speed things up. But again, it's always good to understand the process, so you can do it manually if you ever need to. Think of it like knowing how to drive a manual car – you might prefer automatic most of the time, but it's a valuable skill to have!
When you add 60,084 and 90799, you're essentially combining these two numbers into a single total. If you break it down, you're adding the ones place, the tens place, the hundreds place, and so on, carrying over when necessary. If you do the math, you'll find that 60,084 plus 90799 equals 150,883. Nice! We've successfully completed the addition part of our equation.
This is another moment where we can pause and appreciate our progress. We've taken two numbers and combined them into one, making our expression even simpler. We've transformed 60,084 + 90799 into 150,883. That's a significant step forward! Now, we're just one operation away from the final answer. We need to subtract this new number from the result of our second multiplication. We're in the home stretch now, guys, so let's keep our focus and finish strong. Onward to subtraction!
Final Subtraction: 150,883 - 36,016,650
Alright, everyone, this is it – the final step! We've made it to the subtraction part of our equation. We need to subtract 150,883 from 36,016,650. Now, this might look a little tricky because we're subtracting a smaller number from a much larger one. But don't let that intimidate you! We've handled big numbers before, and we can definitely handle this.
When you subtract 150,883 from 36,016,650, you're essentially finding the difference between these two numbers. Since we're subtracting a smaller number from a larger one, we know our answer will be positive. If you do the subtraction, you'll find that 36,016,650 minus 150,883 equals -35,865,767. And there you have it! We've arrived at the final answer.
Conclusion: The Final Answer
Woohoo! We did it, guys! We successfully solved the mathematical expression 76×789 + 90799 - 5475 × 6578. It was a bit of a journey, with multiple steps and some big numbers, but we tackled it like pros. We followed the order of operations, broke the problem down into smaller parts, and conquered each step one at a time. And after all that hard work, we arrived at our final answer: -35,865,767.
Give yourselves a pat on the back, because this was no easy feat! We handled multiplication, addition, and subtraction with confidence and precision. We learned the importance of PEMDAS and how it helps us navigate complex equations. We also saw how breaking down a problem into smaller steps can make even the most daunting challenges feel manageable. So, the next time you're faced with a math problem that looks intimidating, remember this journey. Remember how we took it step by step, and remember that you have the skills and the knowledge to solve it. Keep practicing, keep learning, and keep challenging yourselves. You've got this!
