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Learn Index · Arithmetic and Operations Grade 3–5

Regrouping and borrowing

Exchanging tens, hundreds and so on when a digit is too small to subtract.

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What is regrouping?

Our number system works in tens. When a column has 10 or more, we trade 10 of them for 1 of the next bigger place. When a column doesn’t have enough, we trade 1 of the next bigger place for 10 of the smaller one. This trading is called regrouping, and it works because of place value: each place is worth ten times the place to its right.

  • In addition, regrouping is often called carrying.
  • In subtraction, it’s often called borrowing (or trading).

Seeing it with base-ten blocks

Base-ten blocks make regrouping visible:

Trade Means
10 unit cubes → 1 rod 10 ones = 1 ten
10 rods → 1 flat 10 tens = 1 hundred
1 rod → 10 unit cubes 1 ten = 10 ones

Regrouping in addition (carrying)

Example: 58 + 27

   1
   5 8
 + 2 7
 -----
   8 5
  1. Ones: 8 + 7 = 15. That’s 1 ten and 5 ones. Write 5, carry the 1 ten.
  2. Tens: 5 + 2 + 1 = 8.

Answer: 85.

Regrouping in subtraction (borrowing)

Example: 62 − 38

   5 12
   6  2
 − 3  8
 ------
   2  4
  1. Ones: 2 − 8 can’t be done. Take 1 ten from the 6 tens (leaving 5). The 2 ones become 12.
  2. Ones: 12 − 8 = 4.
  3. Tens: 5 − 3 = 2.

Answer: 24. Check: 24 + 38 = 62 ✓.

Borrowing across zeros

Example: 400 − 167

The ones and tens are both 0. Go to the hundreds:

  1. 4 hundreds → 3 hundreds and 10 tens.
  2. 10 tens → 9 tens and 10 ones.
  3. Now subtract: 10 − 7 = 3, 9 − 6 = 3, 3 − 1 = 2.

Answer: 233.

A shortcut: think of 400 as 399 + 1. Then 399 − 167 = 232, and add 1 → 233.

When do you regroup?

Operation Regroup when…
Adding A column adds to 10 or more
Subtracting The top digit is smaller than the bottom digit

Worked examples

Example 1: 476 + 358

Ones 6 + 8 = 14 (write 4, carry 1). Tens 7 + 5 + 1 = 13 (write 3, carry 1). Hundreds 4 + 3 + 1 = 8. Answer: 834.

Example 2: 731 − 285

Ones: 1 − 5 → borrow: 11 − 5 = 6 (tens now 2). Tens: 2 − 8 → borrow: 12 − 8 = 4 (hundreds now 6). Hundreds: 6 − 2 = 4. Answer: 446.

Example 3: 1,000 − 1

Borrow across all the zeros: 999.

Common mistakes

  • Subtracting the smaller digit from the bigger one in each column (for 62 − 38, writing 36). Always subtract bottom from top, and borrow if needed.
  • Forgetting to reduce the digit you borrowed from.
  • Forgetting to add the carried 1.

Try it yourself

  1. 67 + 48
  2. 93 − 57
  3. 508 − 249
  4. 389 + 476

Answers: 1) 115 2) 36 3) 259 4) 865

Quick recap

  • Regrouping trades 10 of one place for 1 of the next.
  • Carrying happens when a column sum is 10 or more.
  • Borrowing happens when the top digit is too small; borrow across zeros step by step.