Welcome to our lesson on subtraction. Today we'll solve a specific problem: 705 minus 268. Subtraction is the process of taking one number away from another. We'll break this down step by step so you can understand the mechanics behind solving such problems.
Before we solve 705 minus 268, let's understand what each digit represents. In 705, we have 7 hundreds, 0 tens, and 5 ones. In 268, we have 2 hundreds, 6 tens, and 8 ones. Understanding place values is crucial for proper alignment when subtracting multi-digit numbers.
To subtract these numbers correctly, we must align them by their place values. We write 705 on top and 268 directly below it, ensuring ones are under ones, tens under tens, and hundreds under hundreds. This vertical alignment is essential for accurate calculation.
We always start subtraction from the rightmost digit, which is the ones place. Here we have 5 minus 8. Since 5 is smaller than 8, we cannot subtract directly. This situation requires us to borrow from the next higher place value.
Since we can't subtract 8 from 5, we need to borrow from the tens place. However, we notice that the tens place has 0, which means we cannot borrow directly from it. This creates a more complex borrowing situation that requires borrowing from the hundreds place first.
Because the tens place has 0, we must first borrow 1 from the hundreds place. This changes our 7 hundreds to 6 hundreds, and the 0 tens becomes 10 tens. Now we can borrow 1 from these 10 tens, leaving us with 9 tens, and add 10 to our ones place, making it 15 ones.
Now that we have 15 ones minus 8 ones, we can complete this subtraction. Fifteen minus eight equals seven. We write 7 in the ones place of our answer. This demonstrates how borrowing allows us to perform subtractions that initially seemed impossible.
With the ones place completed, we move to the tens place. We now have 9 tens minus 6 tens. Nine minus six equals three, so we write 3 in the tens place of our answer. Notice how the borrowing from earlier affected our tens calculation.
Finally, we subtract the hundreds place. After our earlier borrowing, we have 6 hundreds minus 2 hundreds. Six minus two equals four, so we write 4 in the hundreds place of our answer. This completes all place value subtractions.
To ensure our answer is correct, let's verify it. We found that 705 minus 268 equals 437. To check, we can add 437 plus 268. If we get 705, our subtraction was correct. Let's perform this addition to confirm our result.
There's another way to think about this subtraction problem. Instead of taking away 268 from 705, we can count up from 268 to 705. We can add 2 to get to 270, then add 30 to reach 300, and finally add 405 to arrive at 705. Adding these increments gives us our answer of 437.
When solving problems like 705 minus 268, students often forget to adjust all affected place values during borrowing. Some forget to reduce the hundreds digit after borrowing, while others incorrectly handle the zero in the tens place. Remember to always update each digit that's involved in the borrowing process.