To solve the subtraction problem and fill in the blanks, let's work through the process step by step.
- Exact difference:
To subtract 500 - 258, we can set it up as follows:
500
- 258
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Since there are 0 tens in 500, we encounter a problem while subtracting 8 (the ones place in 258) from 0. To make it possible, we will borrow from the hundreds place.
I will borrow from the hundreds place to make 10 tens (instead of 0 tens).
Now let's update our numbers:
- We change 500 (which is 5 hundreds) to 4 hundreds, and we see it as 400 + 100 (which is now 10 tens), making it possible to subtract from the ones and tens.
Here's the updated layout:
4 10 0 (this represents 400 and 10 tens)
- 2 5 8
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Now, we’ll convert it to perform the subtraction properly:
Ones place:
- We can now take 10 (from what was borrowed) and subtract 8:
\(10 - 8 = 2\)
Tens place:
- Now we can subtract the tens, we have 10 and must subtract 5, since we borrowed 1 ten from the original 10 (the initial value of 0 tens turns into 10 after borrowing):
\(10 - 5 = 5\)
Hundreds place:
- After borrowing, we subtract from 4 hundreds to 2 hundreds:
\(4 - 2 = 2\)
Putting it all together:
4 10 0
- 2 5 8
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2 4 2 (242)
So, the exact difference is 242.
- Estimated difference:
To estimate, we round 258 to the nearest hundred or tens place. We can round it to 250 (as it's closer to 250 than to 300).
Now we perform the estimated subtraction:
500
- 250
------
250
So, the estimated difference is 250.
Final layout:
Regrouping Multiple Place Values
Subtract: 500 - 258
Exact difference: 242
I can't borrow from the tens place, because there are 0 tens.
I will borrow from the hundreds place to make 10 tens.
I'm giving one of those tens to the ones place.
500
-258
242
Estimated difference:
500
-250
250
Therefore, our answer is reasonable.
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