Math Problem: Finding The Missing Addend For 87 * 1000
Let's dive into a fascinating mathematical puzzle! Our main goal is to figure out a missing number. This number, when added to the result of multiplying 87 and 1000, gives us a final sum of 91792. To solve this, we'll use basic arithmetic operations like multiplication and subtraction. Think of it like this: we have a partially filled equation, and our task is to find the piece that completes the picture. Math problems like this are not just about numbers; they're about understanding relationships between numbers and applying the right steps to find a solution. They encourage logical thinking and help us develop our problem-solving skills. This particular problem is a great example of how math can be both challenging and rewarding, as it requires a combination of calculation and reasoning. So, let's get started and break down the steps to find our mystery number!
Understanding the Problem
At the heart of this problem lies a simple mathematical equation that we need to decipher. The question asks us: what number, when added to the product of 87 and 1000, will equal 91792? Let's break it down piece by piece. First, we have the phrase "the product of 87 and 1000." In mathematical terms, "product" means the result of multiplication. So, we need to multiply 87 by 1000. This part is relatively straightforward. Next, we have the phrase "added to." This tells us that we'll be performing an addition operation. We're looking for a number that, when added to the result of our multiplication, gives us a specific total. Finally, we have the target number: 91792. This is the final sum we need to achieve. To visualize this, we can think of the problem as an equation with a missing variable. Let's call our missing number "x." The equation would look something like this: (87 * 1000) + x = 91792. Our mission is to find the value of "x" that makes this equation true. By carefully dissecting the problem statement, we've transformed a word problem into a clear mathematical equation, setting the stage for the next step: solving for the unknown.
Step 1: Calculate the Product of 87 and 1000
The first concrete step in solving our mathematical puzzle is to calculate the product of 87 and 1000. As we discussed earlier, "product" in mathematics signifies multiplication. So, we need to perform the operation 87 multiplied by 1000 (87 * 1000). This calculation is actually quite straightforward, thanks to the nature of multiplying by powers of ten. When you multiply a number by 10, 100, 1000, or any other power of ten, you simply add the corresponding number of zeros to the end of the original number. In this case, we're multiplying by 1000, which has three zeros. Therefore, to find the product of 87 and 1000, we simply add three zeros to the end of 87. This gives us 87000. So, 87 multiplied by 1000 equals 87000. This calculation is a fundamental building block for solving the larger problem. Now that we know the product of 87 and 1000, we can move on to the next step, which involves using this result to find the missing number that, when added to 87000, gives us 91792. With this crucial piece of information in hand, we're one step closer to solving our mystery!
Step 2: Set Up the Equation
Now that we've calculated the product of 87 and 1000, which is 87000, it's time to formalize our problem into a mathematical equation. This will help us visualize the relationships between the numbers and clearly define what we need to solve. Remember, our original question was: what number, when added to the product of 87 and 1000, equals 91792? We can translate this question directly into an equation. Let's represent the unknown number – the one we're trying to find – with the variable "x." This is a common practice in algebra, where variables are used to represent unknown quantities. Now we can express the problem as follows: 87000 (which is the product of 87 and 1000) plus "x" (our unknown number) equals 91792. Mathematically, this is written as: 87000 + x = 91792. This equation is the key to unlocking our solution. It encapsulates all the information given in the problem in a concise and actionable format. We have a known quantity (87000), an unknown quantity (x), and a target sum (91792). Our next step is to isolate "x" on one side of the equation, which will reveal its value. Setting up the equation is a critical step in problem-solving, as it provides a clear roadmap for the remaining steps.
Step 3: Solve for the Unknown Number
With our equation neatly set up as 87000 + x = 91792, the next step is to isolate the unknown variable, "x," and solve for its value. To do this, we need to perform a basic algebraic manipulation. Our goal is to get "x" by itself on one side of the equation. In this case, "x" is being added to 87000. To undo this addition, we need to perform the inverse operation, which is subtraction. Specifically, we will subtract 87000 from both sides of the equation. This is a crucial principle in algebra: whatever operation you perform on one side of the equation, you must also perform on the other side to maintain the equality. So, we subtract 87000 from both sides: 87000 + x - 87000 = 91792 - 87000. On the left side of the equation, 87000 and -87000 cancel each other out, leaving us with just "x." On the right side, we perform the subtraction: 91792 - 87000. This subtraction yields the result 4792. Therefore, our equation simplifies to: x = 4792. This is the solution we've been seeking! The unknown number, "x," is equal to 4792. This means that if we add 4792 to the product of 87 and 1000 (which is 87000), we will indeed get 91792. We've successfully solved for the missing number by applying algebraic principles and performing the necessary calculations. Now, let's summarize our findings and ensure our solution makes sense in the context of the original problem.
Step 4: Verify the Solution
Having found our solution, x = 4792, it's crucial to verify that it indeed satisfies the original problem. This step is a vital part of the problem-solving process, as it helps us catch any potential errors and ensures that our answer is accurate and makes sense in the given context. To verify our solution, we simply substitute the value we found for "x" back into our original equation: 87000 + x = 91792. Replacing "x" with 4792, we get: 87000 + 4792 = 91792. Now, we perform the addition on the left side of the equation: 87000 + 4792. This addition gives us 91792. So, our equation becomes: 91792 = 91792. This is a true statement! The left side of the equation equals the right side, confirming that our solution, x = 4792, is correct. By substituting our solution back into the original equation, we've demonstrated that it satisfies the conditions of the problem. This verification step not only provides us with confidence in our answer but also reinforces our understanding of the problem-solving process. We've successfully found the missing number and confirmed its validity. Now, we can confidently state our final answer.
Final Answer
After carefully working through the problem, calculating the necessary values, setting up and solving the equation, and verifying our solution, we have arrived at the final answer. The question asked: what number should be added to the product of 87 and 1000 to get 91792? Through our step-by-step process, we determined that the missing number is 4792. This means that if we add 4792 to the result of multiplying 87 by 1000, we will obtain 91792. We verified this by substituting 4792 back into our equation and confirming that it holds true. Therefore, we can confidently state that the answer to the problem is 4792. This problem showcases the power of breaking down complex questions into smaller, manageable steps. By using basic arithmetic operations and algebraic principles, we were able to successfully find the solution. This exercise also highlights the importance of verification in problem-solving, ensuring the accuracy and validity of our answer. Math problems like this not only enhance our calculation skills but also strengthen our logical thinking and problem-solving abilities. We encourage you to explore similar mathematical challenges and continue to develop your understanding of numbers and their relationships.
In conclusion, if you are interested in learning more about solving mathematical problems and equations, a great resource to explore is Khan Academy's Algebra Basics. This website offers comprehensive lessons and practice exercises to help you build a strong foundation in algebra and problem-solving.
