Calculate (-49 - 63 - 35 + 21) / -7: Step-by-Step

Hey guys! Math can sometimes feel like navigating a maze, right? But don't worry, we're here to break down this particular problem step by step, so it feels less like a daunting equation and more like a fun puzzle. Today, we’re diving into how to solve the expression (-49 - 63 - 35 + 21) / -7. It might look a bit intimidating at first, but trust me, we'll tackle it together and you'll see it’s totally manageable. So, grab your calculators (or just your brains!) and let’s get started!

Breaking Down the Numerator: -49 - 63 - 35 + 21

The first part of our journey is to simplify the numerator, which is -49 - 63 - 35 + 21. Think of it as a mini-adventure inside the bigger problem. We need to combine these numbers carefully, paying close attention to the signs (those sneaky little pluses and minuses!). When you see a string of additions and subtractions, it’s often easiest to group the negative numbers together and then deal with the positive ones. This way, you keep track of your debts and credits, so to speak.

Let's start by combining the negative numbers: -49, -63, and -35. When we add these together, we're essentially accumulating more negativity. It's like owing someone 49 dollars, then owing them another 63, and then another 35 – the debt just keeps piling up! So, let's do the math: -49 + (-63) + (-35). To make it simpler, we can first add -49 and -63. Imagine you're on a number line, starting at -49 and moving 63 steps further to the left. Where do you end up? Well, -49 plus -63 equals -112. Now we have -112 - 35. This means we’re going even further into the negatives. So, -112 + (-35) gives us -147. We're not done with the numerator yet, but we've made a big step by consolidating all those negative numbers. That’s the bulk of the equation right there.

Now we need to bring in the positive number, +21. So, our numerator now looks like this: -147 + 21. This is where we start to climb back from the depths of negative numbers. Adding a positive number to a negative number is like paying off some of your debt. If you owe 147 dollars but then you pay 21 dollars, you still owe money, but less than before. So, what is -147 + 21? Think of it as starting at -147 on the number line and moving 21 steps to the right. You're getting closer to zero, but you're not quite there yet. Doing the math, -147 + 21 equals -126. And there you have it! We've successfully simplified the numerator to -126. This is a crucial step because now we've reduced a complex string of numbers into a single, manageable figure. We're halfway to solving the whole problem. Keep up the great work!

Dividing by -7: Completing the Calculation

Alright, now that we've tackled the numerator and simplified it to -126, it's time to move on to the final step: dividing by -7. Remember our original problem? It's (-49 - 63 - 35 + 21) / -7. We've already figured out that the part in the parentheses, the numerator, equals -126. So now our equation looks much simpler: -126 / -7. This is where the rules of division, especially when dealing with negative numbers, come into play. Understanding these rules is key to getting the correct answer.

So, what happens when you divide a negative number by another negative number? Here's the golden rule: a negative divided by a negative equals a positive. It might seem a bit counterintuitive at first, but think of it this way: division is the opposite of multiplication. In multiplication, a negative times a negative also gives you a positive. The same principle applies here. It’s like reversing a negative effect, which then turns positive. This rule is super important in mathematics and will come up time and time again, so it’s worth memorizing.

Now that we know the sign of our answer will be positive, let's focus on the numbers themselves. We need to divide 126 by 7. If you're comfortable with long division, you can dive right in. If not, don't worry! We can break it down. Think about how many times 7 goes into 12. It goes in once, with a remainder. So, 7 times 1 is 7, and 12 minus 7 is 5. Now we bring down the 6 from 126, making it 56. So, our new question is: how many times does 7 go into 56? If you know your multiplication tables, you'll know that 7 times 8 equals 56. So, 7 goes into 56 exactly 8 times. That means 126 divided by 7 is 18. Isn't it satisfying when the numbers work out neatly?

We've done the hard work! We know that a negative divided by a negative is a positive, and we've calculated that 126 divided by 7 is 18. So, -126 divided by -7 equals positive 18. And there you have it! We've successfully solved the equation. The answer to (-49 - 63 - 35 + 21) / -7 is 18. See? Not so scary after all!

