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Level 3Grade 3skill: sub_regroup· 7 min read

Subtraction With Regrouping (Borrowing)

In short: When the top digit in a column is smaller than the bottom one, regroup: trade one ten for ten ones so you have enough to subtract. This never changes the number's value — 62 is the same as 5 tens and 12 ones. Work right to left, and when you hit a zero, let the borrow travel further left.

How to subtract with regrouping

Stack the two numbers so the ones sit above the ones and the tens above the tens. Then work one column at a time, starting from the right. The whole game is decided in the ones column: look at the top digit and the bottom digit.

If the top digit is big enough to subtract from, you just subtract. If it is too small — like the 2 in 62 when you are taking away 7 — you regroup: take one ten from the tens column, turn it into ten ones, and hand those over to the ones column so it has enough to work with.

  1. Line up the numbers by place value: ones under ones, tens under tens.
  2. Start in the ones column. Compare the top digit to the bottom digit.
  3. If the top digit is smaller, borrow: cross out the tens digit, make it one smaller, and add 10 to the ones — unless that digit is 0, in which case move left to the next non-zero digit and borrow from there.
  4. Subtract the ones column, then subtract the tens column and any columns further left.

Why regrouping never changes the number Why it works

top < bottom
Regroup: take a ten, add 10 to the ones.

62 − 27: the 2 becomes 12, so 12 − 7 = 5, then 5 − 2 = 3 → 35

top ≥ bottom
No regrouping needed — subtract straight down.

58 − 23: 8 − 3 = 5 and 5 − 2 = 3 → 35

0 on top
You can't borrow from a 0, so the borrow travels further left.

300 − 146: reach past both zeros to the 3 → 154

Here is the one idea worth holding onto: regrouping does not change the value, only its costume. The number 62 is exactly the same whether you write it as "6 tens and 2 ones" or as "5 tens and 12 ones." You are not making 62 bigger or smaller when you borrow — you are just re-dressing it so the ones column has enough to subtract. Once that clicks, borrowing across a row of zeros stops feeling like a trick and starts feeling obvious.

Worked examples

62 − 27 = 35
  1. Ones column: 2 is smaller than 7, so regroup. The 6 tens becomes 5 tens, and the 2 ones becomes 12 ones.
  2. Subtract the ones: 12 − 7 = 5.
  3. Subtract the tens: 5 − 2 = 3.
84 − 59 = 25
  1. Ones column: 4 is smaller than 9, so regroup. The 8 tens becomes 7 tens, and the 4 ones becomes 14 ones.
  2. Subtract the ones: 14 − 9 = 5.
  3. Subtract the tens: 7 − 5 = 2.
405 − 168 = 237
  1. Ones column: 5 is smaller than 8, so we need to regroup — but the tens digit is 0, so we can't borrow from it directly.
  2. Go one more place left: the 4 hundreds becomes 3 hundreds, giving 10 tens. Now borrow one of those tens for the ones: 10 tens becomes 9 tens, and the 5 ones becomes 15 ones.
  3. Subtract the ones: 15 − 8 = 7.
  4. Subtract the tens: 9 − 6 = 3.
  5. Subtract the hundreds: 3 − 1 = 2.
300 − 146 = 154
  1. Ones column: 0 is smaller than 6, and the tens digit is also 0, so the borrow has to come from the hundreds.
  2. Rewrite 300 as 2 hundreds, 9 tens, and 10 ones (still exactly 300).
  3. Subtract the ones: 10 − 6 = 4.
  4. Subtract the tens: 9 − 4 = 5.
  5. Subtract the hundreds: 2 − 1 = 1.

Common mistakes

Borrowing the ones but forgetting to shrink the tens

✗ 44

For 72 − 38, the student correctly turns the 2 into 12 and gets 12 − 8 = 4 in the ones. But they forget that borrowing costs the tens column a ten — they leave the 7 as 7 and compute 7 − 3 = 4, landing on 44.

Fix: Every time you add 10 to the ones, immediately cross out the tens digit and make it one smaller. In 72 − 38 the 7 must become a 6, so the tens step is 6 − 3 = 3, giving the correct 34.

missed_borrow

Adding instead of subtracting

✗ 110

The student reads the columns and adds them: 72 + 38 = 110. This usually happens when the minus sign gets skimmed or a habit of "just combine the numbers" takes over.

Fix: Before you touch the digits, say the problem out loud: "seventy-two take away thirty-eight." The answer must be smaller than 72, so any result above 72 is an instant red flag.

wrong_operation

Landing one away from the answer

✗ 33

The method is right, but a miscount slips in — the student treats 12 − 8 as 3 instead of 4, so the ones digit is off by one and the tens step (6 − 3 = 3) then lands the whole answer on 33 instead of 34.

Fix: Recount the tricky column on your fingers, then check with addition: your answer plus the number you subtracted should rebuild the top number. 34 + 38 = 72 ✓, but 33 + 38 = 71, so 33 can't be right.

off_by_one

Practice: subtraction with regrouping

Work each problem column by column, regrouping whenever the top digit is too small. If any borrow across a zero, those are the trickiest — let the borrow travel left until it reaches a non-zero digit.

Keep going

First, make sure of

Frequently asked questions

What does "regrouping" or "borrowing" actually mean?

It means trading one ten for ten ones (or one hundred for ten tens) so a column has enough to subtract from. The value of the number never changes — 62 is still 62 whether you write it as 6 tens and 2 ones or as 5 tens and 12 ones. You are just re-dressing it so the ones column has enough to work with.

How do I know when I need to regroup?

Look only at the top and bottom digits in the column you are working on. If the top digit is smaller than the bottom one, you regroup. If the top digit is equal to or bigger than the bottom one, subtract straight down with no borrowing.

How do I subtract when there's a zero to borrow from, like 300 − 146?

You can't borrow from a 0, so the borrow travels further left until it reaches a digit it can take from. For 300 − 146, rewrite 300 as 2 hundreds, 9 tens, and 10 ones (still exactly 300), then subtract each column: 10 − 6 = 4, 9 − 4 = 5, 2 − 1 = 1, giving 154.

How can I check my subtraction answer?

Add your answer to the number you took away — you should get back the number you started with. For 72 − 38 = 34, check that 34 + 38 = 72. If it doesn't rebuild the top number exactly, you've made a slip somewhere, usually an off-by-one miscount.

Why is my answer bigger than the number I started with?

That almost always means you added instead of subtracted. A subtraction answer must be smaller than the top number, so if 72 − 38 gives you 110, that's a signal you combined the numbers instead of taking one away. Reread the sign and start again from the ones column.