Regrouping (Borrowing): When subtracting, if the top digit is smaller than the bottom digit in a column, borrow 1 from the next higher place value.
- Align numbers by place value (ones under ones, tens under tens)
- Start subtracting from the rightmost column (ones)
- If top digit is smaller, borrow 1 from the next column
- Subtract each column moving left
Write the numbers vertically, aligning place values:
2 - 8: Since 2 is less than 8, we need to regroup/borrow.
Borrow 1 ten from the tens column: 5 tens becomes 4 tens, and 2 ones becomes 12 ones.
Now we have: 12 - 8 = 4
After borrowing: 4 - 1 = 3
52 - 18 = 34
• Regrouping: When top digit is smaller, borrow 1 from next place value
• Place value: 1 ten equals 10 ones
• Subtraction: Subtract digits in same place value columns
Multiple regrouping: Sometimes you need to borrow across multiple place values when digits in multiple columns are too small.
Write the numbers vertically, aligning place values:
1 - 7: Since 1 is less than 7, we need to regroup.
But the tens column has 2, which is also less than 5, so we need to borrow from the hundreds column first.
4 hundreds becomes 3 hundreds, and 2 tens becomes 12 tens.
Then, 12 tens becomes 11 tens, and 1 one becomes 11 ones.
Now we have: 11 - 7 = 4
After borrowing: 11 - 5 = 6
After borrowing: 3 - 1 = 2
421 - 157 = 264
• Multiple regrouping: Borrow across multiple place values when needed
• Place value: 1 hundred equals 10 tens; 1 ten equals 10 ones
• Subtraction: Subtract digits in same place value columns
Word problems: Real-world scenarios that require mathematical operations to solve. Identify key information and convert to mathematical expressions.
Sarah started with 305 stickers and gave away 138, so we need to subtract: 305 - 138
Write the numbers vertically, aligning place values:
5 - 8: Since 5 is less than 8, we need to regroup.
But the tens column has 0, so we need to borrow from the hundreds column first.
3 hundreds becomes 2 hundreds, and 0 tens becomes 10 tens.
Then, 10 tens becomes 9 tens, and 5 ones becomes 15 ones.
Now we have: 15 - 8 = 7
After borrowing: 9 - 3 = 6
After borrowing: 2 - 1 = 1
Sarah has 167 stickers left.
• Word problems: Convert real-world situations to mathematical expressions
• Regrouping: When top digit is smaller, borrow from next place value
• Place value: 1 hundred equals 10 tens; 1 ten equals 10 ones
Regrouping: Reorganizing numbers by borrowing from higher place values
Place Value: The value of a digit based on its position (ones, tens, hundreds)
Subtraction: Finding the difference between two numbers
- Align numbers: Write numbers vertically with place values aligned
- Start from right: Begin with ones column
- Check for regrouping: If top digit is smaller, borrow from next column
- Subtract each column: Move left, repeating as needed
Ones: The rightmost digit represents individual units
Tens: The second digit from right represents groups of ten
Hundreds: The third digit from right represents groups of one hundred
- Set up: Write the larger number on top, aligning by place value
- Compare: In each column, check if top digit ≥ bottom digit
- Borrow if needed: If top < bottom, borrow 1 from next higher place value
- Subtract: Perform subtraction in each column
- Verify: Add your answer to the subtracted number to check
• Alignment: Always align numbers by place value
• Direction: Work from right to left
• Borrowing: When top < bottom, borrow 1 from next place value
• Value exchange: 1 hundred = 10 tens = 100 ones
• Verification: Add answer to subtracted number to check
Visual Subtraction Process
When borrowing, decrease the higher place value by 1 and increase the lower by 10.
To verify: Minuend - Subtrahend = Difference
Check: Difference + Subtrahend = Minuend
Example: 52 - 18 = 34, check: 34 + 18 = 52 ✓
Student Questions & Expert Answers
Question: Why do I need to borrow in subtraction? It seems confusing when I have to take from another column.
Answer: Great question! Borrowing (or regrouping) is necessary when you try to subtract a larger number from a smaller number in the same place value. For example, in 52 - 18, when subtracting the ones (2 - 8), you can't take 8 from 2.
Think of it like exchanging money: if you have $52 and want to give someone $18, but you only have 2 ones and need to give 8 ones, you'd go to your tens and say "I'll break one ten into 10 ones." Now you have 12 ones (2 original + 10 from the borrowed ten), so you can give 8 and keep 4.
This maintains the total value while allowing the subtraction in each place value column.
Question: My child gets confused when there are zeros in the number, like 305 - 138. How can I help them understand this?
Answer: Zeros can be tricky because you can't borrow from zero! In 305 - 138, when you need to subtract the ones (5 - 8), you can't borrow from the tens because it's zero.
You have to go to the hundreds column: Take 1 hundred (making 3 hundreds become 2 hundreds), which gives you 10 tens. Then take 1 ten from those 10 tens (making it 9 tens), which gives you 10 ones. Now you have 15 ones to subtract 8 from.
Use manipulatives like base-ten blocks to physically show this process. Start with 3 hundreds, 0 tens, 5 ones, and show how to break apart a hundred to make tens, then a ten to make ones.
Question: How can I check if my subtraction answer is correct? Sometimes I'm not sure if I did it right.
Answer: The best way to check subtraction is to use addition! Remember that subtraction and addition are opposite operations.
For example, if you calculated 52 - 18 = 34, check by adding: 34 + 18 = 52. If you get back to your original number, your answer is correct!
You can also estimate: 52 is close to 50 and 18 is close to 20, so the answer should be close to 50 - 20 = 30. Your answer of 34 is close to 30, so it makes sense.
Another tip: count up from your answer to the original number. Starting from 34 and counting up 18 should get you to 52.