Adding and Subtracting with Regrouping: The Complete Guide

If your child freezes the moment a column of digits adds up past 9, or crosses out numbers frantically during subtraction, you have found the right page. Regrouping — sometimes called carrying or borrowing — is the single most important arithmetic skill students learn in early elementary school, and it trips up more students than almost any other topic.

Regrouping is the process of exchanging units between place-value columns to make addition or subtraction possible using the standard algorithm. In addition, when a column’s sum reaches 10 or more, you carry 1 to the next column. In subtraction, when the top digit is smaller than the bottom digit, you borrow 1 from the next column. Both operations preserve the total value of the number.

• Understand what regrouping is and why it works mathematically.
• Follow clear step-by-step procedures for both addition and subtraction.
• Avoid the five most common regrouping mistakes.
• Practice with a free printable worksheet (with answer key).

What Is Regrouping in Math?

Think of place-value columns as buckets: the ones bucket, the tens bucket, the hundreds bucket, and so on. Each bucket can hold only the digits 0-9. When a bucket overflows (sum ≥ 10 in addition) or runs dry (top digit < bottom digit in subtraction), you regroup — you move units between buckets to keep everything balanced.

The term “regrouping” replaced the older terms “carrying” and “borrowing” in most modern curricula because it more accurately describes what is happening: you are not borrowing anything that needs to be paid back. You are simply re-expressing the same number in a different grouping.

[IMAGE: A set of base-10 blocks showing 13 ones being regrouped into 1 ten and 3 ones | ALT: base-10 blocks regrouping 13 ones into 1 ten rod and 3 unit cubes for elementary math]

Why Does Regrouping Matter?

Regrouping is the foundation of multi-digit arithmetic — every algorithm students use in Grades 3 through 12 builds on it. Without a solid grasp of regrouping, long multiplication, long division, and even fraction operations become much harder because students are fighting the mechanics instead of thinking about the math.

Beyond school, regrouping appears in everyday life: making change, calculating totals on a receipt, measuring ingredients, and even programming (binary addition uses the same carry logic). It is not an abstract school exercise — it is how humans have done arithmetic for centuries.

How to Add with Regrouping (Step-by-Step)

You need to carry in addition whenever the digits in any column add up to 10 or more. Here is the exact procedure, followed by two fully worked examples.

1. Stack the numbers vertically, aligning ones under ones, tens under tens, hundreds under hundreds.
2. Start in the ones column (always work right to left).
3. Add the ones digits. If the sum is 9 or less, write it below the line. If the sum is 10 or more, write only the ones digit below the line and write a small “1” above the tens column.
4. Move to the tens column. Add the tens digits plus any carried “1”. Apply the same rule: write the ones digit of the sum below the line; carry the tens digit if needed.
5. Repeat for each column moving left. The final column’s full sum (including any carry) is written in full.
6. Check by estimating: round each number to the nearest ten and verify your answer is close.

    ¹
    47
  + 36
  ----
    83
  

   ¹¹
   347
 + 285
 -----
   632
  

  Column:   H    T    O
            3    4    7
          + 2    8    5
          ─────────────
  Step 1:            12  → write 2, carry 1 to T
  Step 2:       4+8+1=13 → write 3, carry 1 to H
  Step 3:  3+2+1=6
          ─────────────
  Result:   6    3    2   = 632
  

How to Subtract with Regrouping (Step-by-Step)

You need to borrow in subtraction whenever the top digit in a column is smaller than the bottom digit. The procedure is the mirror image of carrying.

1. Stack the numbers vertically, larger number on top, aligning columns.
2. Start in the ones column.
3. Compare the top and bottom digits. If the top digit is greater than or equal to the bottom, subtract normally.
4. If the top digit is smaller, borrow 1 from the tens column: cross out the tens digit, write one less above it, and add 10 to the ones column’s top digit. Now subtract.
5. Move to the tens column (using the reduced digit if you borrowed). Repeat the comparison and borrow if needed.
6. Continue left until all columns are done.
7. Check by adding: your answer + the bottom number should equal the top number.

    4 11 13
    5  2  3
  - 1  6  7
  ---------
    3  5  6
  

How Do You Subtract Across Zeros?

Subtracting across zeros is the hardest regrouping scenario, and it is where most students make errors. When you need to borrow but the next column has a zero, you cannot borrow from it directly — you must keep moving left until you find a non-zero digit, then cascade the borrowing back rightward.

    6  9 10
    7  0  0
  - 3  4  5
  ---------
    3  5  5
  

What Are the Most Common Regrouping Mistakes?

These five errors account for the vast majority of wrong answers on regrouping problems. Recognizing them is the first step to eliminating them.

Practice Worksheet — 12 Problems (Easy to Hard)

Work through these problems using the step-by-step methods above. Show your work in columns. When you are done, check your answers with the key below.

How to use this worksheet: Print the PDF (button below) for a clean copy, or solve directly on this page. After finishing all 12 problems, open the Answer Key to self-check. Circle any wrong answers and re-solve them — do not just copy the answer.

1. 47 + 36 = ______
2. 65 + 58 = ______
3. 134 + 279 = ______
4. 347 + 285 = ______
5. 456 + 378 = ______
6. 72 – 45 = ______
7. 83 – 57 = ______
8. 231 – 98 = ______
9. 523 – 167 = ______
10. 704 – 368 = ______
11. 1002 – 475 = ______
12. 3456 + 1785 = ______

  ¹
  189
+ 243
-----
  432
      

  5  9 10
  6  0  0
- 2  5  3
---------
  3  4  7
      

   ¹¹¹
  1347
+ 2856
------
  4203