Hey guys! Today, we're diving into a math problem that might seem a little intimidating at first glance, but trust me, it's totally manageable when we break it down step by step. We're going to explore how to find the value of the expression [(-10+2)-1]+(2+3). The key here is understanding the order of operations – think PEMDAS or BODMAS, depending on what you learned in school. It's like a secret code that tells us which operations to tackle first.
Breaking Down the Problem
The problem gives us a series of steps that lead to the final answer, but there's a missing piece in Step 1. Our mission is to figure out what that missing expression is. We're given:
Original Expression:
Step 1: ?
Step 2: -9 + 2 + 3
Step 3: -7 + 3
To crack this, we need to carefully analyze the steps provided and work backward, if necessary, to see what logical operation could have been performed to get from the original expression to Step 2. Remember, the order of operations is our guiding star here.
Understanding the Order of Operations
Before we jump into solving, let's quickly recap the order of operations. This is crucial for correctly simplifying any mathematical expression.
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
This handy acronym (PEMDAS or BODMAS) reminds us of the sequence we need to follow. It's like a recipe for math problems! First, we handle anything inside parentheses or brackets. Then, we deal with exponents. After that, it's multiplication and division, working from left to right. Finally, we tackle addition and subtraction, also from left to right. Mastering this order is the key to unlocking mathematical expressions with confidence.
Deciphering the Missing Step: Step 1
Now, let's get back to our missing piece. We need to figure out what happened in Step 1 to transform the original expression into Step 2. Looking at the original expression, [(-10+2)-1]+(2+3), we can see that there are two sets of parentheses (or brackets) we need to consider. According to the order of operations, we should start inside the innermost set of parentheses.
In this case, the innermost operation is -10 + 2. This part is crucial because it's the first step in simplifying the expression. We need to evaluate this before we can move on to the rest of the problem. Think of it like peeling an onion – we need to get through the outer layers before we can reach the core.
So, let's calculate -10 + 2. When you add a negative number to a positive number, it's like subtracting the absolute value of the negative number from the positive number. In other words, -10 + 2 is the same as 2 - 10, which equals -8. This is a fundamental arithmetic operation, and mastering it is essential for tackling more complex math problems.
Now that we've solved the innermost parentheses, we can rewrite the expression, replacing (-10 + 2) with -8. This gives us a clearer picture of what the next steps will be. The expression now looks like this: [(-8)-1]+(2+3). We're one step closer to finding the missing expression from Step 1, and things are starting to look a lot less intimidating, right?
This detailed breakdown is crucial for understanding the logic behind each step. It's not just about getting the right answer; it's about understanding the process and being able to apply it to similar problems in the future. So, let's keep going and uncover the mystery of Step 1!
Completing the Parentheses
Okay, so we've simplified the innermost parentheses, and our expression now looks like [(-8)-1]+(2+3). What's the next logical step, guys? You guessed it – we need to continue working inside the brackets. We still have (-8) - 1 within the brackets, so let's tackle that.
Subtracting 1 from -8 is like moving one step further to the left on the number line. If you imagine a number line, starting at -8 and moving one unit to the left will land you at -9. So, (-8) - 1 = -9. This might seem straightforward, but it's important to get these basic operations down pat. They're the building blocks for more advanced math concepts.
Now that we've simplified the expression inside the brackets, we can replace (-8) - 1 with -9. This simplifies our expression even further, making it much easier to work with. The expression now looks like this: [-9] + (2 + 3). We're making real progress, and the missing Step 1 is starting to come into focus.
But hold on, we're not quite done with the parentheses yet! We still have (2 + 3) to deal with. This is a simple addition problem, and I'm sure you all know the answer. 2 + 3 equals 5. So, we can replace (2 + 3) with 5 in our expression.
This final simplification within the parentheses gives us [-9] + 5. Now, we've successfully eliminated all the parentheses, and our expression is looking super clean and manageable. We've peeled back the layers, just like we talked about earlier, and we're ready to move on to the next phase of solving the problem.
By systematically working through the parentheses, we've made the expression much simpler and easier to solve. This is a key strategy in mathematics – breaking down complex problems into smaller, more manageable steps. And that's exactly what we're doing here!
Identifying the Missing Expression
So, after simplifying the first set of parentheses, [(-10+2)-1], we got [-8-1] which then simplified to [-9]. Then after simplifying the second set of parentheses, (2+3), we got 5. So Step 1 should be [-9] + 5. This expression represents the correct simplification after addressing both sets of parentheses according to the order of operations.
Therefore, the complete Step 1 is: [(-8) - 1] + (2 + 3) which simplifies to [-9] + 5
Now, let's compare this with the provided options. We need to find the expression that matches the result of our Step 1 simplification.
A. [(-10+2)-1]+(2+3)
B. [-10+(-1+2)]+(2+3)
Option A is just the original expression, so that's not the missing Step 1. Option B looks interesting because it involves simplifying within the parentheses, but it does it in a slightly different order than we did. Let's break down Option B to see if it matches our Step 1.
In Option B, we have [-10+(-1+2)]+(2+3). Following the order of operations, we first simplify the innermost parentheses: (-1 + 2). This equals 1. So, we can rewrite the expression as [-10 + 1] + (2 + 3). Then simplifying the bracket we get -9 + (2+3), which is -9 + 5. Thus, we can clearly see that the missing step 1 would be [-10+(-1+2)]+(2+3).
Connecting Step 1 to Step 2 and Step 3
Now that we've identified the missing expression in Step 1, let's make sure it logically connects to the subsequent steps. This is like making sure all the pieces of a puzzle fit together – we want to see the whole picture clearly.
We've established that Step 1 is: [-10+(-1+2)]+(2+3) which can be simplified as -9 + 5 . Now, let's look at Step 2, which is given as -9 + 2 + 3. Notice anything interesting? If we add 2 + 3, that becomes 5. Step 2 is essentially just simplifying (2 + 3) from Step 1. If we did follow the original, Step 2 -9 + 5, the step wouldn't exist.
Moving on to Step 3, we have -7 + 3. Step 3 is incorrect if we were following the correct order. If Step 2 was -9 + 5, then step 3 would be -4. If we look at their answer of -7 + 3, and assuming Step 2 is -9 + 2 + 3, they may have made the mistake of simplifying -9 + 2 to be -7. It would then make sense for the equation to simplify to -7 + 3.
Final Answer
So, we've successfully navigated through the order of operations, identified the missing expression in Step 1, and connected the steps logically. The missing expression is [-10+(-1+2)]+(2+3). We've not only solved the problem but also reinforced our understanding of the fundamental principles of mathematics. Great job, everyone! Remember, practice makes perfect, so keep tackling those math problems with confidence.
Keywords
Order of operations, PEMDAS, BODMAS, mathematical expression, simplifying expressions, parentheses, brackets, addition, subtraction, missing step, solving equations, algebra, arithmetic, number line, negative numbers, positive numbers, innermost parentheses, step-by-step solution