Regrouping with zeros in 3-digit subtraction involves a specific process of borrowing from higher place values when the digit in the ones or tens place of the minuend (the number you're subtracting from) is smaller than the digit in the same place value in the subtrahend (the number you're subtracting). When zeros are involved, this process requires multiple steps.
Here's a breakdown of how to regroup when there are zeros in the tens or hundreds place:
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Identify the Need to Regroup: Start by assessing each column (ones, tens, hundreds) to determine if regrouping is necessary. Regrouping is needed if the digit in the top number (minuend) is smaller than the digit in the bottom number (subtrahend) for that column.
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Regrouping from the Hundreds Place: If there's a zero in the tens place and you need to subtract from the ones place, you must borrow from the hundreds place first.
- According to Mr. Pearson, you can "box" the hundreds and tens digits together to treat them as a single number of tens. For example, in the number 806, you consider '80' as 80 tens.
- Borrow 1 from the hundreds place, reducing the hundreds digit by 1. For example, if you start with 800, and need to subtract from the ones place you borrow one hundred, the 8 in the hundreds place becomes 7.
- Add the borrowed 100 to the tens place, making it 10 tens (since it was previously 0).
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Regrouping from the Tens Place: Now that the tens place has a value, you can borrow from it to help the ones place.
- Take one ten from the tens place and add it to the ones place as 10 ones.
- Reduce the tens digit by 1. For example, if you had 10 tens, taking one away leaves you with 9 tens.
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Perform the Subtraction: Once you've successfully regrouped, you can subtract each column individually.
Example:
Let's say you want to solve 806 - 389:
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You need to subtract 9 from 6 in the ones place, which requires regrouping.
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Regroup from the hundreds place: The '8' in the hundreds place becomes '7', and the tens place becomes '10' (representing 100).
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Regroup from the tens place: Borrow 1 ten from the 10 tens, making it '9' tens. Add the borrowed ten to the ones place, turning the '6' into '16'.
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Now subtract:
- 16 - 9 = 7 (ones place)
- 9 - 8 = 1 (tens place)
- 7 - 3 = 4 (hundreds place)
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The answer is 417.
Visual Representation:
| Place Value | Hundreds | Tens | Ones |
|---|---|---|---|
| Original | 8 | 0 | 6 |
| Regroup 1 | 7 | 10 | 6 |
| Regroup 2 | 7 | 9 | 16 |
| Subtrahend | 3 | 8 | 9 |
| Difference | 4 | 1 | 7 |
Key Takeaways:
- When faced with zeros, regroup from the highest place value first (hundreds).
- Break down the regrouping process into smaller, manageable steps.
- Double-check your work to ensure accuracy, especially after regrouping multiple times.
By understanding and practicing these steps, you can confidently tackle 3-digit subtraction problems involving zeros.
