Step-by-Step Solution -18 + 12 Divided By (-8 + 10) Multiplied By (-16 + 17)

Hey guys! Math can sometimes look scary, especially when you see a long equation filled with different operations. But don't worry, we're going to break down this problem step by step so it's super easy to understand. Today, we're tackling this equation: -18 + 12 ÷ (-8 + 10) × (-16 + 17). Sounds intimidating, right? Trust me, it's not as bad as it looks! We'll use something called the order of operations (PEMDAS/BODMAS) to solve it. This just tells us the correct sequence to do things in. Think of it like a recipe – you need to add ingredients in the right order to get the best result. In math, the order is: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). So, let's dive in and make this math problem a piece of cake!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we jump into solving the equation, it's really important to understand the order of operations. You might have heard of it as PEMDAS or BODMAS – they're basically the same thing, just different acronyms to help you remember the order. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. BODMAS stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. See? Same order, just different words. The key thing is following this order to ensure we get the correct answer. Imagine if we just started adding and subtracting from left to right – we'd end up with a totally wrong result! So, let's break down what each of these means in the context of our equation.

First up, we have Parentheses (or Brackets). This means we need to solve anything inside parentheses before we do anything else. It's like the parentheses are saying, "Hey, solve me first!" Next, we have Exponents (or Orders). These are those little numbers that tell you to multiply a number by itself a certain number of times (like 2³ which means 2 × 2 × 2). We don't have any exponents in our current equation, but it's good to know for future problems. Then comes Multiplication and Division. These are on the same level, so we do them from left to right. This is a super important point! We don't always do multiplication before division; we just do whichever comes first when reading the equation from left to right. Finally, we have Addition and Subtraction. Just like multiplication and division, these are on the same level and done from left to right. So, we don't always add before we subtract; we do whichever operation appears first from left to right. Understanding this order is the secret sauce to solving complex equations. With PEMDAS/BODMAS in our toolkit, we can confidently approach any math problem. It’s like having a map that guides us through the process, making sure we don’t get lost along the way. So, let's keep this order in mind as we tackle our equation step by step!

Step 1: Solving the Parentheses

Okay, so the first thing we need to do, according to PEMDAS/BODMAS, is tackle those parentheses. Our equation is -18 + 12 ÷ (-8 + 10) × (-16 + 17). We've got two sets of parentheses here: (-8 + 10) and (-16 + 17). Let's start with the first one: (-8 + 10). This is a simple addition problem. Think of it like you owe someone 8 dollars, but you have 10 dollars. If you pay them back, how much money do you have left? You'd have 2 dollars. So, -8 + 10 = 2. Easy peasy! Now let's move on to the second set of parentheses: (-16 + 17). This is another addition problem, but this time we're adding a negative number to a positive number. Think of it like this: you owe someone 16 dollars, but you have 17 dollars. If you pay them back, how much money do you have left? You'd have 1 dollar. So, -16 + 17 = 1. Great job! We've solved the parentheses. Now our equation looks a lot simpler: -18 + 12 ÷ 2 × 1. See how much cleaner that looks? By focusing on the parentheses first, we've already made a huge step towards solving the whole problem. It’s like clearing the clutter on your desk before you start a big project – it helps you focus and makes the whole task seem less overwhelming. Remember, breaking down complex problems into smaller, manageable steps is a key strategy in math (and in life!). We’ve taken care of the parentheses, so we’re ready to move on to the next step in our PEMDAS/BODMAS journey. Keep up the awesome work, guys! We're getting there!

Step 2: Division

Alright, we've conquered the parentheses! Now it's time to move on to the next operation in our PEMDAS/BODMAS order. Looking at our simplified equation, -18 + 12 ÷ 2 × 1, we see that we have division and multiplication. Remember, we do these from left to right. So, first up is division: 12 ÷ 2. This is a pretty straightforward division problem. How many times does 2 go into 12? The answer is 6. So, 12 ÷ 2 = 6. Fantastic! We've knocked out the division part. Now our equation is looking even simpler: -18 + 6 × 1. Notice how each step we take makes the problem more manageable? It's like we're peeling away layers of an onion, getting closer and closer to the core. This is why following the order of operations is so crucial. It keeps us organized and prevents us from making mistakes. Imagine if we tried to add -18 and 12 before doing the division – we'd get a completely different (and wrong) answer! So, by sticking to PEMDAS/BODMAS, we're ensuring that we're on the right track. We’ve successfully completed the division, and the problem is continuing to shrink before our eyes. Next up, we have multiplication, which we'll tackle in the next step. You’re doing an amazing job following along, guys! Let’s keep this momentum going!

Step 3: Multiplication

Okay, we're on a roll! We've handled the parentheses and the division, so now it's time for multiplication. Our equation currently looks like this: -18 + 6 × 1. We have a simple multiplication problem here: 6 × 1. Anything multiplied by 1 is just itself, so 6 × 1 = 6. Perfect! We've taken care of the multiplication. Now our equation is even simpler: -18 + 6. We're getting so close to the finish line! You can almost taste the mathematical victory. This step highlights the power of breaking down a complex problem into smaller, more manageable steps. By following the order of operations, we've transformed a seemingly daunting equation into a series of simple calculations. It's like building a house – you don't try to put up the roof before you've laid the foundation. Each step builds upon the previous one, leading us closer to the final solution. We’ve completed the multiplication, and we’re left with a simple addition problem. Get ready to put the final piece of the puzzle in place! You guys are doing such a great job; let's finish strong!

Step 4: Addition

Alright, guys, it's the final stretch! We've conquered the parentheses, division, and multiplication. Now we're left with just one operation: addition. Our equation is -18 + 6. This is the last step, and we've totally got this! Think of it like you owe someone 18 dollars, but you have 6 dollars. If you pay them back, how much money do you still owe? You would still owe 12 dollars. So, -18 + 6 = -12. Boom! We've solved the equation! The answer is -12. Give yourselves a huge pat on the back – you've tackled a potentially tricky math problem with skill and confidence. This final step really demonstrates the elegance of the order of operations. By following PEMDAS/BODMAS, we were able to systematically simplify the equation until we arrived at the solution. It’s like following a treasure map – each step leads us closer to the hidden treasure, and in this case, the treasure is the answer! We’ve reached the end of our mathematical journey, and we’ve emerged victorious. You guys have shown that you can handle even the most intimidating-looking equations. Remember, math is just like any other skill – the more you practice, the better you get. So, keep practicing, keep exploring, and keep conquering those math challenges!

Final Answer: -12

So, there you have it! We successfully solved the equation -18 + 12 ÷ (-8 + 10) × (-16 + 17) using the order of operations (PEMDAS/BODMAS). We broke down the problem into smaller, manageable steps: solving the parentheses first, then division, then multiplication, and finally, addition. Each step built upon the previous one, leading us to the final answer: -12. Congratulations on making it to the end! You've not only learned how to solve this specific equation, but you've also reinforced your understanding of the order of operations, a fundamental concept in mathematics. This skill will serve you well in all your future math endeavors. Remember, the key to success in math is practice and perseverance. Don't be afraid to tackle challenging problems, and always remember to break them down into smaller steps. And most importantly, don't be afraid to ask for help when you need it. Math is a journey, and we're all in it together. You guys have done an amazing job today! Keep up the great work, and never stop exploring the wonderful world of math. And remember, even the most complex problems can be solved with a little bit of patience, a clear understanding of the rules, and a step-by-step approach. So, go forth and conquer those equations!