Solve: -15.2 - 15.5 - 0.7 Numerical Solution

by TextBrain Team 45 views

Hey guys! Today, we're diving into a math problem that involves subtracting decimals. It might seem a bit tricky at first, but don't worry, we'll break it down step by step so it's super easy to understand. Our mission is to find the value of the expression -15.2 - 15.5 - 0.7. Remember, when we're dealing with negative numbers and subtraction, it's like adding debts together. So, let's get started and figure out how to tackle this problem!

Understanding the Problem

Before we jump into solving, let's make sure we understand what the problem is asking. We have the expression -15.2 - 15.5 - 0.7. This means we're starting with a negative number (-15.2) and then subtracting two more numbers (15.5 and 0.7) from it. Think of it like this: you owe $15.20, then you owe another $15.50, and then you owe an additional $0.70. How much do you owe in total? That's what we need to figure out. The key here is recognizing that subtracting a positive number from a negative number results in a more negative number. It's like digging a deeper hole. So, our final answer will definitely be a negative number. Now that we understand the problem, let's explore different methods to solve it. We'll look at combining the negative numbers and also using a number line to visualize the process. By understanding these different approaches, we can choose the one that makes the most sense to us and ensures we get the correct answer. Remember, math isn't just about getting the right answer; it's about understanding the why behind the answer. So, let's dive deeper and see how we can solve this expression!

Method 1: Combining Negative Numbers

One way to solve this problem is by combining the negative numbers. When you're subtracting, especially with negative numbers involved, it can be helpful to think of it as adding negative values together. So, let's rewrite our expression -15.2 - 15.5 - 0.7 to better reflect this idea. We can rewrite subtraction as addition of a negative number: -15.2 + (-15.5) + (-0.7). Now, we're dealing with a series of additions of negative numbers, which might feel a little less confusing. The next step is to combine these numbers. We can start by adding the first two numbers together: -15.2 + (-15.5). When you add two negative numbers, you add their absolute values (the numbers without the negative sign) and then put a negative sign in front. So, we add 15.2 and 15.5: 15.2 + 15.5 = 30.7. Now, we put the negative sign back in, so we have -30.7. We've successfully combined the first two numbers! Now, we have a simpler expression: -30.7 + (-0.7). We still have one more addition to do. We're adding two negative numbers again, so we follow the same process. We add their absolute values: 30.7 + 0.7 = 31.4. And then, we put the negative sign back in, giving us -31.4. Therefore, -15.2 - 15.5 - 0.7 = -31.4. By breaking the problem down into smaller steps and focusing on combining the negative values, we've arrived at our solution. This method emphasizes the idea of accumulating debt or negative quantities, which can be a helpful way to visualize the problem.

Method 2: Using a Number Line

Another way to visualize and solve this problem is by using a number line. Number lines are fantastic tools for understanding addition and subtraction, especially when dealing with negative numbers. Let's imagine a horizontal line that extends infinitely in both directions. The center point is zero, and numbers increase as you move to the right and decrease as you move to the left. Negative numbers are located to the left of zero, and positive numbers are to the right. To solve -15.2 - 15.5 - 0.7 using a number line, we'll start at -15.2. Find this point on your imaginary number line. This is our starting position. Now, we need to subtract 15.5. Subtracting on a number line means moving to the left. So, we'll move 15.5 units to the left from -15.2. This brings us to -30.7. Think about it: we're moving further into the negative territory. Next, we need to subtract 0.7. Again, subtracting means moving to the left on the number line. We'll move 0.7 units to the left from -30.7. This lands us at -31.4. So, visually, we've moved from -15.2, then to -30.7, and finally to -31.4. Each subtraction is a step to the left, making the number more negative. Using a number line can be particularly helpful for those who are visual learners. It provides a concrete representation of the numbers and the operations we're performing. By seeing the movements on the line, it can become clearer how subtraction affects negative numbers. It reinforces the idea that subtracting a positive number from a negative number results in a number that is further away from zero in the negative direction.

Detailed Solution

Let's recap and present the detailed solution. We want to find the value of -15.2 - 15.5 - 0.7. We've explored two methods: combining negative numbers and using a number line. Both methods lead us to the same answer, which is a great way to confirm our work. Here's the step-by-step breakdown of combining negative numbers:

  1. Rewrite the expression: -15.2 - 15.5 - 0.7 = -15.2 + (-15.5) + (-0.7)
  2. Add the first two negative numbers: -15.2 + (-15.5) = -30.7
  3. Add the result to the last negative number: -30.7 + (-0.7) = -31.4

Therefore, -15.2 - 15.5 - 0.7 = -31.4.

If we were using the number line method, we would visualize starting at -15.2, moving 15.5 units to the left, and then moving another 0.7 units to the left, ending up at -31.4. The key takeaway here is that when you subtract a positive number (or add a negative number) from another negative number, you are moving further away from zero in the negative direction. The result is a larger negative number (larger in absolute value, but smaller in value because it's negative). This problem highlights the importance of understanding how negative numbers work and how subtraction affects them. It's a fundamental concept in mathematics that builds the foundation for more complex calculations. Now, you've seen two different approaches to solving this problem, and you can choose the one that resonates most with you. Practice makes perfect, so try similar problems to solidify your understanding!

Final Answer

Okay, guys, we've worked through this problem step by step, using two different methods to ensure we understand what's going on. We started with the expression -15.2 - 15.5 - 0.7 and explored how to solve it by combining negative numbers and visualizing it on a number line. Both approaches led us to the same answer, which confirms that our solution is correct. After carefully adding the negative values together, we arrived at our final answer: -31.4 So, the value of -15.2 - 15.5 - 0.7 is -31.4. Remember, when dealing with subtraction and negative numbers, it's helpful to think of it as adding debts together. Each subtraction is like adding another negative value, making the overall result more negative. Using a number line can also be a powerful tool for visualizing these operations and understanding how the numbers change. Keep practicing with similar problems, and you'll become a pro at handling negative numbers! Math can be challenging, but breaking it down into smaller steps and understanding the underlying concepts makes it much more manageable. Great job, everyone! We nailed it! 🚀