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Level 3Grade 3skill: add_regroup· 7 min read

Addition With Regrouping (Carrying)

In short: When the ones column adds to 10 or more, trade 10 ones for 1 ten and carry that ten into the tens column. Always add right to left, write every carry down, and remember that carrying only renames the number, it never changes how much you have.

How to add with regrouping

Regrouping is the move you make when a column overflows. When the ones add up to 10 or more, you can't fit that answer in a single column, so you trade 10 ones for 1 ten and slide that ten over to where the tens live. People also call this carrying. It is the same idea either way.

Take 47 + 38. Line them up so ones sit over ones and tens sit over tens. Start on the right, always. Ones first: 7 + 8 = 15. That 15 is one ten and five ones, so you write the 5 in the ones place and carry the 1 up to the top of the tens column. Now the tens: 4 + 3 + 1 = 8. Nothing overflows, so you write 8. The answer is 85.

  1. Stack the numbers so the ones line up under the ones and the tens under the tens.
  2. Add the ones column first.
  3. If the ones total is 10 or more, write the right-hand digit and carry the 1 to the top of the tens column.
  4. Add the tens column, including any 1 you carried.
  5. If the tens overflow too, carry again into the hundreds. Write the final answer.

Why carrying works Why it works

Do the ones reach 10?
If the ones add to 10 or more, you must carry a ten. If they stay under 10, you don't.

7 + 8 = 15, so carry. 3 + 4 = 7, so don't.

Where the carry lands
The carried 1 always joins the tens column, never the ones. It is one ten, not one one.

In 47 + 38 the small 1 sits above the 4 and the 3.

Carries can chain
Adding the carry can push the tens over 10 too, so you carry again into the hundreds.

68 + 57: ones give 15 (carry 1), then 6 + 5 + 1 = 12 (carry again) → 125.

Here is the one thing worth remembering: regrouping never changes the number, it only renames it. Fifteen ones and "one ten plus five ones" are the exact same amount. You are not adding anything extra when you carry, you are just repackaging ten loose ones into a single neat ten so it fits in the next column.

Worked examples

47 + 38 = 85
  1. Ones: 7 + 8 = 15. Write 5, carry 1.
  2. Tens: 4 + 3 + 1 = 8. Write 8.
68 + 57 (the carry chains) = 125
  1. Ones: 8 + 7 = 15. Write 5, carry 1.
  2. Tens: 6 + 5 + 1 = 12. That's over 10, so write 2 and carry 1 into the hundreds.
  3. Hundreds: 0 + 0 + 1 = 1. Write 1.
96 + 8 (carrying into a new column) = 104
  1. Ones: 6 + 8 = 14. Write 4, carry 1.
  2. Tens: 9 + 0 + 1 = 10. Write 0 and carry 1 into the hundreds.
  3. Hundreds: 1. Write 1.
385 + 247 (two carries in a row) = 632
  1. Ones: 5 + 7 = 12. Write 2, carry 1.
  2. Tens: 8 + 4 + 1 = 13. Write 3, carry 1.
  3. Hundreds: 3 + 2 + 1 = 6. Write 6.

Common mistakes

Forgetting to carry the ten

✗ 75

For 47 + 38 the ones make 7 + 8 = 15, but if you only write the 5 and forget the little 1, the tens become just 4 + 3 = 7. You lose a whole ten and land on 75.

Fix: Whenever the ones total is 10 or more, park the carried 1 at the top of the tens column before you add that column. Write it down, don't just hold it in your head.

missed_carry

Adding the carry one time too many

✗ 95

For 47 + 38 the tens column is 4 + 3 + 1 = 8. But it's easy to count the carried 1 one time too many — running it as 4 + 3 + 1 + 1 = 9 — which writes a 9 in the tens and gives 95. One extra tick and the tens digit is off by one.

Fix: Carry the 1 exactly once. After you park it above the tens column, add each tens digit and that single 1 one time only: 4 + 3 + 1 = 8.

off_by_one

Subtracting instead of adding

✗ 9

The plus sign got read as a minus. For 47 + 38 that turns into 47 − 38 = 9, which isn't even close to the real total of 85.

Fix: Check the sign before you start. Addition makes the answer bigger than both numbers, so if your answer is smaller than what you started with, you subtracted by accident.

wrong_operation

Practice: addition with regrouping

Add each pair, carrying whenever the ones reach 10 or more. Work right to left and write down every carry.

Keep going

First, make sure of

Frequently asked questions

What does "regrouping" mean in addition?

Regrouping means trading 10 ones for 1 ten (or 10 tens for 1 hundred) when a column adds up to 10 or more. It's the same thing as "carrying" — you repackage the overflow so it fits in the next column to the left.

Which column do I start with?

Always start on the right, with the ones column. If you start on the left you won't know whether a carry is coming, and carries only travel leftward.

Where does the carried 1 go?

It goes to the top of the tens column, because it stands for one ten. It never joins the ones column. If the tens then overflow, the next carry goes into the hundreds.

How do I know if I even need to regroup?

Add the ones column first. If the total is 10 or more, you regroup. If it's 9 or less, there's nothing to carry and you just write it down.

What's the fastest way to catch a mistake?

Estimate first. 47 + 38 is roughly 50 + 40 = 90, so an answer of 85 looks right but 75 or 9 clearly doesn't. A quick rounded guess flags a dropped carry or a wrong operation instantly.