Addition with Four and Five Digit Numbers

Adding four-digit (like $3{,}456$) and five-digit numbers (like $12{,}345$) is just like adding smaller numbers. The secret is to keep everything organized and take it one column at a time!

The Golden Rule: Line Up the Digits

Always stack your numbers vertically before you add. Make sure the ones are over the ones, tens over tens, hundreds over hundreds, and so on. If one number is shorter than the other, make sure they are perfectly lined up on the right side.

Steps for Column Addition

1. Start on the right: Always begin adding in the ones place.
2. Add and Carry: If a column adds up to $10$ or more, write down the right digit and carry the left digit (usually a $1$) to the top of the next column to the left.
3. Move left: Continue adding column by column (tens, hundreds, thousands, ten thousands), making sure to include any carried numbers in your addition.

Example 1: Four-Digit Addition

Let's add $3{,}456 + 2{,}789$.

$$\begin{array}{r} 3{,}456 \\ + 2{,}789 \\ \hline 6{,}245 \end{array}$$

• Ones: $6 + 9 = 15$. Write $5$, carry $1$.
• Tens: $5 + 8 + 1 \text{ (carried)} = 14$. Write $4$, carry $1$.
• Hundreds: $4 + 7 + 1 \text{ (carried)} = 12$. Write $2$, carry $1$.
• Thousands: $3 + 2 + 1 \text{ (carried)} = 6$.

Answer: $6{,}245$

Example 2: Five-Digit Addition

Let's add $12{,}345 + 8{,}765$.

$$\begin{array}{r} 12{,}345 \\ + \phantom{0}8{,}765 \\ \hline 21{,}110 \end{array}$$

• Ones: $5 + 5 = 10$. Write $0$, carry $1$.
• Tens: $4 + 6 + 1 \text{ (carried)} = 11$. Write $1$, carry $1$.
• Hundreds: $3 + 7 + 1 \text{ (carried)} = 11$. Write $1$, carry $1$.
• Thousands: $2 + 8 + 1 \text{ (carried)} = 11$. Write $1$, carry $1$.
• Ten Thousands: $1 + 1 \text{ (carried)} = 2$.

Answer: $21{,}110$