Question

Regrouping Multiple Place Values
Subtract: 500 - 258
Exact difference:

I can't borrow from the tens place, because there are 0 tens.
I will borrow from the hundreds place to make _ tens.
I'm giving one of those tens to the ones place.

500
-258
------
____

Estimated difference:
500
-250
-------
____

Therefore, our answer is reasonable.

Answer 1

Let's work through the problem step-by-step:

### Exact Difference: 500 - 258

1. **Set up the problem**:
```
500
- 258
```

2. **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.

3. **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).

4. **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: \(4 - 2 = 2\)

5. **Putting it all together**:
```
500
- 258
------
242
```

### Estimated Difference: 500 - 250

1. **Set up the estimation**:
```
500
- 250
```

2. **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: \(4 - 2 = 2\)

3. **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.