3-Digit Subtraction with Regrouping (Borrowing)

What is 3-digit subtraction with regrouping?

Regrouping (also called borrowing) is what you do when a digit on the top of a subtraction is smaller than the digit below it. Since you cannot take a bigger number away from a smaller one, you borrow 1 from the next column on the left — that borrowed 1 is worth 10 in the current column. You then cross out the old digit, write the new (smaller) value above the column you borrowed from, and subtract as usual.

Use the animation above to watch this happen step by step for 20 different problems, then follow the written method below.

The method — step by step

1. Line up the numbers by place value: hundreds under hundreds, tens under tens, ones under ones.
2. Start from the ones (right-most) column. If the top digit is greater than or equal to the bottom digit, just subtract.
3. If the top digit is smaller, regroup: borrow 1 from the column to the left. Reduce that left digit by 1, and add 10 to the current column.
4. Subtract the current column and write the answer below the line.
5. Move left to the tens, then the hundreds, repeating steps 2–4.

Worked example: 548 − 459

Column	What happens	Result
Ones	8 − 9 → 8 is smaller, so borrow 1 ten. The 4 tens become 3, and the ones become 18. Now 18 − 9.	9
Tens	3 − 5 → 3 is smaller, so borrow 1 hundred. The 5 hundreds become 4, and the tens become 13. Now 13 − 5.	8
Hundreds	4 − 4	0

So 548 − 459 = 89. (The leading 0 in the hundreds place is dropped.)

Borrowing across a zero

When the column you want to borrow from is a 0, you cannot take 1 from it directly. Instead, borrow from the next non-zero column further left. That column drops by 1, every 0 in between becomes 9, and the starting column gains 10.

Example — 860 − 87: to subtract the ones (0 − 7) you must borrow, but the tens are 6, so you borrow from the tens (6 → 5) and the ones become 10; then 10 − 7 = 3. Continue with the tens: 5 − 8 needs a borrow from the hundreds (8 → 7), tens become 15, 15 − 8 = 7; hundreds 7 − 0 = 7. Answer: 773.

Common mistakes to avoid

• Forgetting to reduce the borrowed-from digit. If you add 10 to a column, the column you borrowed from must go down by 1.
• Subtracting the smaller digit from the larger out of habit (e.g. writing 8 − 9 as 1). Always subtract top − bottom, and regroup when the top is smaller.
• Mishandling zeros. When borrowing across a 0, the 0 becomes 9 — don't skip it.
• Not lining up place values, which leads to subtracting the wrong digits.

Practice problems

Try these in the animation above (tap “Choose a problem”): 481 − 398, 964 − 285, 953 − 179, 873 − 398, 856 − 588, 718 − 679, 881 − 795, 625 − 159. Work each one on paper first, then play the steps to check your borrowing.

Quick tip

Regrouping is just trading: 1 ten = 10 ones, and 1 hundred = 10 tens. Every time you borrow, you are trading one larger unit for ten smaller ones — the total value never changes, which is why the answer stays correct.