Solving (-9)+[4×(-3)]-(7÷1): Steps And Solution

Hey guys! Today, we're diving into a math problem that might look a bit intimidating at first glance, but don't worry, we'll break it down step by step. The problem is: (-9) + [4 × (-3)] - (7 ÷ 1). We're going to walk through the solution together, so you'll not only get the answer but also understand the process. Understanding the order of operations is key here, so let's get started!

Understanding the Order of Operations

Before we jump into solving the problem, it's super important to understand 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)

This order tells us which operations to perform first. In our problem, we have parentheses, multiplication, division, addition, and subtraction. So, we'll tackle them in the PEMDAS order.

Remember, following this order ensures we get the correct answer. It's like following a recipe – if you mix up the steps, the final result won't be what you expect. This principle of following the correct order is fundamental not just in mathematics but also in various other fields, like computer programming and even cooking. By consistently applying the order of operations, we establish a clear and logical path to problem-solving, reducing errors and fostering a deeper understanding of mathematical concepts. Mastering PEMDAS is crucial for anyone looking to excel in math, as it forms the backbone of many algebraic and arithmetic operations. So, keep this in mind as we move forward! When you see a mathematical expression, always remember PEMDAS to guide your steps and ensure accuracy.

Step-by-Step Solution

Let's apply PEMDAS to our problem: (-9) + [4 × (-3)] - (7 ÷ 1).

Step 1: Parentheses and Brackets

First, we deal with anything inside parentheses and brackets. We have two operations within parentheses and brackets:

• 4 × (-3)
• 7 ÷ 1

Let's calculate these:

• 4 × (-3) = -12
• 7 ÷ 1 = 7

Now, our equation looks like this: (-9) + (-12) - 7.

Step 2: Addition and Subtraction

Next, we perform addition and subtraction from left to right. We have:

• (-9) + (-12)
• - 7

Let's calculate these step by step:

• (-9) + (-12) = -21

Now, our equation is: -21 - 7.

• -21 - 7 = -28

So, the final answer is -28.

Breaking Down the Steps Further

To really understand what’s happening, let’s break down each operation a bit more. When we multiply 4 by -3, we're essentially adding -3 four times: -3 + -3 + -3 + -3, which gives us -12. Remember, a positive number multiplied by a negative number results in a negative number. This concept is crucial for mastering arithmetic and algebra, as it appears frequently in various mathematical contexts. Understanding the rules of multiplying positive and negative numbers helps prevent common mistakes and builds a strong foundation for more complex calculations. Now, when dividing 7 by 1, we’re asking how many times 1 fits into 7, which is simply 7. Division by 1 always results in the original number, a fundamental rule that’s good to remember. Once we have these intermediate results, the problem becomes a series of additions and subtractions. Adding -9 and -12 is the same as moving further into the negative side of the number line, resulting in -21. Finally, subtracting 7 from -21 means we move even further into the negative numbers, ending up at -28. Each of these steps is a small piece of the puzzle, and understanding them individually helps in grasping the overall solution.

Why is the Order of Operations Important?

You might be wondering, why do we need this specific order? Why can't we just do the operations as they come? Well, without a standard order, we could get different answers depending on how we calculate the problem. Imagine the chaos if every math problem had multiple correct answers! That's why the order of operations is so important – it provides a clear and consistent way to solve mathematical expressions. The order of operations ensures consistency and accuracy in calculations. It’s like a universal language in mathematics; no matter who solves the problem, the answer will be the same if the correct order is followed. This standardization is crucial not just in academic settings but also in real-world applications, such as engineering, finance, and computer science. Imagine designing a bridge or calculating financial transactions; any ambiguity in the order of calculations could lead to disastrous outcomes. Therefore, understanding and applying the order of operations is a fundamental skill that goes beyond the classroom, enabling precise and reliable problem-solving in various fields.

Common Mistakes to Avoid

When solving problems like this, there are a few common mistakes people often make. Let's go over them so you can avoid them:

1. Forgetting the Order of Operations: This is the biggest one! If you don't follow PEMDAS, you're likely to get the wrong answer. Always double-check that you're doing the operations in the correct order.
2. Incorrectly Handling Negative Numbers: It's easy to mix up the rules for adding, subtracting, multiplying, and dividing negative numbers. Remember that a positive times a negative is a negative, and subtracting a negative is the same as adding a positive.
3. Skipping Steps: It might be tempting to try to do everything in your head, but it's much safer to write out each step. This way, you can catch any mistakes you make along the way.

Strategies for Avoiding Mistakes

To further minimize errors, consider adopting a few practical strategies. First, always rewrite the equation after each step. This not only keeps your work organized but also helps you visually track the progress and spot any potential miscalculations. Rewriting the equation after each step helps prevent errors. By visually reinforcing each operation, you create a clear pathway for your solution, making it easier to review and confirm your work. Second, if you're unsure about a particular operation, double-check the rules or use a calculator to verify your answer. This is especially useful when dealing with negative numbers or more complex operations. Calculators can be valuable tools for ensuring accuracy, but they should not replace your understanding of the underlying mathematical principles. Finally, practice makes perfect. The more you solve problems, the more comfortable you'll become with the order of operations and the different types of calculations involved. Regular practice builds both speed and accuracy, allowing you to tackle mathematical problems with confidence. Remember, even the most experienced mathematicians make mistakes occasionally, so don't be discouraged by errors. Instead, view them as opportunities for learning and improvement.

Real-World Applications

Okay, so we've solved this problem, but you might be thinking,