Grade 3 Math

3-Digit Subtraction With Regrouping

In 3-digit subtraction with regrouping, a column does not have enough on top, so you trade with the next place: 1 ten becomes 10 ones, or 1 hundred becomes 10 tens. Work from right to left, one column at a time, and check the answer with addition.

How to subtract 3-digit numbers with regrouping

Write the numbers in columns: ones under ones, tens under tens, hundreds under hundreds.
Start with the ones. If the top digit is smaller than the bottom digit, regroup 1 ten as 10 ones: cross out the tens digit and write one less above it.
Subtract the ones. Repeat the check in the tens column; if needed, regroup 1 hundred as 10 tens.
Subtract the tens, then the hundreds.
Check: answer + the number you subtracted = the top number.

Regrouping once: 852 − 418

Ones: 2 − 8 does not work. Regroup 1 ten: 5 tens become 4 tens, and 2 ones become 12 ones. 12 − 8 = 4.
Tens: 4 − 1 = 3.
Hundreds: 8 − 4 = 4.

Answer: 434. Check: 434 + 418 = 852.

Regrouping twice: 645 − 367

Ones: 5 − 7 does not work. Regroup 1 ten: 4 tens become 3 tens, and 5 ones become 15 ones. 15 − 7 = 8.
Tens: 3 − 6 does not work. Regroup 1 hundred: 6 hundreds become 5 hundreds, and 3 tens become 13 tens. 13 − 6 = 7.
Hundreds: 5 − 3 = 2.

Answer: 278. Check: 278 + 367 = 645.

Subtracting across zeros

Zeros make subtraction tricky: in 503 − 268 the ones need more, but there are no tens to regroup. The trick is to go one place further left. 503 is 5 hundreds, 0 tens and 3 ones. Regroup 1 hundred as 10 tens, then 1 of those tens as 10 ones, and 503 becomes 4 hundreds, 9 tens and 13 ones.

503 − 268

Ones: 3 − 8 does not work, and the tens digit is 0. Regroup 1 hundred as 10 tens: 4 hundreds, 10 tens.
Regroup 1 of the tens as 10 ones: 9 tens, 13 ones. 13 − 8 = 5.
Tens: 9 − 6 = 3.
Hundreds: 4 − 2 = 2.

Answer: 235. Check: 235 + 268 = 503.

A shortcut for the same idea: read 503 as 50 tens and 3 ones. Take 1 ten and you have 49 tens and 13 ones, so the top number becomes 4, 9, 13. It works for 400 − 136 too: 400 becomes 3 hundreds, 9 tens and 10 ones, and the answer is 264.

Look first: where do you need to regroup?

Before solving, compare the digits column by column. In 645 − 367 the top digit is smaller in the ones (5 and 7) and in the tens (4 and 6), so there are two regroupings. In 768 − 425 every top digit is bigger, so no regrouping is needed. An estimate catches slips: 645 − 367 is about 650 − 370 = 280.

Examples

  645
− 367
  −−−
   ???

278

  853
− 458
  −−−
   ???

395

Practice online Printable worksheet

Practice problems with answers

Solve these problems on paper or out loud, then check the answer key. The online practice and the printable worksheet give a new set every time.

```
  372
− 207
  ---
```
```
  563
− 159
  ---
```
```
  578
− 179
  ---
```
```
  310
− 211
  ---
```
```
  488
− 199
  ---
```
```
  791
− 152
  ---
```
```
  361
− 205
  ---
```
```
  922
− 745
  ---
```

Show answers

Common mistakes

Taking the smaller digit from the bigger one in every column: 645 − 367 becomes 322 instead of 278.
Regrouping but forgetting to make the next place one less: 645 − 367 = 388.
Leaving 10 tens after regrouping across a zero: in 503 − 268 one of those tens went to the ones, so there are 9 tens left. Otherwise the answer comes out as 245 instead of 235.

Questions parents ask

What is 3-digit subtraction with regrouping?

It is subtracting numbers from 100 to 999 when a digit in the top number is smaller than the digit below it. You then trade 1 ten for 10 ones or 1 hundred for 10 tens, which used to be called borrowing.

How do you subtract across zeros?

Regroup from the first place to the left that is not zero. In 503 − 268, 1 hundred becomes 10 tens and 1 ten becomes 10 ones, so the top number reads 4 hundreds, 9 tens and 13 ones. The answer is 235.

How many times can you regroup in one problem?

At most twice with 3-digit numbers: once into the ones and once into the tens, as in 645 − 367 = 278 or 503 − 268 = 235.

What grade learns 3-digit subtraction with regrouping?

Third grade: the Common Core standard 3.NBT.A.2 asks children to add and subtract fluently within 1000. Many second graders meet it earlier with base-ten blocks (2.NBT.B.7).