7th Grade Math: Solving Number Operations

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7th Grade Math: Solving Number Operations

Hey guys! Let's break down these math problems step by step to make sure we get the correct answers. It looks like you've already given it a shot, which is awesome! Let's double-check your work and clarify a few things to help you understand these operations better.

Solving (-8) + (+1) + (+10)

Okay, so we have (-8) + (+1) + (+10). When we're dealing with addition and subtraction of integers, it's all about understanding the signs and their effects on the numbers. Let's go through it:

  1. Start with the first two numbers: (-8) + (+1). This is like saying you owe someone 8 bucks, but you pay them back 1 buck. So, you still owe them, but now it's 7 bucks. Mathematically, this is -8 + 1 = -7.
  2. Now, add the result to the next number: -7 + (+10). This is like saying you owe someone 7 bucks, but now you get 10 bucks. After paying them back, you'll have some money left over. Specifically, you'll have 3 bucks. Mathematically, this is -7 + 10 = 3.

So, the correct answer is 3, not -3. You were super close, though! Just a little slip-up with the signs. Remember, it's crucial to keep track of whether you're adding or subtracting and which number is larger in magnitude to determine the sign of the result.

Understanding the Number Line

A great way to visualize this is by using a number line. Imagine you start at -8. Adding +1 means you move one step to the right, landing you at -7. Then, adding +10 means you move ten steps to the right from -7. Count them out: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3. You end up at 3. Using a number line can make these operations more intuitive and less abstract.

Tips for Accuracy

  • Rewrite the expression: Sometimes, rewriting the expression can help clarify things. For example, (-8) + (+1) + (+10) can be written as -8 + 1 + 10. This might make it easier to see the operations more clearly.
  • Group positive and negative numbers: Another strategy is to group all the positive numbers together and all the negative numbers together. In this case, you have -8 and then +1 + 10, which is +11. Now, you just need to calculate -8 + 11, which equals 3.
  • Double-check your work: Always take a moment to double-check your calculations. It’s easy to make a small mistake, especially when dealing with negative numbers. A quick review can save you from errors.

Solving (-12) + (-7) + (+4)

Alright, let's tackle the next one: (-12) + (-7) + (+4). This one involves adding two negative numbers and then adding a positive number. Let's break it down:

  1. Start with the first two numbers: (-12) + (-7). When you add two negative numbers, you're essentially combining debts. If you owe someone 12 bucks and then you borrow another 7 bucks, your total debt is 19 bucks. Mathematically, this is -12 + (-7) = -19.
  2. Now, add the result to the next number: -19 + (+4). This is like saying you owe someone 19 bucks, but you pay them back 4 bucks. You still owe them, but now it's less. Specifically, you owe them 15 bucks. Mathematically, this is -19 + 4 = -15.

So, you got this one right! The correct answer is -15. Great job! You nailed the negative number operations here. Understanding how to combine negative numbers is super important, especially when you get into more complex math problems.

Real-World Analogy

Think of negative numbers as money you owe and positive numbers as money you have. If you owe $12 (-12) and then borrow another $7 (-7), you now owe a total of $19 (-19). If you then find $4 (+4), you can pay off part of your debt, but you still owe $15 (-15).

Why This Matters

Mastering these basic operations is super important because they form the foundation for more advanced math topics. Whether you're solving algebraic equations or working with complex financial calculations, a solid understanding of integer operations will make everything easier.

Quick Recap and Tips

  • Adding two negative numbers: Combine the numbers and keep the negative sign. Example: (-5) + (-3) = -8.
  • Adding a positive and a negative number: Find the difference between the numbers and take the sign of the larger number. Example: (-10) + (+6) = -4 (because 10 - 6 = 4, and 10 is larger, so the answer is negative).
  • Use a number line: Visualize the operations on a number line to make it clearer.
  • Practice regularly: The more you practice, the more comfortable you'll become with these operations. Try solving a few problems every day to reinforce your understanding.

Conclusion

So, to recap:

  • (-8) + (+1) + (+10) = 3
  • (-12) + (-7) + (+4) = -15

Keep practicing, and you'll become a pro at these in no time! Remember to take your time, double-check your work, and don't be afraid to use tools like number lines to help you visualize the problems. You've got this! If you ever get stuck again, don't hesitate to ask for help. Math can be challenging, but with a little bit of practice and the right strategies, you can totally conquer it.