Addition Within 1,000 with Regrouping

When adding three-digit numbers, you will often find that the numbers in a column add up to $10$ or more. When this happens, you need to regroup (or carry) the extra value to the next column. Sometimes, you will even need to regroup more than once in the same problem!

How to Add with Regrouping

To solve addition problems using column addition, follow these simple steps:

1. Stack the numbers so the ones, tens, and hundreds places line up perfectly.
2. Add the ones column. If the sum is $10$ or more, write the ones digit at the bottom and carry the tens digit (a $1$) to the top of the tens column.
3. Add the tens column, making sure to include the $1$ you carried over. If the sum is $10$ or more, write down the ones digit and carry the $1$ to the hundreds column.
4. Add the hundreds column, again remembering to include any carried $1$.

Example 1: Double Regrouping

Let's add: $398 + 567$

First, stack the numbers:

\begin{array}{r@{\quad}l} 398 \\ + 567 \\ \hline \end{array}

Step 1: Add the ones. $8 + 7 = 15$. Write down the $5$ and carry the $1$ to the tens column.

Step 2: Add the tens. $9 + 6 + 1 \text{ (carried)} = 16$. Write down the $6$ and carry the $1$ to the hundreds column.

Step 3: Add the hundreds. $3 + 5 + 1 \text{ (carried)} = 9$. Write down the $9$.

Answer: $398 + 567 = 965$

Example 2: Regrouping into the Thousands

Sometimes, adding three-digit numbers will result in an answer greater than $1,000$. The steps remain exactly the same!

Let's add: $687 + 459$

Step 1: Add the ones. $7 + 9 = 16$. Write down $6$, carry $1$.

Step 2: Add the tens. $8 + 5 + 1 \text{ (carried)} = 14$. Write down $4$, carry $1$.

Step 3: Add the hundreds. $6 + 4 + 1 \text{ (carried)} = 11$. Since there are no more columns to the left, simply write down the $11$ at the bottom.

Answer: $687 + 459 = 1146$

Quick Tip for Success

Always write your carried numbers neatly at the top of the next column so you don't forget to add them! Taking it one column at a time makes even the biggest addition problems easy to solve.