Which Operation Equals 124 × 13 A Math Problem Solved

Hey guys! Let's dive into a math problem that might seem tricky at first glance, but I promise it's totally manageable once we break it down. We're going to figure out which of the given operations is equivalent to 124 × 13. Get ready to put on your math hats, and let's get started!

The Challenge: Finding the Equivalent Operation

Our main goal is to pinpoint the operation that yields the same result as multiplying 124 by 13. This is where our understanding of the distributive property and basic arithmetic comes into play. We're given a few options, and our mission is to evaluate each one to see which one matches our target. Remember, math isn't just about getting the right answer; it's about understanding why the answer is right. So, let’s roll up our sleeves and dissect each option step by step!

Option A: (124 × 15) – (124 × 2)

In this section, we're going to meticulously analyze Option A: (124 × 15) – (124 × 2) to determine if it's the equivalent operation we're searching for. We'll break down each part of the expression, perform the necessary calculations, and then compare the result with our target, which is the product of 124 and 13. So, let's dive deep into the numbers and see if Option A holds the key to our math mystery.

First, let's calculate 124 × 15. This multiplication can be a bit hefty, so let's take it step by step. Multiplying 124 by 10 gives us 1240. Next, we multiply 124 by 5, which is half of 124 × 10, giving us 620. Adding these two results (1240 + 620) gives us 1860. So, 124 × 15 equals 1860. Now, we move on to the second part of the expression: 124 × 2. This one's a bit easier! Doubling 124 gives us 248. Great! We've calculated both parts of Option A.

Now that we have the results of both multiplications, we can perform the subtraction. We have 1860 (the result of 124 × 15) minus 248 (the result of 124 × 2). Subtracting 248 from 1860 can be done either manually or with a calculator. The result is 1612. So, Option A, when fully calculated, equals 1612. But is this the same as 124 × 13? Let’s hold that thought for a moment while we analyze the other options.

Before we move on, let's quickly calculate 124 × 13 to have our target number ready. Multiplying 124 by 10 is 1240. Multiplying 124 by 3 is 372. Adding these together (1240 + 372) gives us 1612. Aha! So, 124 × 13 does indeed equal 1612. This is a crucial step in verifying if Option A is the correct answer. We've done the heavy lifting of calculating both parts of the expression and arrived at a single number.

Comparing our result from Option A (1612) with the direct calculation of 124 × 13 (which is also 1612), we can see that they match perfectly. This means that Option A: (124 × 15) – (124 × 2) is indeed equivalent to 124 × 13. We've successfully navigated through the calculations and found a match! But, just to be thorough, let's briefly consider the other options to understand why they don't fit the bill. This will solidify our understanding and ensure we've truly grasped the concept.

Option B: (124 × 9) + (124 × 5)

Alright, let's shift our focus to Option B: (124 × 9) + (124 × 5). We're going to follow the same meticulous approach we used for Option A: break down the expression, calculate each part, and then add the results together. The goal here is to see if Option B also lands on the same target number as 124 × 13, which we already know is 1612. So, let's get those mental gears turning and dive into the calculations!

First up, we need to figure out what 124 × 9 is. This might seem a bit daunting, but we can use some mental math tricks to make it easier. Think of 9 as (10 – 1). So, we can calculate 124 × 10 (which is 1240) and then subtract 124 from it. That gives us 1240 – 124 = 1116. So, 124 × 9 equals 1116. Awesome! We've tackled the first part of the expression.

Next, let's calculate 124 × 5. This one's a little more straightforward. We can think of multiplying by 5 as multiplying by 10 and then dividing by 2. So, 124 × 10 is 1240, and half of that is 620. Therefore, 124 × 5 equals 620. We've now calculated both parts of Option B's expression. We're making good progress!

Now that we have the results of both multiplications, we can add them together. We have 1116 (the result of 124 × 9) plus 620 (the result of 124 × 5). Adding these two numbers gives us 1736. So, Option B, when fully calculated, equals 1736. This is a significant number, and it's crucial to compare it with our target.

Remember, our target number is the result of 124 × 13, which we calculated earlier to be 1612. Comparing the result of Option B (1736) with our target (1612), we can clearly see that they do not match. This means that Option B is not equivalent to 124 × 13. We've successfully eliminated one more option! It's important to go through this process to understand why certain options are incorrect. This reinforces our understanding of the underlying mathematical principles.

Option C: (124 × 14) – (124 × 2)

Now, let's turn our attention to Option C: (124 × 14) – (124 × 2). Just like with the previous options, we're going to break this down into manageable parts, calculate each one, and then perform the subtraction. Our trusty target number, the result of 124 × 13 (which is 1612), will be our benchmark. Let's see if Option C hits the mark!

First, we need to calculate 124 × 14. This one might look a little intimidating, but we can tackle it strategically. We can think of 14 as (10 + 4). So, we'll calculate 124 × 10 and 124 × 4 separately, then add the results. 124 × 10 is easy – it's 1240. Now, 124 × 4 can be thought of as doubling 124 twice. 124 doubled is 248, and doubling 248 gives us 496. So, 124 × 4 equals 496. Adding these together (1240 + 496) gives us 1736. Therefore, 124 × 14 equals 1736. We've conquered the first part!

