The number you are subtracting from
The number being subtracted
Difference
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Sources & Methodology
Long subtraction methodology follows the standard algorithm as defined in Common Core State Standards for Mathematics (CCSSM) and verified against Khan Academy primary arithmetic curriculum.
Khan Academy — Multi-Digit Subtraction Review
Standard curriculum reference for the column subtraction method, regrouping, and place value alignment used in this calculator
Common Core State Standards — CCSS.Math.Content.4.NBT.B.4
Fluently subtract multi-digit whole numbers using the standard algorithm — the authoritative US curriculum definition of long subtraction with regrouping
Methodology: Numbers are right-aligned by place value. Each column is processed from right (ones) to left. When the top digit is less than the bottom digit, the top digit borrows 10 from the adjacent left column, and that left column's top digit is reduced by 1. If the left column is 0, cascading borrows proceed further left. Verification: difference + subtrahend must equal minuend.
⏱ Last reviewed: April 2026
How to Do Long Subtraction with Regrouping
Long subtraction with regrouping (borrowing) is the standard written method for subtracting multi-digit numbers. Numbers are stacked vertically aligned by place value. When a digit in the top number is smaller than the digit directly below it, you regroup by borrowing 10 from the next column to the left, allowing the subtraction to proceed.
The Standard Algorithm
Difference = Minuend − Subtrahend
Step 1: Write minuend on top, subtrahend below, right-aligned by place value
Step 2: Starting at ones column — if top ≥ bottom: subtract directly
Step 3: If top < bottom: borrow 1 from the left column (top += 10, left top -= 1)
Step 4: If the left column top is 0, cascade the borrow further left
Step 5: Repeat for every column. Leading zeros in the result are dropped.
Step 2: Starting at ones column — if top ≥ bottom: subtract directly
Step 3: If top < bottom: borrow 1 from the left column (top += 10, left top -= 1)
Step 4: If the left column top is 0, cascade the borrow further left
Step 5: Repeat for every column. Leading zeros in the result are dropped.
Worked Example: 7006 − 3849
| Column | Top | Bottom | Borrow? | Adjusted Top | Difference |
|---|---|---|---|---|---|
| Ones | 6 | 9 | Yes — cascade from thousands | 16 | 7 |
| Tens | 0 → 9 (after cascade) | 4 | Yes — from hundreds | 9 | 5 |
| Hundreds | 0 → 9 (after cascade) | 8 | Yes — from thousands | 9 | 1 |
| Thousands | 7 → 6 (after lending) | 3 | No | 6 | 3 |
Result: 3,157. Verify: 3,157 + 3,849 = 7,006 ✔
Cascading Borrows
When a zero appears in the column you need to borrow from, you must skip over it and borrow from the next non-zero column to the left. Each zero along the way becomes a 9, and the non-zero column decreases by 1. For example, to borrow for the ones column in 1000 − 1: borrow from thousands (7000 becomes 6000), tens and hundreds each become 9 → 16 − 1 = 15.
How to Check Your Answer
Add the difference back to the subtrahend. The result must equal the original minuend. This is the inverse operation check: if A − B = C, then C + B must = A. For 7006 − 3849 = 3157: check 3157 + 3849 = 7006 ✔
💡 Terminology: The top number is the minuend. The number being subtracted is the subtrahend. The answer is the difference. Borrowing is formally called regrouping in modern curricula because you are reorganising 1 ten into 10 ones — not actually borrowing anything.
Frequently Asked Questions
Long subtraction with regrouping is the standard written method for subtracting multi-digit numbers. Numbers are stacked vertically right-aligned by place value. When a top digit is smaller than the bottom digit in the same column, you regroup — borrowing 10 from the next column left — so subtraction can proceed. It is also called column subtraction or the standard subtraction algorithm.
1) Write the larger number on top, smaller below, right-aligned. 2) Start at the ones column. If top ≥ bottom, subtract directly. 3) If top < bottom, borrow 1 from the tens column: add 10 to the ones top digit, reduce the tens top digit by 1. 4) Complete the ones subtraction. 5) Move to tens column and repeat. 6) Continue for every column left.
Regrouping means reorganising place values to make subtraction possible. When the ones top digit is less than the ones bottom digit, you regroup by converting 1 ten into 10 ones. The ones top digit increases by 10, and the tens top digit decreases by 1. The total value of the number does not change — only how it is expressed across columns.
Borrowing and regrouping describe exactly the same mathematical operation. Borrowing is the traditional term — it evokes taking from the next column. Regrouping is the modern preferred term in curriculum standards (CCSSM), emphasising that you are reorganising 1 ten as 10 ones rather than borrowing. Both are correct; modern teaching prefers regrouping.
When you need to borrow but the adjacent left column is 0, you must cascade the borrow further left until you reach a non-zero digit. That non-zero digit decreases by 1, and every 0 between it and the original column becomes a 9. For example, in 5000 − 3: borrow from thousands (5000 → 4999 effectively), giving 10 − 3 = 7 in the ones column.
Use the inverse operation: add the difference back to the subtrahend. If the result equals the original minuend, the subtraction is correct. For example: 7006 − 3849 = 3157. Check: 3157 + 3849 = 7006 ✔. This works because subtraction and addition are inverse operations, so they must undo each other perfectly.
The five most common errors: 1) Forgetting to reduce the borrowed-from digit by 1. 2) Misaligning numbers — always right-align. 3) Subtracting top from bottom when top is smaller, instead of borrowing. 4) Failing to cascade borrows through consecutive zeros. 5) Losing track of which digit was already reduced when multiple borrows happen in the same problem.
If the overall subtrahend (bottom number) is larger than the minuend (top number), the result is a negative number. The standard method is to swap the numbers — compute (larger − smaller) using long subtraction — and then prefix a minus sign to the result. This calculator shows both the absolute difference and whether the result is negative.
In a subtraction A − B = C: A is the minuend (the number being reduced), B is the subtrahend (the amount being taken away), and C is the difference (the result). The minuend goes on top in column subtraction. The subtrahend goes on the bottom. The difference is written below the line after completing all columns.
Right-align all numbers — ones under ones, tens under tens. The shorter number has implied leading zeros in its higher place value columns. Subtract normally. In those high columns, you simply subtract 0 from the top digit (or 0 − 0 if the top number also has no digit there), accounting for any borrows that came from the right.
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