Written Column Addition

Column addition lines up numbers by place value and adds from right to left, carrying any overflow into the next column.

What Is Column Addition?

Column addition is a written method for adding large numbers. You line the numbers up so that ones are under ones, tens are under tens, and so on, then work from right to left.

Column Addition Rule

\text{ones} \to \text{tens} \to \text{hundreds} \to \ldots

Always start from the rightmost column (ones) and move left. Carry any digit greater than 9 into the next column.

Step-by-Step Method

1
Write the numbers in columns
Line up the digits by place value — ones under ones, tens under tens, hundreds under hundreds, and so on. Draw a line underneath.
2
Add the ones column
Add the digits in the ones column. If the sum is 10 or more, write the units digit below the line and carry the tens digit into the tens column above.
3
Add the tens column
Add the tens digits together with any carried digit. Again carry if the sum reaches 10 or more.
4
Continue left
Repeat for hundreds, thousands, and so on until all columns are done.
5
Write the final answer
The digits below the line (plus any final carry) form your answer.

Worked Example

Calculate 47 386 + 25 947

Write the numbers in columns:

  47 386
+ 25 947
--------

Ones: 6 + 7 = 13 → write 3, carry 1

Tens: 8 + 4 + 1 (carry) = 13 → write 3, carry 1

Hundreds: 3 + 9 + 1 (carry) = 13 → write 3, carry 1

Thousands: 7 + 5 + 1 (carry) = 13 → write 3, carry 1

Ten-thousands: 4 + 2 + 1 (carry) = 7 → write 7

Result: 73 333

Tip Always double-check your column alignment before you start. A misaligned digit is the most common source of errors in column addition.

Real-World Applications

Real world: adding travel distances

A school trip covers three legs: 12 450 m from school to the museum, 8 620 m from the museum to the park, and 5 830 m back to school. What is the total distance?

  12 450
   8 620
+  5 830
--------

Ones: 0 + 0 + 0 = 0

Tens: 5 + 2 + 3 = 10 → write 0, carry 1

Hundreds: 4 + 6 + 8 + 1 = 19 → write 9, carry 1

Thousands: 2 + 8 + 5 + 1 = 16 → write 6, carry 1

Ten-thousands: 1 + 1 = 2

Total distance: 26 900 m

Real world: adding prices

A bicycle costs 189 €, a helmet costs 34 € and a lock costs 22 €. How much does the shopper pay altogether?

  189
   34
+  22
----

Ones: 9 + 4 + 2 = 15 → write 5, carry 1

Tens: 8 + 3 + 2 + 1 = 14 → write 4, carry 1

Hundreds: 1 + 1 = 2

Total: 245 €

Real world: adding populations

Three villages have 3 420, 1 875, and 2 308 inhabitants. Find the total population.

  3 420
  1 875
+ 2 308
-------

Ones: 0 + 5 + 8 = 13 → write 3, carry 1

Tens: 2 + 7 + 0 + 1 = 10 → write 0, carry 1

Hundreds: 4 + 8 + 3 + 1 = 16 → write 6, carry 1

Thousands: 3 + 1 + 2 + 1 = 7

Total population: 7 603

Common Mistakes

Writing digits in the wrong column (e.g. putting a two-digit sum directly without carrying)
Forgetting to add the carried digit
Not aligning numbers by place value when they have different numbers of digits

Practice Problems

Calculate 36 524 + 47 839.

Show answer

Ones: 4+9=13, write 3 carry 1. Tens: 2+3+1=6. Hundreds: 5+8=13, write 3 carry 1. Thousands: 6+7+1=14, write 4 carry 1. Ten-thousands: 3+4+1=8. Answer: 84 363.

A bookshop sold 1 248 books in March, 2 075 in April, and 1 936 in May. How many books were sold altogether?

Show answer

1 248 + 2 075 + 1 936 = 5 259 books.