Solving (-49-63-35+21) / -7: A Math Guide

by Pedro Alvarez 42 views

Hey guys! Let's break down this math problem together. We've got a bit of an equation here: -49-63-35+21, and we need to divide the whole thing by -7. Sounds intimidating? Don't worry, we'll take it one step at a time. Math can seem like a monster sometimes, but it's really just a puzzle with rules, and once you know the rules, you can solve anything!

Understanding the Order of Operations

Before we dive into the numbers, let's quickly chat about the order of operations. Remember PEMDAS (or BODMAS, depending on where you learned math)? It's our trusty guide to solving math problems. It stands for:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

In our case, we have a series of additions and subtractions inside the parentheses (well, implied parentheses, since it's the numerator of our division). So, we'll tackle those first, working from left to right. This is super important, because doing things in the wrong order can totally mess up your answer. Think of it like baking a cake – you can't ice it before you bake it, right? Math is the same way.

Step 1: Simplifying the Numerator

Our numerator is -49 - 63 - 35 + 21. Let's break it down:

  1. -49 - 63: When we subtract a positive number from a negative number, it's like moving further into the negative zone. So, -49 - 63 becomes -112. Imagine a number line – you start at -49 and move 63 spaces to the left. That's a long walk into the negatives!
  2. -112 - 35: Again, we're subtracting a positive from a negative, so we keep moving further negative. -112 - 35 equals -147. We're getting further and further away from zero.
  3. -147 + 21: Now we're adding a positive number to a negative number. This is like taking a step back towards zero. -147 + 21 equals -126. We've still got a negative number, but we're a little closer to the positive side now.

So, the numerator simplifies to -126. We've conquered the top half of our fraction! Feels good, right? We've taken a big, scary-looking string of numbers and turned it into a single, manageable number. That's the power of breaking things down into smaller steps.

Step 2: Dividing by -7

Now we have -126 / -7. This is where the rules of dividing with negative numbers come into play. Remember the golden rule: a negative divided by a negative is a positive!

So, -126 / -7 is the same as asking, "How many times does 7 go into 126?" And since both numbers are negative, our answer will be positive. This is a key concept to remember. Negatives can be tricky, but once you understand the rules, they become your friends.

Let's do the division. 7 goes into 12 once, with a remainder of 5. Bring down the 6, and we have 56. 7 goes into 56 eight times. So, 126 / 7 = 18.

Since a negative divided by a negative is a positive, -126 / -7 = 18.

The Final Answer

Therefore, the answer to -49-63-35+21 divided by -7 is 18. We did it! We took a seemingly complex problem and broke it down into manageable steps. And that, my friends, is how you conquer math!

Why is this important?

You might be thinking, "Okay, I can solve this problem now, but why does it even matter?" Well, arithmetic expressions like this pop up everywhere in real life, even if you don't realize it. Think about budgeting your money, calculating discounts, or even figuring out cooking measurements. The skills you learn solving these problems build a foundation for more advanced math and problem-solving in general. Plus, there's a certain satisfaction in cracking a tough problem, right?

Practice Makes Perfect

So, the best way to get better at these types of problems is to practice! Try making up your own expressions and solving them. Play around with different numbers and operations. The more you practice, the more comfortable you'll become with the rules and the easier it will be to solve even the trickiest problems.

Let's Recap the Key Takeaways

  • PEMDAS/BODMAS is your friend: Always remember the order of operations.
  • Break it down: Complex problems become easier when you tackle them one step at a time.
  • Negative rules are crucial: Remember that a negative divided by a negative is a positive.
  • Practice, practice, practice: The more you do, the better you'll get.

Math might seem daunting at times, but it's a skill that anyone can learn with a little effort and the right approach. So keep practicing, keep asking questions, and keep challenging yourself. You got this!

Exploring Similar Problems

Now that we've tackled this specific problem, let's think about how these skills translate to other scenarios. What if we had a problem with exponents involved? Or parentheses nested inside other parentheses? The same principles apply! We just need to follow the order of operations and break things down step by step.

What About Exponents?

If our expression included exponents (like squares or cubes), we'd tackle those before multiplication, division, addition, or subtraction. For example, if we had something like (2^3 + 5) / 3, we'd first calculate 2^3 (which is 2 * 2 * 2 = 8), then add 5, and finally divide by 3. Exponents are just a shorthand way of writing repeated multiplication, so don't let them intimidate you.

Nested Parentheses

Sometimes, you'll encounter parentheses inside other parentheses. When this happens, you work from the innermost parentheses outwards. Imagine it like peeling an onion – you have to get through the outer layers to reach the core. So, if we had something like [10 - (2 + 3)] * 4, we'd first calculate 2 + 3 (which is 5), then subtract that from 10, and finally multiply by 4. It might look complex at first, but just take it one layer at a time.

Common Mistakes to Avoid

Even with a solid understanding of the rules, it's easy to make mistakes in math. Here are a few common pitfalls to watch out for:

  • Forgetting the order of operations: This is the biggest one! Always double-check that you're following PEMDAS/BODMAS.
  • Mixing up negative signs: Pay close attention to those negatives! A simple sign error can throw off your entire answer.
  • Skipping steps: It's tempting to try and do things in your head, but it's often safer to write out each step, especially when dealing with complex expressions.
  • Not checking your work: Always take a few minutes to review your calculations and make sure everything looks right. It's much better to catch a mistake yourself than to get the wrong answer!

By being aware of these common mistakes, you can significantly improve your accuracy and confidence in math. Remember, everyone makes mistakes sometimes – it's how we learn! The key is to identify your errors and learn from them.

Resources for Further Learning

If you're looking to deepen your understanding of arithmetic expressions and other math topics, there are tons of great resources available:

  • Online math websites and apps: Khan Academy, Wolfram Alpha, and many others offer free lessons, practice problems, and step-by-step solutions.
  • Textbooks and workbooks: Your school's math textbook is a valuable resource, and there are also many excellent workbooks available for extra practice.
  • Tutoring: If you're struggling with a particular concept, consider seeking help from a tutor or teacher.
  • Online communities and forums: There are many online communities where you can ask questions, discuss problems, and connect with other math learners.

Don't be afraid to explore different resources and find what works best for you. Learning math is a journey, and there are many paths you can take.

Final Thoughts

So, we've tackled a tricky arithmetic expression, explored similar problems, discussed common mistakes, and looked at resources for further learning. Hopefully, you're feeling more confident about your math skills now! Remember, math is not about memorizing formulas – it's about understanding concepts and developing problem-solving skills. Keep practicing, keep exploring, and keep challenging yourself. You've got this!