Welcome to our lesson on subtraction, where we'll explore how to solve mathematical problems by taking one number away from another. Today, we're going to work through the specific problem: what is 755 minus 298? Subtraction is one of the four basic arithmetic operations, and it's essential for everyday calculations. Understanding the process will help you solve similar problems with confidence. Let's begin by breaking down this problem into manageable steps. By the end of this lesson, you'll know exactly how to find the answer to 755 - 298.
Before we solve our subtraction problem, let's understand the place values of our numbers. In 755, we have 7 hundreds, 5 tens, and 5 ones. In 298, we have 2 hundreds, 9 tens, and 8 ones. Each digit's position determines its value in the overall number. The hundreds place is the leftmost digit, followed by tens, then ones on the right. Understanding these place values is crucial because we'll subtract digit by digit, starting from the rightmost position. This systematic approach ensures we handle each place value correctly.
To solve 755 - 298, we need to write the numbers vertically with proper alignment. We place 755 on top and 298 directly below it, making sure the ones, tens, and hundreds places line up. The minus sign goes to the left of the bottom number. This vertical arrangement helps us subtract column by column from right to left. Each column represents a specific place value, which makes our calculation organized and systematic. Proper alignment is essential to avoid mistakes in our subtraction process.
Let's start subtracting from the ones place: 5 minus 8. We immediately notice that 5 is smaller than 8, which means we need to borrow from the tens place. This borrowing process is necessary whenever the top digit is smaller than the bottom digit. We cannot subtract 8 from 5 in regular subtraction, so we must regroup our numbers. This is a common situation in subtraction that requires careful attention to place values. Borrowing will allow us to make the top digit larger so we can complete the subtraction.
Since we can't subtract 8 from 5, we need to borrow 1 ten from the tens place. The 5 in the tens place becomes 4, and we add 10 to the ones place. Our 5 ones become 15 ones after borrowing. Now we can subtract: 15 minus 8 equals 7. This borrowing process maintains the overall value of the number while redistributing it for easier calculation. The key is understanding that 1 ten equals 10 ones, which is why we add 10 to the ones column. This regrouping doesn't change the number's total value, just its representation.
Now we move to the tens place, where we have 4 tens minus 9 tens. Remember, we borrowed 1 ten earlier, so our original 5 tens became 4 tens. Again, we face a situation where the top digit is smaller: 4 is less than 9. This means we need to borrow again, this time from the hundreds place. We'll take 1 hundred and convert it to 10 tens, adding to our existing tens. This second borrowing is necessary to complete our subtraction properly. The process is similar to what we did with the ones place, just moving one place value to the left.
We borrow 1 hundred from the 7 hundreds, which reduces it to 6 hundreds. That borrowed hundred converts to 10 tens, which we add to our 4 tens, giving us 14 tens. Now we can subtract in the tens column: 14 tens minus 9 tens equals 5 tens. This demonstrates how borrowing works across multiple place values when needed. Each borrowing maintains the number's overall value while redistributing it for easier calculation. The process ensures we can complete each column's subtraction without negative results.
Finally, we subtract in the hundreds place: 6 hundreds minus 2 hundreds equals 4 hundreds. Remember, we borrowed 1 hundred earlier, so we're working with 6 instead of the original 7. This final subtraction is straightforward since 6 is greater than 2. We've now completed all three columns of our subtraction problem. Each step has been carefully executed to maintain accuracy throughout the calculation. The hundreds place gives us our final significant digit in the answer.
Let's verify our answer by adding our result to the number we subtracted. If we calculated correctly, 457 plus 298 should equal 755. Adding the ones place: 7 plus 8 equals 15, so we write 5 and carry 1. Adding the tens: 5 plus 9 plus 1 equals 15, so we write 5 and carry 1. Adding the hundreds: 4 plus 2 plus 1 equals 7. Our verification confirms that 457 plus 298 equals 755, proving our subtraction was correct. This verification step is crucial for ensuring accuracy in mathematical calculations.
Let's explore an alternative method called counting up, which can be helpful for some subtraction problems. Instead of subtracting 298 from 755, we can ask: what number added to 298 equals 755? We start from 298 and count up to 755. First, add 2 to get to 300, then add 455 to reach 755. Adding these jumps together: 2 plus 455 equals 457. This method can be particularly useful when subtracting numbers close to round numbers. Both methods should give us the same result, confirming our answer is correct. Different approaches can help verify our work and deepen our understanding.
Subtraction problems like 755 minus 298 appear in many real-world situations. For example, if you have $755 in your bank account and spend $298, you'd have $457 remaining. Or if a journey is 755 miles long and you've traveled 298 miles, you have 457 miles left to go. Understanding subtraction helps with budgeting, measuring distances, calculating time differences, and many other daily activities. The skills we've practiced today transfer directly to these practical applications. Mathematics becomes meaningful when we connect it to real-life situations we encounter regularly.