Why This Matters: Real-World Applications

You might be thinking, “Okay, I can solve this equation now, but when am I ever going to use this in real life?” That’s a valid question! It’s important to understand not just how to do something, but why it matters. While you might not encounter this exact problem on a daily basis, the skills you’ve used to solve it are incredibly valuable in many real-world scenarios. Mathematical thinking is a crucial skill in so many different aspects of life.

Think about managing your finances, for instance. Balancing a budget involves adding and subtracting expenses and income, just like we did with the numerator in our equation. If you're running a business, you need to calculate profits and losses, which often involves dealing with negative numbers (losses) and positive numbers (gains). Knowing how to accurately combine these numbers is essential for making sound financial decisions. This is super critical for financial literacy.

Another area where these skills come in handy is in science and engineering. Many scientific calculations involve complex equations with positive and negative values. For example, calculating changes in temperature, determining electrical currents, or understanding chemical reactions all require a solid understanding of how to work with different types of numbers. These fields heavily rely on accurate calculations. Even in everyday situations like cooking, you might need to adjust a recipe that calls for dividing ingredients, and understanding fractions and division is key to getting it right.

Beyond the specific numbers and operations, the process we used to solve this problem is just as important. We broke down a complex problem into smaller, more manageable steps. This is a problem-solving strategy that can be applied to almost any challenge you face, whether it’s in math, science, your job, or your personal life. Learning to approach problems methodically, one step at a time, is a skill that will serve you well in countless situations. It's all about the approach!

Common Mistakes to Avoid

Now that we've nailed the solution, let’s quickly talk about some common pitfalls people often encounter when solving similar problems. Knowing these mistakes can help you steer clear of them and ensure you get the right answer every time. Prevention is better than cure, right?

One of the biggest mistakes is messing up the order of operations. Remember PEMDAS or BODMAS? This acronym helps you remember the correct order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In our problem, we had parentheses, so we tackled that first. If you skip this step or do the operations in the wrong order, you're likely to end up with the wrong answer. Order matters, guys!

Another common mistake is mishandling negative signs. It’s so easy to lose track of a negative sign, especially when you're dealing with multiple numbers. Always double-check that you've included the correct signs in your calculations. A simple way to avoid this is to group negative numbers together, as we did earlier, and then deal with them separately. Keep an eye on those negatives!

Finally, mistakes can happen when dividing negative numbers. Remember the rule: a negative divided by a negative is a positive. It’s a common error to forget this rule and end up with a negative answer when it should be positive. Drill this rule into your head! Also, make sure you’re comfortable with your division facts. If you struggle with division, it might be worth brushing up on your times tables. Practicing these basic skills can make a big difference in your overall math confidence.

Practice Makes Perfect: Try It Yourself!

So, we've walked through the solution, discussed real-world applications, and highlighted common mistakes. Now it’s your turn to shine! The best way to master any math skill is to practice, practice, practice. Practice makes perfect, as they say! Try tackling similar problems on your own. You can even change the numbers in this equation and see if you can still solve it. The more you practice, the more comfortable and confident you’ll become.

Here’s a challenge for you: try solving this problem: (-60 - 45 - 25 + 30) / -5. Follow the same steps we used in this article. First, simplify the numerator by combining the negative numbers and then adding the positive number. Then, divide the result by -5. Give it a go, and see what you come up with! Don’t be afraid to make mistakes – that’s how we learn. And if you get stuck, go back and review the steps we covered earlier.

Conclusion

Congratulations! You’ve made it to the end of our step-by-step guide on how to calculate (-49 - 63 - 35 + 21) / -7. We've broken down the problem, explored the concepts, and even discussed real-world applications. Remember, math isn't about memorizing formulas – it's about understanding the logic and applying it to solve problems. You've got this!

We started by simplifying the numerator, carefully combining the negative and positive numbers. Then, we tackled the division, remembering the crucial rule that a negative divided by a negative is a positive. We also looked at how these skills apply to everyday situations and highlighted common mistakes to avoid. It's all about mastering the basics.

Most importantly, we emphasized the value of practice. So, keep practicing, keep challenging yourself, and remember that every problem you solve makes you a little bit stronger in math. Keep up the great work, guys! And remember, if you ever get stuck, there are plenty of resources available to help you, including articles like this one. Math is a journey, and every step you take brings you closer to mastering it. Happy calculating!