Expert Column Subtraction: Regrouping Across Multiple Columns!

Hello Subtraction Superstars! You’ve become amazing at column subtraction, even with regrouping (or “borrowing”). Now, get ready for the ultimate 3-digit challenge: subtracting two 3-digit numbers where you might need to regroup not just once, but in multiple columns! This means you might need to borrow from the tens to help the ones, AND from the hundreds to help the tens, all in the same problem! It takes careful work, but you can totally do it!

The Art of Multiple Regrouping: A Step-by-Step Guide

Remember, the golden rules are always:

1. Line up your numbers perfectly by place value (Hundreds, Tens, Ones).
2. Always start with the ones column and work from right to left.
3. Regroup (borrow/exchange) when the top digit in a column is smaller than the bottom digit.

Let’s Subtract with Multiple Regrouping: Example 523 − 147

This example will show us how to regroup twice!

Step 1: Set up your column subtraction.

  H T O  (H for Hundreds, T for Tens, O for Ones)
  5 2 3
− 1 4 7
-------  (Draw a line for your answer)

Step 2: Look at the Ones Column – Do we need to regroup? In the ‘Ones’ (O) column, we have 3 take away 7 (3 − 7). We can’t take 7 from 3. So, yes, we need to regroup from the tens place!

Step 3: Regroup from the Tens to the Ones.

• Go to the ‘Tens’ (T) column of the top number (523). It has 2 tens.
• We “borrow” 1 ten from these 2 tens. The 2 tens becomes 1 ten. (Cross out 2, write 1 above).
• The borrowed 1 ten becomes 10 ones. Add these to the 3 ones: 10 + 3 = 13 ones. (Cross out 3, write 13 above).

<!– end list –>

     ¹ ¹³   <-- Shows 2 tens became 1 ten, 3 ones became 13 ones
  H T O
  5 2 3
− 1 4 7
-------

Step 4: Now Subtract the Ones Column. We now have 13 ones take away 7 ones (13 − 7). 13 − 7 = 6. Write 6 under the ones column.

     ¹ ¹³
  H T O
  5 2 3
− 1 4 7
-------
      6

Step 5: Look at the Tens Column – Do we need to regroup AGAIN? In the ‘Tens’ (T) column, we now have 1 ten (after we borrowed one) take away 4 tens (1 − 4). We can’t take 4 from 1. So, yes, we need to regroup again, this time from the hundreds place!

Step 6: Regroup from the Hundreds to the Tens.

• Go to the ‘Hundreds’ (H) column of the top number (523). It has 5 hundreds.
• We “borrow” 1 hundred from these 5 hundreds. The 5 hundreds becomes 4 hundreds. (Cross out 5, write 4 above).
• The borrowed 1 hundred becomes 10 tens. Add these to the 1 ten we had left: 10 + 1 = 11 tens. (Cross out the previous 1, write 11 above).

<!– end list –>

   ⁴ ¹¹ ¹³  <-- Shows 5H became 4H, 1T became 11T, 3O became 13O
  H T  O
  5 2  3
− 1 4  7
---------

Step 7: Now Subtract the Tens Column. We now have 11 tens take away 4 tens (11 − 4). 11 − 4 = 7. Write 7 under the tens column.

   ⁴ ¹¹ ¹³
  H T  O
  5 2  3
− 1 4  7
---------
    7  6

Step 8: Subtract the Hundreds Column. Finally, look at the ‘Hundreds’ (H) column. We have 4 hundreds (after we borrowed one) take away 1 hundred (4 − 1). 4 − 1 = 3. Write 3 under the hundreds column.

   ⁴ ¹¹ ¹³
  H T  O
  5 2  3
− 1 4  7
---------
  3 7  6

So, 523 − 147 = 376! You’ve successfully regrouped in multiple columns! That’s expert work!

Practice Your Expert Regrouping! (18 Questions)

Ready to become an expert at multiple regrouping? Here are 18 column subtraction questions with two 3-digit numbers. You’ll often need to regroup more than once. Take your time, work through each column carefully, and remember your regrouping steps!

(Your web app with the 18 questions will go here. The app must clearly support or show multiple regrouping steps.)

Why is Mastering Multiple Regrouping So Awesome?

• Solves Almost Any Subtraction: This skill allows you to subtract nearly any whole numbers accurately.
• Shows True Place Value Understanding: You deeply understand how hundreds, tens, and ones can be exchanged.
• Essential for Higher Maths: You’ll use this skill in more advanced maths topics.
• Makes You a Calculation Champion: Being able to do this shows incredible maths strength and perseverance!

Guidance for Grown-Ups: Supporting Multiple Regrouping

Subtracting two 3-digit numbers with regrouping in multiple columns (e.g., from tens to ones, and then from hundreds to tens) is one of the most complex procedural skills in primary arithmetic. It requires solid place value understanding and careful attention to detail.

• Master Prerequisite Skills First: Ensure children are very confident with regrouping in just one column (e.g., 2-digit minus 2-digit with regrouping, or 3-digit minus 2-digit with regrouping from tens to ones only) before tackling multiple regroupings.
• Always Use Base-Ten Blocks for Introduction/Remediation: Physically exchanging 1 hundred for 10 tens, and 1 ten for 10 ones, is the clearest way to demonstrate the concept. Allow children to manipulate the blocks.
• Consistent and Clear Notation: The way regrouping is recorded (crossing out, writing new digits above) must be very clear and consistent.
• Verbalise Every Single Step: Encourage children to talk through each decision: “Can I do 3 take away 7? No. So I need to go to the tens. I’ll take 1 ten, leaving 1 ten. That 1 ten becomes 10 ones, so now I have 13 ones…”
• Patience is Key: This can take time and lots of practice to master. Celebrate effort and small successes. Break down problems that cause errors to find the specific point of misunderstanding.