Column Addition

What you will learn

• Line up numbers by place value.
• Add in columns, carrying when needed.
• Check an answer by estimating.

Before you start: you should know place value and how to round. See Place Value to a Million and Rounding and Estimating.

The idea

Adding in your head works for small numbers. For bigger ones, the column method keeps things tidy. It uses place value: ones are added to ones, tens to tens, and so on.

Line up the digits

Write the numbers one under the other with the ones in the same column on the right. Put the plus sign on the left and draw a line under the numbers.

Start with the ones column on the right and work left. Write each column’s total in the answer row.

Carrying

If a column adds to ten or more, you cannot fit it in one digit. Write the ones digit of the total and carry the tens digit to the next column on the left.

The carried digit is a ten (or a hundred) in disguise. Remember to add it in when you reach the next column.

Numbers of different lengths

If one number is shorter, still line up the ones. Imagine empty places as zeros.

Check by estimating

Round each number and add the rounded numbers. $4658 + 736 \approx 4700 + 700 = 5400$. The exact answer, $5394$, is close, so it is believable.

Worked examples

Example 1: With a carry

Work out $587 + 246$.

1. Ones: $7 + 6 = 13$. Write $3$, carry $1$.
2. Tens: $8 + 4 + 1 = 13$. Write $3$, carry $1$.
3. Hundreds: $5 + 2 + 1 = 8$.

Answer: $833$.

Example 2: A zero in the middle

Work out $305 + 296$.

1. Ones: $5 + 6 = 11$. Write $1$, carry $1$.
2. Tens: $0 + 9 + 1 = 10$. Write $0$, carry $1$.
3. Hundreds: $3 + 2 + 1 = 6$.

Answer: $601$.

Example 3: Add and check

Work out $1{,}478 + 3{,}965$ and check by estimating.

1. Ones: $8 + 5 = 13$, write $3$, carry $1$.
2. Tens: $7 + 6 + 1 = 14$, write $4$, carry $1$.
3. Hundreds: $4 + 9 + 1 = 14$, write $4$, carry $1$.
4. Thousands: $1 + 3 + 1 = 5$. Total $5{,}443$.
5. Estimate: $1500 + 4000 = 5500$. Close to $5443$.

Answer: $5{,}443$.

The most common slip is not lining up the ones. Always start with ones under ones, not with the left edges lined up.

Why it matters

Column addition is the way we add large totals: bills, scores, distances. The same layout is used for decimals and money, and the carrying idea comes back in column multiplication.