Math Problems Solved: Step-by-Step Solutions

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Hey everyone! Let's dive into some math problems today. We'll break down each problem step-by-step so you can easily follow along and understand the solutions. Whether you're a math whiz or just starting out, this guide will help you grasp the concepts. We'll be tackling several problems, covering addition and subtraction with both whole numbers and decimals. Ready? Let's get started!

Problem 1: -0.25 - 3

Alright, let's start with our first problem: -0.25 - 3. This one involves subtracting a positive number from a negative decimal. Remember, when you subtract a positive number from a negative number, you're essentially moving further into the negative territory. Think of it like this: you're already in debt (-0.25), and then you add more debt (-3). To solve this, you can visualize a number line. Start at -0.25 and move 3 units to the left. Alternatively, you can simply add the absolute values of the numbers and keep the negative sign. So, 0.25 + 3 = 3.25. Since both numbers were negative, the answer remains negative. Therefore, -0.25 - 3 = -3.25. See? Not too bad, right? We're off to a good start! Mastering these basic operations is crucial for tackling more complex problems later on. Always pay attention to the signs – they make all the difference! Keep practicing, and you'll become a pro at these in no time. The key is to understand that when you combine two negative values, the result is an even larger negative value. It is like owing money to two different people, which means your debt increases, and that applies to math as well.

Detailed Breakdown

  • Understanding the Signs: Recognizing that both numbers are negative.
  • Adding the Values: 0.25 + 3 = 3.25.
  • Applying the Negative Sign: Since both were negative, the answer is -3.25.

Problem 2: -9 - 0.75

Okay, let's move on to the second problem: -9 - 0.75. This is another subtraction problem, but this time we're subtracting a decimal from a whole number that is negative. Similar to the previous example, we're essentially increasing the negative value. Think of it as owing nine dollars and then borrowing an additional 0.75. To solve this, we can again visualize a number line or simply add the absolute values and keep the negative sign. Adding 9 and 0.75 gives us 9.75. Since both values are negative, the final answer is also negative. Thus, -9 - 0.75 = -9.75. See how each step builds on the last? We started with a negative number and made it even more negative. Remember, the negative sign indicates direction – in this case, a direction away from zero on the number line. Keep in mind, the more you practice, the easier it will become. Let's keep going and strengthen our understanding of these core principles! It is very easy as long as you pay attention to the signs. You can also imagine that you are in debt, and if you incur more debt, your overall debt goes up.

Detailed Breakdown

  • Understanding the Signs: Both values are negative.
  • Adding the Values: 9 + 0.75 = 9.75.
  • Applying the Negative Sign: Therefore, the answer is -9.75.

Problem 3: -3 - 2

Alright, let's tackle our third problem: -3 - 2. This is another subtraction problem where we're subtracting a positive number from a negative one. In essence, you are starting with a debt of 3 and increasing your debt by 2. It's similar to the first two problems, but now we're working with whole numbers. To solve this, imagine a number line: start at -3 and move two units to the left. Alternatively, add the absolute values of the numbers (3 + 2 = 5) and keep the negative sign. So, -3 - 2 = -5. This should feel more straightforward now, right? The pattern is consistent: when you subtract a positive number from a negative number, the result becomes more negative. The more negative, the further away from zero. You are just accumulating more and more debt. Keep in mind that negative numbers are less than zero and that we can easily find the answer by imagining it as debt.

Detailed Breakdown

  • Understanding the Signs: We are subtracting a positive number from a negative.
  • Adding the Values: 3 + 2 = 5.
  • Applying the Negative Sign: The answer is -5.

Problem 4: -27 - 5

Here we go, problem number four: -27 - 5. This problem is very similar to the last one. We're subtracting a positive number from a negative one. Let's break it down! You can envision this on a number line: starting at -27 and moving 5 units to the left. You are increasing your debt. Add the absolute values (27 + 5 = 32), and since we're dealing with negative numbers, the answer is -32. Therefore, -27 - 5 = -32. Again, the key takeaway is that subtracting a positive number from a negative number makes the result even more negative. This concept is fundamental to understanding number operations. Keep in mind that when we subtract a positive number from a negative number, the result becomes more negative. This principle is consistent throughout all the problems we have tackled so far. That’s why it is critical to familiarize yourself with these fundamental concepts.

