Subtraction with Regrouping: Step by Step
Column subtraction starts with the ones and moves left. When a top digit is smaller than the digit below it, 1 is regrouped from the next place: the digit to the left goes down by 1 and the small digit gains 10.
In the worked example the regrouped digits are crossed out and their new values written above, a common way to keep track of the regrouping.
When is it taught?
- Grade 2 (CCSS 2.NBT.B.7): add and subtract within 1000, composing and decomposing tens and hundreds.
- Grade 3 (CCSS 3.NBT.A.2): fluently subtract within 1000.
- Grade 4 (CCSS 4.NBT.B.4): fluently subtract multi-digit whole numbers using the standard algorithm.
Worked example: 7352 − 2816
7352−2816
6134127352−28164536
Left: the problem. Right: the worked answer with regrouping marks, as in our answer keys.
Step by step
- 1Ones: 2 is less than 6, so regroup 1 ten as 10 ones: 12 − 6 = 6.
- 2The tens digit 5 gave 1 to the right and is now 4. Tens: 4 − 1 = 3.
- 3Hundreds: 3 is less than 8, so regroup 1 thousand as 10 hundreds: 13 − 8 = 5.
- 4The thousands digit 7 gave 1 to the right and is now 6. Thousands: 6 − 2 = 4.
- 5The difference is 4536.
- 6Check by adding: 4536 + 2816 = 7352.
Common mistakes
- Subtracting the smaller digit from the larger one in every column (writing 6 − 2 instead of regrouping for 2 − 6).
- Forgetting that the digit that gave 1 away is now 1 smaller.
- Checking: add the answer to the number that was subtracted — you must get the top number back.
Printable subtraction practice
- 2-digit − 2-digit subtractionGrade 2 · CCSS 2.NBT.B.5
- 3-digit subtraction with regroupingGrade 3 · CCSS 3.NBT.A.2
- 4-digit subtraction with regroupingGrade 4 · CCSS 4.NBT.B.4