2-Digit Addition and Subtraction With Regrouping
Regrouping happens when a column does not work on its own: 7 ones + 8 ones make 15 ones, so 10 ones are traded for 1 ten. Subtraction works the other way: when there are not enough ones, one ten is broken into 10 ones.
What does regrouping mean?
In 47 + 38 the ones make 7 + 8 = 15. Fifteen ones are too many for the ones place, so 10 of them become 1 new ten and 5 ones stay. Older books call this "carrying".
In 72 − 45 you cannot take 5 ones away from 2 ones, so you open one of the 7 tens. 72 becomes 6 tens and 12 ones, still the same number. This used to be called "borrowing".
2-digit addition with regrouping
- Line up the numbers: ones under ones, tens under tens.
- Add the ones. If the sum is 10 or more, write the ones digit and put a small 1 above the tens column.
- Add the tens, including the regrouped 1.
47 + 38
47 + 38 -- 85
- Ones: 7 + 8 = 15. Write 5 and regroup 1 ten.
- Tens: 4 + 3 + 1 = 8.
Answer: 85
Some children prefer to add the tens first in their heads: 37 + 28 → 37 + 20 = 57, then 57 + 8 = 65. Both ways give the same answer; the column method is easier to check on paper.
2-digit subtraction with regrouping
- Line up the numbers and start with the ones.
- If the top ones digit is smaller than the bottom one, regroup: cross out the tens digit, write one less above it, and add 10 to the ones.
- Subtract the ones, then the tens.
- Check by adding: answer + the number you subtracted = the top number.
72 − 45
72 − 45 -- 27
- Ones: 2 − 5 does not work. Regroup 1 ten: 7 tens become 6 tens, and 2 ones become 12 ones.
- Ones: 12 − 5 = 7.
- Tens: 6 − 4 = 2.
Answer: 27. Check: 27 + 45 = 72.
With a zero: 60 − 24
60 − 24 -- 36
- Ones: 0 − 4 does not work. Regroup: 6 tens become 5 tens, and 0 ones become 10 ones.
- Ones: 10 − 4 = 6.
- Tens: 5 − 2 = 3.
Answer: 36
When do you need to regroup?
Look before you solve. In addition, regroup when the ones add up to 10 or more: in 36 + 47, 6 + 7 = 13. In subtraction, regroup when the top ones digit is smaller: in 53 − 28, 3 is less than 8. Problems like 34 + 25 and 58 − 23 need no regrouping at all.
Examples
46 + 7 = ?
82 - 25 = ?
34 + 21 = ?
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.
- 78 − 29 = ___
- 83 − ___ = 26
- 29 + 34 = ___
- ___ + 15 = 42
- 77 + 23 = ___
- 37 + 28 = ___
- 68 − ___ = 49
- ___ − 79 = 1
Show answers
- 49
- 57
- 63
- 27
- 100
- 65
- 19
- 80
Common mistakes
- Forgetting the regrouped ten: 47 + 38 = 75 instead of 85.
- Writing the whole ones sum in the answer: 47 + 38 = 715.
- Taking the smaller digit from the bigger one in each column: 72 − 45 = 33 instead of 27.
- Regrouping but not making the tens one less: 72 − 45 = 37.
Questions parents ask
What is regrouping in math?
Regrouping means trading between places: 10 ones for 1 ten in addition, or 1 ten for 10 ones in subtraction. It is the same idea as carrying and borrowing, but the word reminds kids that the value stays the same: 72 is 7 tens and 2 ones or 6 tens and 12 ones.
When do kids learn 2-digit addition and subtraction with regrouping?
In 2nd grade. The Common Core standard 2.NBT.B.5 asks children to add and subtract fluently within 100. Regrouping with 3-digit numbers follows in 3rd grade.
Should my child use base-ten blocks?
Yes, at the start. Building 72 with 7 rods and 2 cubes and then swapping a rod for 10 cubes shows exactly what regrouping means. Once the trade is clear, the written method makes sense and the blocks can go away.
How can my child check the answer?
For subtraction, add back: 27 + 45 = 72. For addition, estimate: 47 + 38 is about 50 + 40 = 90, so 85 is reasonable.