Calculating A + B - C Given A + B = 876975 And C As The Smallest Even Six-Digit Number

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Hey guys! Today, we're diving into a fun math problem where we need to figure out the value of a + b - c. We know that a + b = 876,975, and c is a special number – it's the smallest even six-digit number with all its digits being different. Sounds like a cool challenge, right? Let's break it down step by step to make sure we get it perfect.

Understanding the Problem

Okay, so our main goal here is to find the value of a simple expression: a + b - c. The beauty of this problem lies in how we define the values. We already know what a + b equals: 876,975. That's a great start! The trickier part is figuring out what c is. We're told that c is the smallest even six-digit number but there's a catch – all its digits must be different. This means we can't just use something like 100,000 (which is the smallest six-digit number) because it has repeating digits (all those zeros!). We need to be a bit more clever to find the right value for c. Thinking about the smallest even six-digit number with distinct digits involves a mix of place value understanding and a bit of combinatorial thinking, making it a super engaging exercise for anyone looking to sharpen their math skills. Now, let’s delve deeper into how to pinpoint this elusive number c.

Finding the Value of c: The Smallest Even Six-Digit Number with Distinct Digits

Let's tackle the most interesting part of the problem: finding the value of c. Remember, c needs to be the smallest even six-digit number, and it has to have six different digits. So, how do we crack this? First, let's think about the structure of a six-digit number. It has places for hundred thousands, ten thousands, thousands, hundreds, tens, and ones. To make the number as small as possible, we want to use the smallest digits in the highest place values. However, we also need to keep in mind the distinct digit requirement and the fact that the number has to be even.

  • Hundred Thousands Place: To make the number as small as possible, we'll start with the smallest non-zero digit, which is 1. So, the hundred thousands place will be 1.
  • Ten Thousands Place: Next up is the ten thousands place. We want the smallest digit here, but we've already used 1, so we'll go with 0. Great, we have 10 so far!
  • Thousands Place: Moving on to the thousands place, the smallest available digit is 2 (since 0 and 1 are already taken). Now we're at 102, looking good.
  • Hundreds Place: For the hundreds place, we can use 3, as it's the next smallest digit. Our number is shaping up to be 1023__.
  • Tens Place: We'll use 4 for the tens place. Now our number is 10234_.
  • Ones Place: This is where we need to be extra careful because the number has to be even. The smallest even digit we haven't used yet is 6 (0, 2, and 4 are already in use). So, the ones place will be 6.

Putting it all together, the smallest even six-digit number with distinct digits is 102,346. That's our value for c! Now that we have found c, we are one step closer to solving the entire expression. Finding the smallest even number while adhering to the unique digit constraint showcases the practical application of number theory and logical deduction.

Calculating a + b - c

Now that we've successfully navigated the trickiest part – figuring out what c is (102,346) – the rest is smooth sailing! Remember, we're trying to find the value of a + b - c. We already know that a + b = 876,975. So, all we need to do is subtract c from this sum.

The expression we need to solve is:

876,975 - 102,346

Let's break down the subtraction:

  • Starting from the rightmost digits:
    • 5 - 6: We can't subtract 6 from 5 directly, so we need to borrow 1 from the tens place. That makes it 15 - 6 = 9.
    • Now the tens place is 6 (since we borrowed 1), so 6 - 4 = 2.
    • In the hundreds place, 9 - 3 = 6.
    • In the thousands place, 6 - 2 = 4.
    • In the ten thousands place, 7 - 0 = 7.
    • Finally, in the hundred thousands place, 8 - 1 = 7.

So, 876,975 - 102,346 = 774,629

Therefore, a + b - c = 774,629. And just like that, we've solved it! This calculation underscores the importance of understanding basic arithmetic operations and place value, skills that are pivotal not just in mathematics but in everyday life as well.

Final Answer

Alright guys, after carefully breaking down the problem and going through each step, we've arrived at our final answer. We started with the expression a + b - c, knew that a + b was 876,975, and then we cleverly figured out that c, the smallest even six-digit number with distinct digits, is 102,346. After performing the subtraction, we found that:

a + b - c = 774,629

So, there you have it! This problem was a fantastic mix of basic arithmetic and logical thinking. It wasn't just about subtracting numbers; it was about understanding what the problem was asking, figuring out a tricky value (c), and then putting it all together. These kinds of problems are great for building our problem-solving skills and making math a bit more fun. Remember, every mathematical challenge is an opportunity to strengthen our understanding and enhance our abilities. Embracing such challenges not only builds our numerical acumen but also refines our critical thinking process. Keep practicing, keep exploring, and keep enjoying the world of numbers! Until next time, keep those calculators handy and those brains buzzing!