Column addition: how it works, step by step

How do you do column addition?

To do column addition, line the numbers up by place value, draw a line underneath, and add one column at a time from right to left: ones first, then tens, then hundreds. Each column's total goes under the line in that column.

The steps are:

1. Write the numbers one under the other, with the ones lined up on the right.
2. Add the ones. Write the answer under the ones column.
3. Add the tens, then the hundreds, and so on, writing each answer underneath.
4. If a column adds up to 10 or more, write the ones digit of that total and carry the ten into the next column, as a small digit under the answer line.

Lining up matters because each column holds one kind of number. The 3 in 324 is 3 hundreds, so it can only be added to other hundreds. If place value still feels shaky, our place value guide is a good place to start.

Column addition with no carrying

The simplest column addition has no column that adds up to 10 or more. Here is 324 + 152:

1. Add the ones: 4 + 2 = 6. Write 6 in the ones column.
2. Add the tens: 2 + 5 = 7. Write 7 in the tens column.
3. Add the hundreds: 3 + 1 = 4. Write 4 in the hundreds column.

Schools encourage children to say what each column is worth: "4 ones plus 2 ones is equal to 6 ones, 2 tens plus 5 tens is equal to 7 tens". That language keeps the value of each digit in view, the same idea as partitioning a number into hundreds, tens and ones.

Column addition with carrying

When a column adds up to 10 or more, there are too many to fit in that column, so the extra ten moves into the next column. This is called carrying (some teachers call it regrouping). Here is 347 + 225:

1. Add the ones: 7 + 5 = 12. That's 1 ten and 2 ones: write 2 in the ones column and carry 1 into the tens column.
2. Add the tens: 4 + 2 + 1 = 7 (including the 1 ten carried). Write 7 in the tens column.
3. Add the hundreds: 3 + 2 = 5. Write 5 in the hundreds column.

The 7 ones and 5 ones make 12 ones, which is 1 ten and 2 ones. The 2 stays in the ones column and the 1 ten is carried. Then the tens column has 4 + 2 + 1, including the carried ten.

The carried digit is written small under the answer line, under the column it is going into. Some schools write it in a different spot, so follow what your child's class does.

Column addition examples with bigger numbers

The method doesn't change for bigger numbers: there are just more columns. Year 4 children use column addition with four-digit numbers, like 3,658 + 2,475, which carries in three columns:

1. Add the ones: 8 + 5 = 13. That's 1 ten and 3 ones: write 3 in the ones column and carry 1 into the tens column.
2. Add the tens: 5 + 7 + 1 = 13 (including the 1 ten carried). That's 1 hundred and 3 tens: write 3 in the tens column and carry 1 into the hundreds column.
3. Add the hundreds: 6 + 4 + 1 = 11 (including the 1 hundred carried). That's 1 thousand and 1 hundred: write 1 in the hundreds column and carry 1 into the thousands column.
4. Add the thousands: 3 + 2 + 1 = 6 (including the 1 thousand carried). Write 6 in the thousands column.

In Year 5, children add numbers with more than 4 digits in exactly the same way.

Adding three numbers in columns

Column addition works for more than two numbers. Write all three underneath each other and add down each column. Government guidance suggests adding the digits in whichever order is easiest, such as looking for pairs that make 10. Here is 127 + 43 + 49:

1. Add the ones: 7 + 3 + 9 = 19. That's 1 ten and 9 ones: write 9 in the ones column and carry 1 into the tens column.
2. Add the tens: 2 + 4 + 4 + 1 = 11 (including the 1 ten carried). That's 1 hundred and 1 ten: write 1 in the tens column and carry 1 into the hundreds column.
3. Add the hundreds: 1 + 1 = 2 (including the 1 hundred carried). Write 2 in the hundreds column.

In the ones column, 7 + 3 makes 10, so adding those first and then the 9 gives 19 quickly.

Adding decimals in columns

From Year 5, children add decimals in columns too, and the key rule is to line up the decimal points. Ones go under ones, tenths under tenths and hundredths under hundredths, and the decimal point in the answer goes straight below the others. The method then works just as it does for whole numbers.

For 4.75 + 2.6, it helps to write 2.6 as 2.60 so both numbers have the same number of decimal places. Then add the hundredths (5 + 0), the tenths (7 + 6 = 13, so write 3 and carry 1 into the ones) and the ones (4 + 2 + 1). The answer is 7.35. We don't have a drawn diagram for decimals yet, so this one is in words.

Estimating and checking the answer

Before working it out, children estimate the answer by rounding. For 347 + 225, round to 350 + 230 = 580. The answer, 572, is close to that, so it's likely to be right. If the written answer came out as 5,072 or 472, the estimate would show something had gone wrong.

After working it out, they check using the inverse. Subtraction undoes addition, so take one of the numbers away from the answer and you should get the other: 572 − 225 = 347. That uses column subtraction, which children learn alongside column addition. Adding the numbers in a different order is another check.

When is column addition taught?

Column addition is taught in Year 3, with numbers up to three digits. The curriculum then moves to four digits in Year 4 and more than four digits in Year 5, and children keep using it in Year 6.

Some schools let Year 2 children set out two-digit sums in columns with counters or dots, to get them thinking in tens and ones, but the formal method isn't expected until Year 3. Before then, children need to know their number bonds and the addition facts that cross 10, like 8 + 6 = 14, because every column uses them.

Column addition isn't always the best choice. Government guidance gives 164 + 36 as an example: 64 and 36 make 100, so the answer is 200 without writing anything down. A number line or mental partitioning is often quicker for small sums.

Common column addition mistakes

• Lining up from the left. For 1,245 + 32, writing 32 under the 1 and 2 gives 4,445 instead of 1,277. Always line up the ones on the right.
• Forgetting the carried digit. In 347 + 225, writing 2 in the ones but forgetting to add the carried ten gives 562 instead of 572.
• Writing the whole column total. Writing 12 in the ones column instead of writing 2 and carrying 1.
• Starting from the left. Adding the hundreds first means carries land in columns already finished. Start with the ones.
• Slow column facts. Counting on fingers in every column makes slips more likely. Quick recall of facts like 7 + 5 helps more than anything else.

How to help at home

• Use squared paper. One digit per square keeps the columns straight.
• Ask for the estimate first. "About how much will it be?" before any working out.
• Use money. Adding prices with £1, 10p and 1p coins shows carrying in action: ten 1p coins swap for one 10p.
• Practise the facts. Quick-fire addition facts within 20 make every column faster.
• Follow the school's layout. Ask your child to show you where they write the carried digit, and stick to that.

Column addition questions to try

1. 243 + 516
2. 368 + 275
3. 4,586 + 2,739
4. 156 + 87 + 39
5. 5.4 + 3.75
6. A school raised £158 at a cake sale and £267 at a fair. How much did it raise altogether?

Answers

1. 759 (no carrying)
2. 643
3. 7,325
4. 282
5. 9.15 (write 5.4 as 5.40 and line up the decimal points)
6. £425

For the rest of these years, see the Year 3 maths, Year 4 maths and Year 5 maths guides, or the KS2 maths overview.