Solving The Math Expression (-9-5)²×4-56+224(-7) A Step-by-Step Guide

Hey guys! Let's dive into this math problem and break it down step by step. This looks like a fun one involving order of operations, so let’s get started! We’re tackling the expression: (-9-5)²×4-56+224:(-7). It might look intimidating at first, but don’t worry, we'll get through it together. Understanding the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is crucial. This handy rule tells us the sequence in which we need to perform the operations to get the correct answer.

First off, we need to deal with the parentheses. Inside the parentheses, we have -9-5. This is a straightforward subtraction problem. When you subtract 5 from -9, you're essentially moving further into the negative numbers. Think of it like you’re already 9 steps behind, and then you take another 5 steps back. So, -9-5 equals -14. Now our expression looks like this: (-14)²×4-56+224:(-7). See? We're already making progress! Next up are the exponents. We have (-14)², which means -14 multiplied by itself. Remember, a negative number multiplied by a negative number gives a positive result. So, (-14) * (-14) is 196. Our expression now becomes: 196×4-56+224:(-7). We're getting there!

Now we move on to multiplication and division, working from left to right. We first encounter 196×4. If you multiply 196 by 4, you get 784. So, our expression is now: 784-56+224:(-7). Next in line is the division: 224:(-7). When you divide a positive number by a negative number, the result is negative. 224 divided by 7 is 32, so 224:(-7) equals -32. Our expression has transformed into: 784-56-32. Almost there! Finally, we handle addition and subtraction, again from left to right. We start with 784-56. Subtracting 56 from 784 gives us 728. Now we have: 728-32. And lastly, we subtract 32 from 728, which leaves us with 696. So, the final answer to our problem (-9-5)²×4-56+224:(-7) is 696. Awesome job, guys! We tackled a seemingly complex problem by breaking it down into smaller, manageable steps. Remember, the key to solving math problems like this is to follow the order of operations and take your time. Let’s keep practicing and conquering more math challenges!

Breaking Down the Math: A Step-by-Step Solution to (-9-5)²×4-56+224:(-7)

Hey everyone! In this article, we're going to take a deep dive into solving a specific mathematical expression: (-9-5)²×4-56+224:(-7). Math problems like these can seem a bit daunting at first glance, but with a clear understanding of the order of operations and a methodical approach, we can break it down into manageable steps. Our main focus will be on following the correct sequence of operations, which is crucial for arriving at the correct solution. We’ll use the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) as our guide. This ensures that we tackle each part of the expression in the right order. So, grab your thinking caps, and let's get started!

Let’s begin with the first component of our problem: the parentheses. Inside the parentheses, we have -9-5. This is a straightforward subtraction operation involving negative numbers. To solve -9-5, we need to consider that subtracting a positive number from a negative number moves us further into the negative range. Think of a number line; if you start at -9 and move 5 units to the left, you end up at -14. So, -9-5 equals -14. Now that we've simplified the expression within the parentheses, we can rewrite our original problem as: (-14)²×4-56+224:(-7). We're already one step closer to the solution! The next operation we need to address, according to PEMDAS, is the exponent. We have (-14)², which means -14 raised to the power of 2, or -14 multiplied by itself. Remember the rule that a negative number multiplied by a negative number results in a positive number. So, we calculate -14 multiplied by -14. The result is 196. This means (-14)² equals 196. Our expression now looks like this: 196×4-56+224:(-7). We're making good progress! Now, we move on to the multiplication and division operations. According to PEMDAS, we perform these operations from left to right. The first multiplication we encounter is 196×4. Multiplying 196 by 4 gives us 784. So, our expression becomes: 784-56+224:(-7). Next, we handle the division: 224:(-7). When dividing a positive number by a negative number, the result is negative. 224 divided by 7 is 32, so 224:(-7) equals -32. Now, our expression is: 784-56-32. We're almost at the final step!

The last operations we need to perform are addition and subtraction. Again, we work from left to right. We start with 784-56. Subtracting 56 from 784 gives us 728. So, our expression now simplifies to: 728-32. Finally, we subtract 32 from 728. This gives us the result of 696. Therefore, the final answer to the mathematical expression (-9-5)²×4-56+224:(-7) is 696. Congratulations! We've successfully navigated through the entire problem, breaking it down step by step. By following the order of operations and taking a methodical approach, we were able to solve what initially appeared to be a complex equation. Remember, consistent practice and a clear understanding of the rules are key to mastering mathematical problems. Keep up the great work, guys!

Step-by-Step Guide to Solving (-9-5)²×4-56+224:(-7)

Hello everyone! Let’s break down a mathematical problem that might look a bit tricky at first: (-9-5)²×4-56+224:(-7). Don't worry, we're going to tackle this together step by step. The secret to solving complex mathematical expressions is to follow the order of operations, commonly known as PEMDAS. This acronym stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Following PEMDAS ensures that we perform the operations in the correct sequence, which is essential for getting the right answer. We'll go through each step meticulously, so you can understand the process clearly. Our goal is not just to find the answer but also to understand how we arrive at that answer. So, let’s put on our math hats and get started!

The first step, according to PEMDAS, is to address anything within parentheses. In our expression, we have (-9-5) inside the parentheses. This means we need to perform the subtraction of 5 from -9. When you subtract a positive number from a negative number, you're essentially moving further into the negative numbers on the number line. So, if we start at -9 and subtract 5, we end up at -14. Therefore, -9-5 equals -14. With this simplification, our expression now looks like this: (-14)²×4-56+224:(-7). See how much simpler it looks already? Next, we need to deal with exponents. We have (-14)², which means -14 raised to the power of 2. This is the same as -14 multiplied by itself: -14 * -14. Remember the rule that a negative number multiplied by a negative number results in a positive number. So, -14 multiplied by -14 equals 196. Now our expression is: 196×4-56+224:(-7). We're making good progress! Now it's time for multiplication and division. PEMDAS tells us to perform these operations from left to right. The first operation we encounter is multiplication: 196×4. If you multiply 196 by 4, you get 784. So, our expression becomes: 784-56+224:(-7). Next up is division: 224:(-7). When you divide a positive number by a negative number, the result is a negative number. 224 divided by 7 is 32, so 224:(-7) equals -32. Our expression has now transformed into: 784-56-32. Almost there!

Finally, we tackle addition and subtraction, working from left to right. We start with 784-56. When you subtract 56 from 784, you get 728. So, our expression simplifies to: 728-32. The last step is to subtract 32 from 728. This gives us the final result: 696. Therefore, the solution to the mathematical expression (-9-5)²×4-56+224:(-7) is 696. Great job, guys! We’ve successfully broken down a potentially complex problem into a series of manageable steps and found the answer. Remember, the key to mastering these types of problems is understanding and applying the order of operations (PEMDAS) consistently. Keep practicing, and you'll become a math whiz in no time! This approach not only helps in solving mathematical problems accurately but also builds confidence in tackling more complex challenges. So, let’s celebrate our achievement and gear up for the next mathematical adventure!