Column addition, subtraction and short division explained for parents
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"Carrying" is now called exchanging. So is "borrowing", although some schools say regrouping. The bus stop method is short division under a friendlier name. If your child's homework looks unfamiliar, the vocabulary has usually changed more than the maths.
Every written method rests on one idea: each column is a place value, and ten in one column is worth one in the column to its left. Exchanging is simply swapping between those two forms.
In the national curriculum for England, formal column addition and subtraction appear in Year 3, short multiplication in Year 4, and long multiplication and short division in Year 5. Long division follows in Year 6. Schools pace this differently, so look in your child's exercise book before you start explaining.
Estimate first
Before writing anything, round the numbers and work out a rough answer in your head.
- 476 + 358 is about 500 + 350 = 850
- 347 × 6 is about 350 × 6 = 2,100
If the written answer is nowhere near the estimate, something has gone wrong. This single habit catches more errors than anything else on this page.
Column addition: 476 + 358
Line the numbers up so that ones sit under ones and tens under tens. Start on the right.
- Ones: 6 + 8 = 14. Write 4 and exchange the ten into the tens column, as a small 1.
- Tens: 7 + 5 = 12, plus the exchanged 1 makes 13. Write 3 and exchange 1 into the hundreds.
- Hundreds: 4 + 3 + 1 = 8.
Answer: 834, close to the estimate of 850.
Some schools put the small exchanged digit under the answer line, others at the top of the column. Either is fine if your child is consistent.
Column subtraction: 502 − 178
This is the calculation that causes the most tears, because of the zero.
- Ones: 2 − 8 cannot be done, so we need to exchange. The tens column holds 0, so there is nothing to take from yet.
- Go to the hundreds. Exchange one hundred for ten tens: the 5 becomes 4 and the tens column now holds 10.
- Exchange one of those tens for ten ones: the tens become 9 and the ones become 12.
- Ones: 12 − 8 = 4. Tens: 9 − 7 = 2. Hundreds: 4 − 1 = 3.
Answer: 324. Check by adding: 324 + 178 = 502.
Say it in place value language as you go: "We have 5 hundreds, 0 tens and 2 ones. We're changing one hundred into ten tens." If that still feels abstract, swap a £1 coin for ten 10p coins on the table.
Short multiplication: 347 × 6
- Ones: 7 × 6 = 42. Write 2, exchange 4 into the tens.
- Tens: 4 × 6 = 24, plus 4 makes 28. Write 8, exchange 2.
- Hundreds: 3 × 6 = 18, plus 2 makes 20. Write 20.
Answer: 2,082. The estimate was about 2,100, so this looks right.
Long multiplication: 47 × 23
Long multiplication splits the second number into tens and ones, then adds the two rows.
- Multiply by the 3 ones: 47 × 3 = 141.
- Multiply by the 2 tens, which is really 20. Write a 0 in the ones column as a placeholder, then 47 × 2 = 94 beside it, giving 940.
- Add the rows: 141 + 940 = 1,081.
The placeholder zero is the step that most often goes missing. A child who writes 94 instead of 940 gets 235, and the estimate (50 × 20 = 1,000) shows straight away that this is far too small.
Short division, the bus stop: 852 ÷ 4
Short division is the one written method that starts on the left.
- How many 4s in 8? Two. Write 2 on top.
- How many 4s in 5? One, remainder 1. Write 1 on top and carry the 1 to sit in front of the 2, making 12.
- How many 4s in 12? Three.
Answer: 213. Check: 213 × 4 = 852.
When there is a remainder: 625 ÷ 4
- 6 ÷ 4 = 1 remainder 2. Carry the 2 to make 22.
- 22 ÷ 4 = 5 remainder 2. Carry the 2 to make 25.
- 25 ÷ 4 = 6 remainder 1.
Answer: 156 remainder 1. By Year 6, children may be asked to write this as a fraction (156¼) or a decimal (156.25), or to decide what the remainder means in context. If 625 people need cars that take 4 passengers each, you need 157 cars, not 156.
Long division (Year 6): 7,248 ÷ 24
Long division is short division with the working written out underneath, which helps when the divisor has two digits. Before starting, write the first few multiples of 24 down the side: 24, 48, 72, 96, 120. It saves a lot of guessing.
- 7 ÷ 24 is 0, so look at the first two digits instead: 72 ÷ 24 = 3, because 3 × 24 = 72. Write 3 on top, write 72 under the 72 and subtract: 0.
- Bring down the 4. 4 ÷ 24 = 0, so write 0 on top. The remainder is still 4.
- Bring down the 8 to make 48. 48 ÷ 24 = 2. Write 2 on top; 48 − 48 = 0.
Answer: 302. Check: 302 × 24 = 7,248. The zero in step 2 is the one children leave out, giving 32, which an estimate (about 7,000 ÷ 25 = 280) shows cannot be right.
Decimals in columns
From Year 5, children add and subtract decimals with the same column method. The one rule that matters is that the decimal points line up, one under the other.
4.6 + 2.75. Write 4.6 as 4.60 so both numbers have two decimal places. Then add as normal from the right: 0 + 5 = 5, 6 + 7 = 13 (write 3, exchange 1), 4 + 2 + 1 = 7. Answer: 7.35.
A child who lines up the right-hand digits instead (6 under 5) gets 3.21, which is smaller than one of the numbers being added. The estimate, about 5 + 3 = 8, gives it away.
The mistakes that come up most
| What you see | What went wrong | What helps |
|---|---|---|
| 502 − 178 = 476 | Took the smaller digit from the bigger one in each column | Ask "Which number is on top?" before each column |
| 1,250 + 87 = 9,950 | Lined the numbers up on the left | Squared paper, one digit per square |
| 47 × 23 = 235 | Missed the placeholder zero | Write the 0 before multiplying by the tens |
| Exchanged digit ignored | Small digit written but forgotten | Cross it out once it has been used |
| Slow, effortful 7 × 6 | Times tables not yet secure | Short daily recall practice |
The last row matters more than it looks. If a child is counting on fingers for 7 × 6, the method collapses under the effort. Our weekly times tables plan is the best fix.
Five to try together
Estimate first, use the written method, then check with the inverse.
- 368 + 457
- 701 − 246
- 238 × 7
- 36 × 24
- 936 ÷ 8
Answers: 1) 825 2) 455 3) 1,666 4) 864 5) 117
When an answer is wrong, do not correct the whole thing. Ask your child to talk you through it column by column and stop at the step where it slipped. That tells them exactly what to fix.
It also helps to know when not to use a written method. 300 + 450 or 99 × 3 are quicker in your head. A good question for any calculation is "Do I need to write this down?"
If maths homework regularly ends in upset, our article on a child who says "I'm bad at maths" sits well alongside this one.
Sources and further reading
- National curriculum in England: mathematics programmes of study – the statutory content for each year group, including when each written method is introduced.
- Key stage 2: mathematics test framework – how the Year 6 arithmetic and reasoning papers are designed.
- National curriculum assessments: past test materials – recent KS2 arithmetic papers, useful for seeing the layouts children meet.
