Let's work through the problem step-by-step:
Exact Difference: 500 - 258
-
Set up the problem:
500 - 258 -
Subtract from the ones place:
- Since we have 0 in the ones place of 500, we cannot subtract 8 from 0. So, we need to borrow from the tens place.
-
Borrowing from the tens place:
- We can't borrow directly from the tens place (0 tens) but can borrow from the hundreds. We take 1 hundred (making 400) and convert it into 10 tens. Now, we have 10 tens in the tens place and 0 in the ones place.
- This means we now have 10 ones (from the tens we just made).
-
Now, we perform the subtraction:
- From the ones place: \(10 - 8 = 2\)
- We have borrowed 1 ten, so we have 9 tens left in the tens place. Now subtract the tens: \(9 - 5 = 4\)
- Finally, in the hundreds place: \(4 - 2 = 2\)
-
Putting it all together:
500 - 258 ------ 242
Estimated Difference: 500 - 250
-
Set up the estimation:
500 - 250 -
Perform the subtraction directly:
- In the ones place: \(0 - 0 = 0\)
- In the tens place: \(0 - 5\) (can’t do this, so we also need to borrow):
- Borrowing from the hundreds makes the first digit 4 and gives us 10 in the tens place.
- Now we have \(10 - 5 = 5\)
- In the hundreds place after borrowing: \(4 - 2 = 2\)
-
Putting it all together:
500 - 250 ------ 250
Conclusion
The estimated difference was found to be 250. The exact difference is 242.
Both calculations yield reasonably close results, indicating that our subtraction is correct.
Final Answer:
- Exact difference: 242
- Estimated difference: 250
- Therefore, the answer is reasonable.
2 answers