Three-Digit Addition

Adding three-digit numbers is just like adding smaller numbers, but with one extra column! We use column addition to line up the hundreds, tens, and ones. Sometimes, when a column adds up to 10 or more, we need to carry (or regroup) a 1 to the next column on the left.

How to Add Three-Digit Numbers

Let's solve $367 + 458$ step by step.

Step 1: Line up the numbers Stack the numbers so the ones, tens, and hundreds columns match up perfectly.

$$\begin{array}{rrrr} & 3 & 6 & 7 \\ +& 4 & 5 & 8 \\ \hline \end{array}$$

Step 2: Add the Ones Always start on the right side! Add the ones column: $7 + 8 = 15$. Since 15 is 10 or more, write down the $5$ and carry the 1 to the tens column.

$$\begin{array}{rrrr} & & \color{red}1 & \\ & 3 & 6 & 7 \\ +& 4 & 5 & 8 \\ \hline & & & 5 \end{array}$$

Step 3: Add the Tens Next, add the tens column, and don't forget the 1 you carried over! $1 \text{ (carried)} + 6 + 5 = 12$. Write down the $2$ and carry the 1 to the hundreds column.

$$\begin{array}{rrrr} & \color{red}1 & \color{red}1 & \\ & 3 & 6 & 7 \\ +& 4 & 5 & 8 \\ \hline & & 2 & 5 \end{array}$$

Step 4: Add the Hundreds Finally, add the hundreds column, including the new carried 1. $1 \text{ (carried)} + 3 + 4 = 8$.

$$\begin{array}{rrrr} & \color{red}1 & \color{red}1 & \\ & 3 & 6 & 7 \\ +& 4 & 5 & 8 \\ \hline & 8 & 2 & 5 \end{array}$$

So, $367 + 458 = 825$.

More Examples

Example 1: $245 + 389$

• Ones: $5 + 9 = 14$ (Write 4, carry 1)
• Tens: $1 \text{ (carried)} + 4 + 8 = 13$ (Write 3, carry 1)
• Hundreds: $1 \text{ (carried)} + 2 + 3 = 6$
• Answer: $245 + 389 = 634$

Example 2: $506 + 297$

• Ones: $6 + 7 = 13$ (Write 3, carry 1)
• Tens: $1 \text{ (carried)} + 0 + 9 = 10$ (Write 0, carry 1)
• Hundreds: $1 \text{ (carried)} + 5 + 2 = 8$
• Answer: $506 + 297 = 803$

Remember: Always start from the ones column on the right and move to the left!