Solve The Equation: 2569 + 905 = ? + 1984
Hey guys! Let's break down this math problem together. We've got an equation: 2569 + 905 = ☐ + 1984, and our mission is to find out what number goes in that little box. Don't worry, it's easier than it looks! We'll take it step by step, so grab your thinking caps, and let's dive in!
Understanding the Equation
First, let's understand what the equation is telling us. We have two sides, separated by an equals sign (=). This sign means that whatever we have on the left side must be equal to whatever we have on the right side. In our case, we have an addition problem on both sides, but one side has a missing number, which is our mystery box (☐).
To crack this puzzle, we need to figure out what number we can add to 1984 to get the same result as when we add 2569 and 905. Think of it like balancing a scale. Both sides have to weigh the same!
So, let's put on our math hats and get started. Remember, the key here is to keep things balanced. Math is like a super cool balancing act, right? We're going to make sure both sides of our equation are perfectly equal. Let's jump into the first step!
Step 1: Calculate the Left Side
The first thing we need to do is figure out what the left side of the equation equals. We have 2569 + 905. Let's add those numbers together. You can do this by hand, or use a calculator if you prefer. Let's break it down to make it super clear.
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Start by lining up the numbers vertically, making sure the ones, tens, hundreds, and thousands places are all in the correct columns:
2569 + 905 ------ -
Now, let's add the digits column by column, starting from the right (the ones place).
- 9 + 5 = 14. Write down the 4 in the ones place and carry-over the 1 to the tens place.
1 2569 + 905 ------ 4- Next, let's add the tens place. We have 6 + 0 + the carry-over 1, which is 6 + 0 + 1 = 7. Write down the 7 in the tens place.
1 2569 + 905 ------ 74- Now, let's move to the hundreds place. We have 5 + 9, which is 5 + 9 = 14. Write down the 4 in the hundreds place and carry-over the 1 to the thousands place.
1 2569 + 905 ------ 474- Finally, let's add the thousands place. We have 2 + the carry-over 1, which is 2 + 1 = 3. Write down the 3 in the thousands place.
1 2569 + 905 ------ 3474
So, 2569 + 905 = 3474. Awesome! Now we know that the left side of our equation equals 3474. That means the right side of our equation must also equal 3474. We're one step closer to cracking the puzzle. Let's move on to the next step where we'll use this information to find our missing number.
Step 2: Isolate the Missing Number
Okay, now we know that 2569 + 905 = 3474. That means our equation looks like this: 3474 = ☐ + 1984. Our mission is to find out what number needs to go in the box to make the right side also equal 3474.
Think of it like this: we need to figure out what to add to 1984 to get 3474. This is where a little bit of algebraic thinking comes in handy. Don't worry, it's not as scary as it sounds! We're just going to do something super simple to get that box all by itself on one side of the equation. This is called isolating the variable, and it's a powerful tool in math.
The basic idea is that we want to get the box (☐) alone on one side of the equals sign. Right now, it's hanging out with 1984. To get rid of the 1984, we need to do the opposite operation. What's the opposite of addition? Subtraction! So, we're going to subtract 1984 from both sides of the equation. Remember, whatever we do to one side, we have to do to the other to keep things balanced.
So, we rewrite our equation like this:
3474 - 1984 = ☐ + 1984 - 1984
Notice what happens on the right side? We have +1984 and -1984. They cancel each other out, leaving us with just the box! So, our equation simplifies to:
3474 - 1984 = ☐
Now, the box is all alone on the right side, which is exactly what we wanted. The only thing left to do is to subtract 1984 from 3474, and that will tell us what number goes in the box. Let's do that in the next step!
Step 3: Calculate the Missing Number
Alright, we've reached the final stretch! We know that 3474 - 1984 = ☐. All that's left to do is subtract 1984 from 3474 to find our missing number. Let's break it down just like we did before.
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Set up the subtraction problem vertically, lining up the places:
3474 - 1984 ------ -
Now, let's subtract column by column, starting from the ones place.
- 4 - 4 = 0. Write down 0 in the ones place.
3474 - 1984 ------ 0- Move to the tens place. We have 7 - 8. We can't subtract 8 from 7 directly, so we need to borrow 1 from the hundreds place. The 4 in the hundreds place becomes 3, and the 7 in the tens place becomes 17. Now we have 17 - 8 = 9. Write down 9 in the tens place.
2 14 3474 - 1984 ------ 90- Now, let's move to the hundreds place. We have 3 - 9. Again, we can't subtract 9 from 3, so we need to borrow 1 from the thousands place. The 3 in the thousands place becomes 2, and the 3 in the hundreds place becomes 13. Now we have 13 - 9 = 4. Write down 4 in the hundreds place.
2 13 3474 - 1984 ------ 490- Finally, let's subtract the thousands place. We have 2 - 1 = 1. Write down 1 in the thousands place.
2 13 3474 - 1984 ------ 1490
So, 3474 - 1984 = 1490. Woohoo! That means our missing number is 1490. We've solved the equation!
Solution
Let's put it all together. Our original equation was:
2569 + 905 = ☐ + 1984
We found that the missing number (☐) is 1490. So, the completed equation is:
2569 + 905 = 1490 + 1984
And if you add 1490 and 1984, you'll see that it indeed equals 3474, which is the same as 2569 + 905. We nailed it!
Final Thoughts
Great job, everyone! We successfully solved the equation by breaking it down into smaller steps. We calculated the left side, isolated the missing number, and then found the missing number by subtracting. Remember, the key to solving equations is to keep both sides balanced and to use opposite operations to isolate the variable.
Math might seem tricky sometimes, but with practice and a step-by-step approach, you can solve any problem. Keep up the fantastic work, and I'll catch you in the next math challenge!