Next up, we need to calculate 124 × 2. We've actually done this calculation before when we analyzed Option A, but let's do it again to refresh our memory. Multiplying 124 by 2 simply means doubling it, which gives us 248. So, 124 × 2 equals 248. We've successfully calculated both parts of Option C's expression.

Now, it's time to perform the subtraction. We have 1736 (the result of 124 × 14) minus 248 (the result of 124 × 2). Subtracting 248 from 1736 gives us 1488. So, Option C, when fully calculated, equals 1488. This is a crucial number, and we need to compare it to our target.

Our target number, as a reminder, is the result of 124 × 13, which is 1612. Comparing the result of Option C (1488) with our target (1612), we can clearly see that they are different. This means that Option C is not equivalent to 124 × 13. We're getting closer to the solution by methodically eliminating the incorrect options. Each calculation helps solidify our understanding of the math involved.

Option D: (124 × 6) + (124 × 8)

Finally, let's tackle Option D: (124 × 6) + (124 × 8). We're going to stick to our proven strategy: break it down, calculate each part, and then add the results. As always, we'll compare our final result to the target number, which is 1612 (the result of 124 × 13). Let's jump in and see what Option D holds!

First up, we need to figure out 124 × 6. We can think of 6 as (5 + 1). We already know that 124 × 5 is 620 (we calculated this when analyzing Option B). So, we just need to add 124 to that. 620 + 124 equals 744. Therefore, 124 × 6 equals 744. Great! We've conquered the first part of Option D.

Next, let's calculate 124 × 8. We can approach this by thinking of 8 as double 4. We already calculated 124 × 4 when analyzing Option C, and it was 496. So, we need to double 496. Doubling 496 gives us 992. Therefore, 124 × 8 equals 992. We've now calculated both parts of Option D's expression.

Now, it's time to add the results together. We have 744 (the result of 124 × 6) plus 992 (the result of 124 × 8). Adding these two numbers gives us 1736. So, Option D, when fully calculated, equals 1736. This is our final result for this option, and we need to compare it with our target.

As a reminder, our target number is the result of 124 × 13, which we know is 1612. Comparing the result of Option D (1736) with our target (1612), we can clearly see that they do not match. This means that Option D is not equivalent to 124 × 13. We've now analyzed all the options, and we've systematically eliminated the incorrect ones.

The Verdict: Option A is the Winner!

After carefully dissecting each option, we've arrived at a clear conclusion. Option A: (124 × 15) – (124 × 2) is the only operation that is equivalent to 124 × 13. We meticulously calculated each part of the expression, performed the subtraction, and found that it perfectly matched our target number, 1612. The other options, while mathematically sound in their own right, simply didn't yield the same result. This exercise has been a fantastic journey through the world of arithmetic and the distributive property.

We've not only found the correct answer but also reinforced our understanding of why it's correct. We explored different strategies for multiplication and subtraction, and we learned the importance of breaking down complex problems into smaller, more manageable steps. This approach is valuable not just in math but in many areas of life. So, give yourselves a pat on the back, math detectives! You've cracked the code and emerged victorious!

Key Takeaways and Why This Matters

So, guys, what did we learn from this math adventure? First and foremost, we honed our skills in arithmetic. We practiced multiplication and subtraction, and we saw how these operations work together in more complex expressions. But more importantly, we learned the power of the distributive property. This property allows us to break apart multiplication problems into smaller, more manageable chunks, making calculations easier and less prone to error.

Think of the distributive property as a superhero power for your brain! It lets you tackle seemingly tough problems with confidence and precision. In this case, we used it to evaluate expressions like (124 × 15) – (124 × 2). Instead of directly multiplying 124 by 15 and 124 by 2, we could think of it in terms of distributing the 124 across the 15 and the 2. This might seem like a small detail, but it can make a huge difference when you're dealing with larger numbers or more complex equations.

Another key takeaway is the importance of methodical problem-solving. We didn't just guess at the answer. We took a step-by-step approach, carefully calculating each part of each option. We compared our results to the target number, and we systematically eliminated the incorrect options. This process is crucial in math and in life. When you face a challenge, break it down, analyze each component, and tackle it one step at a time. This approach will lead you to the correct solution more often than not.

Finally, we learned the value of verification. We didn't just stop when we found an answer that seemed right. We double-checked our work and compared it to the original problem. This is a critical step in any problem-solving process. It ensures that you haven't made any errors along the way and that your answer is truly accurate. In the world of math, precision is paramount, and verification is your best friend.

So, why does all of this matter? Well, math isn't just about numbers and equations. It's about critical thinking, problem-solving, and analytical skills. These are skills that are valuable in every aspect of life, from managing your finances to making informed decisions in your career. By mastering math concepts like the distributive property and problem-solving strategies, you're not just acing your math tests; you're building a foundation for success in the real world. So keep practicing, keep exploring, and keep challenging yourselves. The world of math is full of fascinating discoveries waiting to be made!