Detailed Breakdown

  • Understanding the Signs: Subtracting a positive from a negative.
  • Adding the Values: 27 + 5 = 32.
  • Applying the Negative Sign: The answer is -32.

Problem 5: -16 - (-7.3)

Now, let's tackle problem five: -16 - (-7.3). This problem introduces a new twist: subtracting a negative number. Remember that subtracting a negative number is the same as adding a positive number. So, we can rewrite the problem as -16 + 7.3. Now we are adding a positive number to a negative. To solve this, we can think of it like this: you owe $16, and then you receive $7.30. Your debt will decrease, but you still have debt. This means you will not move into the positive numbers. To calculate this, subtract the smaller absolute value from the larger one (16 - 7.3 = 8.7) and apply the sign of the larger number (negative). Therefore, -16 - (-7.3) = -8.7. In essence, subtracting a negative number 'cancels' the negative, resulting in an addition. Pay close attention to this principle, as it often causes confusion. This type of problem is very important for many real-life applications.

Detailed Breakdown

  • Understanding the Signs: Subtracting a negative is the same as adding a positive.
  • Rewriting the Problem: -16 + 7.3.
  • Calculating: 16 - 7.3 = 8.7. Applying the negative sign, the answer is -8.7.

Problem 6: -5.8 - 17

Let's keep the momentum going with problem six: -5.8 - 17. This is another case of subtracting a positive number from a negative one. We are increasing a negative number further. It is like owing $5.8 and then borrowing $17 more. To solve this, we will add the absolute values (5.8 + 17 = 22.8) and keep the negative sign. Therefore, -5.8 - 17 = -22.8. This should be quite familiar by now! Remember, when you're subtracting a positive number from a negative one, you are always increasing your debt. Always make sure to check your work; it's easy to make a small mistake. With each problem, the concepts should become clearer and easier to apply.

Detailed Breakdown

  • Understanding the Signs: Subtracting a positive from a negative.
  • Adding the Values: 5.8 + 17 = 22.8.
  • Applying the Negative Sign: The answer is -22.8.

Problem 7: -4.75 - 3

On to problem seven: -4.75 - 3. Another subtraction problem with a negative and a positive number. The method remains the same: add the absolute values (4.75 + 3 = 7.75) and apply the negative sign. So, -4.75 - 3 = -7.75. Consistent practice makes perfect, and with each problem, you're building a stronger understanding of number operations! The negative sign indicates a direction and its effect on the number line. When you subtract a positive number from a negative number, your position on the number line moves further into the negative territory. It is also important to always check your answers to make sure that the numbers you input are correct.

Detailed Breakdown

  • Understanding the Signs: Subtracting a positive from a negative.
  • Adding the Values: 4.75 + 3 = 7.75.
  • Applying the Negative Sign: The answer is -7.75.

Problem 8: -2 - 9.4

Finally, we reach the last problem: -2 - 9.4. It is a subtraction problem. So, we'll add the absolute values (2 + 9.4 = 11.4), and since both values are negative, the answer is negative. Therefore, -2 - 9.4 = -11.4. Congratulations, you've successfully worked through all the problems! You’ve seen and solved several types of problems. Remember, practice is essential. Continue to work through similar problems, and you'll solidify your understanding of these concepts. Always pay attention to the signs – they are the key to getting the correct answers. Keep practicing, and you'll find these problems become easier and easier. This is a very important concept in math. Understanding this concept can also help you in other areas of life!

Detailed Breakdown

  • Understanding the Signs: Subtracting a positive from a negative.
  • Adding the Values: 2 + 9.4 = 11.4.
  • Applying the Negative Sign: The answer is -11.4.

Conclusion

Great job working through all the problems! You've successfully navigated various subtraction problems involving negative numbers and decimals. Remember to practice regularly and always double-check your work. Keep exploring math, and you'll see how these concepts build upon each other! Keep up the great work, and good luck with your math studies! And always remember, if you have any questions, don't hesitate to seek help or review the examples provided. Math is a journey, and every step you take makes you stronger. Keep going, guys!