Solving The Mathematical Expression (-25)×(-4)+(-180)÷(-6)-(-32) A Step-by-Step Guide
Hey guys! Let's dive into solving this mathematical expression together. It looks a bit intimidating at first, but don't worry, we'll break it down step by step. We're going to tackle the expression (-25)×(-4)+(-180)÷(-6)-(-32) using the correct order of operations. Remember PEMDAS/BODMAS? That's our trusty guide here! This article will walk you through each stage, making sure you understand exactly how we arrive at the final answer. So, grab your thinking caps, and let's get started!
Understanding the Order of Operations
Before we even touch the numbers, it's super important to understand the order of operations. You might have heard of it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Both acronyms tell us the same thing: which operations to perform first. Multiplication and division have equal priority, so we work from left to right. The same goes for addition and subtraction. This order ensures we all get the same correct answer, no matter who's doing the math. Think of it as the golden rule of calculations! It keeps everything consistent and avoids confusion. Without this order, we could end up with multiple answers, which would be a mathematical mess! So, always remember your PEMDAS/BODMAS when faced with a complex expression.
Breaking Down the Expression: A Detailed Look
Now, let's take a closer look at our expression: (-25)×(-4)+(-180)÷(-6)-(-32). We've got multiplication, division, addition, and subtraction all in one place! The key is to tackle them in the correct order. First up, we'll handle the multiplication and division. Remember, we move from left to right, so we'll do the multiplication first: (-25) × (-4). A negative times a negative gives us a positive, so that part is pretty straightforward. Next, we'll take care of the division: (-180) ÷ (-6). Again, we're dividing a negative by a negative, so the result will be positive. Once we've sorted out these operations, we'll be left with addition and subtraction. These guys also get tackled from left to right. By breaking down the expression into manageable chunks, we make it way less daunting and much easier to solve. This step-by-step approach is crucial for accuracy and understanding.
Step-by-Step Solution
Okay, let's get our hands dirty and solve this step by step! It’s like following a recipe – each step gets us closer to the delicious final result.
Step 1: Multiplication
First, we tackle the multiplication part of the expression: (-25) × (-4). Remember, a negative number multiplied by another negative number gives us a positive result. So, 25 multiplied by 4 is 100. Therefore, (-25) × (-4) = 100. We've knocked out the first operation, and we're already making progress!
Step 2: Division
Next up, we have the division: (-180) ÷ (-6). Just like with multiplication, when we divide a negative number by another negative number, we get a positive result. So, we need to figure out how many times 6 goes into 180. If you do the math, you'll find that 180 divided by 6 is 30. Therefore, (-180) ÷ (-6) = 30. Another operation down, and we're cruising!
Step 3: Rewriting the Expression
Now that we've handled the multiplication and division, let's rewrite the expression with our results. We started with (-25)×(-4)+(-180)÷(-6)-(-32). After performing the multiplication and division, our expression now looks like this: 100 + 30 - (-32). See how much simpler it looks already? We've condensed the expression, making it easier to manage. This is a great way to keep track of our progress and avoid any confusion as we move forward.
Step 4: Handling the Negatives
Before we jump into addition and subtraction, let's address that double negative: -(-32). Remember that subtracting a negative number is the same as adding its positive counterpart. So, -(-32) becomes +32. Now our expression looks even cleaner: 100 + 30 + 32. We've transformed a potentially confusing part of the equation into a straightforward addition. This little trick is super handy when you're dealing with negatives in math problems.
Step 5: Addition
Finally, we're left with addition! We have 100 + 30 + 32. We can add these numbers from left to right, or we can add them in any order we like – the result will be the same. Let's start by adding 100 + 30, which gives us 130. Now we have 130 + 32. Adding these two numbers together, we get 162. So, the final result of the expression is 162!
Final Result and Conclusion
So, after carefully following each step, we've arrived at the final answer: (-25) × (-4) + (-180) ÷ (-6) - (-32) = 162. Wasn't that a fun journey? By breaking down the expression and tackling each operation in the correct order, we were able to solve it without any stress. Remember, the key is to follow the order of operations (PEMDAS/BODMAS) and take it one step at a time. Math problems like these might seem tricky at first, but with a little practice and the right approach, you can conquer them all! Keep up the awesome work, guys, and happy calculating!
