Math Problem: Solving (-48) + 24 - (-18) And 144 / (-12)

Hey guys! Let's dive into this math problem and break it down step by step. We're going to tackle the expression (-48) + 24 - (-18) and then handle the division of 144 / (-12). It's all about understanding the order of operations and paying close attention to those positive and negative signs. Don't worry, it might seem a bit tricky at first, but with a little practice, you'll be acing these problems in no time. So, let's get started and see how we can solve this together. This problem involves basic arithmetic operations: addition, subtraction, and division. A solid understanding of these operations and how to handle negative numbers is crucial for solving this type of problem. Remember, mathematics is a journey, and every problem we solve is a step forward. Let's make this step a confident one!

Step-by-Step Solution

Alright, let's get down to the nitty-gritty and solve this math problem. We have two parts to deal with: the addition and subtraction part, and the division part. We'll handle them separately and then combine the results. Remember, the key is to be methodical and keep track of those pesky negative signs. Here's how we'll do it:

Part 1: Solving (-48) + 24 - (-18)

First, let's focus on the first part of the expression: (-48) + 24 - (-18). This involves adding and subtracting integers, including negative numbers. It's really all about understanding how these numbers interact with each other. A great way to think about it is to imagine you're dealing with money. If you owe someone $48 (-48) and then you pay back $24 (+24), you still owe them money, but less than before. Then, the subtraction of a negative number is equivalent to addition. In other words, subtracting a debt is like receiving something. It may sound a bit abstract, but it's really the cornerstone of understanding how negative numbers work in addition and subtraction. Let's solve it step by step:

1. (-48) + 24: Start by adding -48 and 24. Since -48 is negative and 24 is positive, we effectively subtract 24 from 48, which gives us 24. Since 48 had the larger absolute value, the result is negative. So, (-48) + 24 = -24.
2. -24 - (-18): Now, we subtract -18 from -24. Subtracting a negative number is the same as adding the positive of that number. So, this becomes -24 + 18. This means that you are owing money, but you pay a bit of it, so it decreases the amount you owe.
3. -24 + 18: Finally, adding -24 and 18, since -24 has the larger absolute value, the result will be negative. The difference between 24 and 18 is 6, so -24 + 18 = -6. This is the result of the first part of the expression.

Part 2: Solving 144 / (-12)

Now, let's move on to the second part of the expression: 144 / (-12). This is a straightforward division problem, but it's crucial to remember the rules for dividing positive and negative numbers. When you divide a positive number by a negative number, the result is always negative. So, let's get to the division:

1. 144 / (-12): Divide 144 by -12. If you divide 144 by 12, you get 12. Since we are dividing by -12, the result is negative. Therefore, 144 / (-12) = -12.

Combining the Results

Now that we've solved both parts of the expression, it's time to put them together. We had two parts of the original problem, with the first part simplified to -6 and the second part simplified to -12. We are going to consider (2) 144/(-12) as 2 * (144 / -12). So it is going to be 2 * -12 which is -24. Therefore, -6 + -24 = -30. So now, the question we need to solve is -6 + (-24).

1. -6 + (-24): Adding -6 and -24. Because they both have negative values, we can add them to result -30.

Therefore, by combining the results from both parts, we get -30. So the correct answer is none of them.

Understanding the Order of Operations

When dealing with mathematical expressions like these, it's essential to understand the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). While this problem doesn't involve exponents, it's a good idea to refresh our memory on the rule. In this case, we first handled the subtraction and addition from left to right, and then handled the division. This ensures we arrive at the correct answer. The order of operations is the backbone of mathematical problem-solving; without it, we might end up with different answers depending on how we solve the problems.

Why These Skills Matter

The ability to solve problems like this is more useful than you might think, guys! These skills build a foundation for more advanced math concepts. Plus, it improves your critical thinking skills. Whether you're balancing a budget, calculating a discount, or just trying to understand data in the real world, these skills come in handy. Math is used everywhere, from understanding financial statements to understanding scientific data. By getting a good grip on these basics, you're setting yourself up for success in many areas of life. It’s also important to remember that mathematics is not just about numbers; it's about logic, patterns, and problem-solving, which are skills valuable in all areas of life.

Practice Makes Perfect!

Keep practicing these types of problems, and you'll become more confident. Try creating your own similar expressions to solve. The more you practice, the easier it will become. Don't be afraid to make mistakes – that's how we learn. If you're struggling, break down the problem into smaller steps. Review the rules for adding, subtracting, multiplying, and dividing positive and negative numbers. Look for online resources, textbooks, or ask a teacher or tutor for help. Remember, the goal is not just to get the right answer, but to understand the process of getting the right answer. The more problems you solve, the more comfortable you'll become with the process. Also, consider explaining the problems to someone else; teaching others is a fantastic way to solidify your understanding.

Conclusion: The Final Answer

So, after all that work, what's the final answer to our math problem? Let's recap: We simplified (-48) + 24 - (-18) to -6, then solved 144 / (-12) as -12, and then multiplied that to 2 to become -24, and finally we solved -6 + (-24) to get -30. Although -30 is not among the option.

Keep practicing, and you'll become a math whiz in no time! Keep up the great work, everyone! The journey of mastering math requires not just learning formulas, but also grasping the concepts and applying them with confidence. Every equation is a puzzle, and with practice, you'll become a skilled puzzle solver. Keep up the great work and enjoy the journey of learning and understanding mathematics! Keep in mind that math is not just about memorizing facts; it's about understanding the