Two-Digit Addition with Regrouping: Step-by-Step for 2nd Graders

What is two-digit addition?

A two-digit number is any whole number from $10$ up to $99$. It has a tens place and a ones place. For example, $47$ has $4$ tens and $7$ ones.

Two-digit addition means combining two such numbers — for example, $34 + 25$ or $47 + 38$. The standard written method uses place value: line up the digits in the same columns, then add column by column starting from the ones.

Adding without regrouping (the easy case)

When the ones digits add up to less than $10$ and the tens digits add up to less than $10$, you can simply add column by column.

Example 1. Compute $34 + 25$.

  3 4
+ 2 5
─────
  5 9

1. Ones column: $4 + 5 = 9$. Write $9$ in the ones place.
2. Tens column: $3 + 2 = 5$. Write $5$ in the tens place.

The answer is $\mathbf{59}$. No regrouping needed.

Adding with regrouping (carrying)

Regrouping is what happens when a column adds up to $10$ or more. Since each place can only hold one digit, we leave the ones digit in that column and carry the tens digit to the next column. Some textbooks call this "carrying."

The rule is simple: every group of $10$ in the ones column becomes $1$ in the tens column.

Example 2. Compute $27 + 35$.

  ¹
  2 7
+ 3 5
─────
  6 2

1. Ones column: $7 + 5 = 12$. That is "$1$ ten and $2$ ones." Write $2$ in the ones place and carry the $1$ above the tens column (the small $^1$ in the picture above).
2. Tens column: $1 + 2 + 3 = 6$. Don't forget the carried $1$. Write $6$ in the tens place.

The answer is $\mathbf{62}$.

A four-step method for any two-digit problem

Use the same four steps every time. They work whether or not regrouping is needed.

1. Line up the digits by place value: ones under ones, tens under tens.
2. Add the ones column. If the result is $10$ or more, write the ones digit and carry the tens digit up.
3. Add the tens column, including any carried digit.
4. Read off the answer.

Worked examples

Example 3. Compute $46 + 39$.

1. Ones: $6 + 9 = 15$. Write $5$, carry $1$.
2. Tens: $1 + 4 + 3 = 8$. Write $8$.

Answer: $\mathbf{85}$.

Example 4. Compute $58 + 24$.

1. Ones: $8 + 4 = 12$. Write $2$, carry $1$.
2. Tens: $1 + 5 + 2 = 8$. Write $8$.

Answer: $\mathbf{82}$.

Example 5. Compute $76 + 19$.

1. Ones: $6 + 9 = 15$. Write $5$, carry $1$.
2. Tens: $1 + 7 + 1 = 9$. Write $9$.

Answer: $\mathbf{95}$.

Example 6. Compute $89 + 47$ (this gives a three-digit answer).

1. Ones: $9 + 7 = 16$. Write $6$, carry $1$.
2. Tens: $1 + 8 + 4 = 13$. The tens column is now $13$ — that's $13$ tens, which is the same as $1$ hundred and $3$ tens. Write $3$ in the tens place and another $1$ in the hundreds place.

Answer: $\mathbf{136}$.

Quick tips that build accuracy

• Use grid paper or draw lines. Misaligned columns are the most common source of mistakes.
• Work right-to-left. Always start with the ones column. Adding the tens first makes regrouping much harder.
• Estimate first. $76 + 19$ should be a little less than $100$ ($80 + 20 = 100$). If you got $85$ or $185$, you would know to recheck.
• Write the carry above the next column. A small $1$ at the top of the tens column reminds you to add it in step 2.

Word problems

Two-digit addition shows up constantly in real-life situations: counting two stacks, combining money, or tracking points across two games.

Example 7. Maya has $34$ stickers. Her friend gives her $28$ more. How many stickers does she have now?

Set up the problem and add: $34 + 28$.

1. Ones: $4 + 8 = 12$. Write $2$, carry $1$.
2. Tens: $1 + 3 + 2 = 6$. Write $6$.

Maya has $62$ stickers.

Common mistakes

• Forgetting to carry. When the ones add to $10$ or more, the extra "$1$ ten" must move into the tens column. Skipping this gives an answer that is $10$ too small.
• Adding the carried digit twice. Only add it once, in the tens column.
• Mis-lining columns. Always write the ones below the ones and the tens below the tens. A digit out of place ruins the whole sum.
• Adding from left to right. That makes regrouping awkward. Always start with the ones column and move left.