The three ways to divide on paper
In English schools children meet three written methods for division, each used at a different stage: chunking (an informal stepping stone), the bus stop method — the formal name for short division — and long division for bigger divisors. They all give the same answer; they differ in how much you write down.
This guide explains all three in plain steps, then shows exactly how the British layout differs from the one used in Italy, Spain, France and Germany — the same maths, written in a completely different shape.
The words: dividend, divisor, quotient, remainder
Before the method, the vocabulary. Every division uses the same four words, and knowing them makes every step easier to follow. We will use 98 ÷ 7 = 14 as the example.
The number being divided — the amount you are sharing out.
The number you divide by — how many groups, or how big each group is.
The answer — how many times the divisor "goes into" the dividend.
What is left over when the divisor does not fit a whole number of times.
The phrase teachers use is "goes into": in 98 ÷ 7 we ask "how many times does 7 go into 9?", then "into 28?". The check is always the same: divisor × quotient + remainder = dividend.
The bus stop method is the formal name for short division. It is the everyday UK method for dividing by a one-digit number, mastered in Year 5. It is called "bus stop" because of the shape you draw: the dividend sits inside, like a bus waiting at the stop.
How to set it out
- Write the dividend inside the bus stop.
- Write the divisor to the left, outside the bus stop.
- The quotient goes on top, one digit above each column.
- Work left to right (unlike addition and subtraction, which start from the right).
Worked example: 98 ÷ 7.
A second example with a remainder left at the end: 432 ÷ 5.
The small carried digit is written in front of the next number: the "3" left over from 43 turns the next "2" into "32". That little carry is the whole trick of short division.
When the divisor has two digits, the remainders get too big to carry in your head, so every step is written out. This is long division, taught in Year 6. It uses the same shape as the bus stop, but you write the multiplication and subtraction underneath.
Divide
How many times does the divisor fit into the digits so far? Write it on top.
Multiply
Multiply that quotient digit by the divisor.
Subtract
Subtract the product to find the partial remainder.
Bring down
Bring down the next digit and start again.
Worked example: 432 ÷ 15.
The cycle never changes: Divide → Multiply → Subtract → Bring down. The hardest part is the first step — estimating how many times a two-digit number fits. A quick way: round 15 to 15, and ask "how many 15s in 43?" Two 15s are 30, three would be 45 (too big), so the digit is 2.
Chunking (also called partial quotients) is an informal method based on repeated subtraction. It is often taught in Years 4–5 as a bridge to formal methods, because it only uses the times-table facts a child already knows confidently.
Worked example: 132 ÷ 8
Take away easy "chunks" of 8 and keep track of how many lots you remove:
- 132 − 80 (that's 10 lots of 8) = 52
- 52 − 40 (that's 5 lots of 8) = 12
- 12 − 8 (that's 1 lot of 8) = 4
- Add the lots: 10 + 5 + 1 = 16, and 4 is left over.
132 ÷ 8 = 16 remainder 4
Chunking is slower but very forgiving: there is no single "right" chunk. A child who is unsure can subtract small, safe lots (2×, 5×, 10×) and still reach the correct answer. It makes the meaning of division — "how many groups fit?" — completely visible.
UK vs Italian/European: the same maths, a different shape
Here is the part most guides skip. The arithmetic of division is identical everywhere — every country divides, multiplies, subtracts and brings down. What changes is the layout on the page and a few classroom habits. Below is the very same calculation, 432 ÷ 15 = 28 remainder 12, written in the three main styles.
🇬🇧UK & US (Anglo-American)
Divisor on the left, dividend inside the bus stop, quotient on top. Subtractions written underneath.
🇮🇹Italy, Spain, France, Portugal
Divisor on the right, behind a vertical bar; the quotient is written below the divisor. The remainder stays bottom-left.
🇩🇪Germany, Austria, Switzerland
Written as an equation: dividend : divisor = quotient, using the colon ":" as the division sign. Subtractions run down the left.
The other real differences
| Feature | UK / US | Italy & Spain | Central Europe |
|---|---|---|---|
| Divisor position | Left, outside | Right, behind a bar | After the colon |
| Quotient position | On top | Below the divisor | After the = sign |
| Division sign | ÷ or / | : or ÷ | : (colon) |
| Times tables learnt to | ×12 | ×10 | ×10 |
| Checking trick taught | Multiply back / estimate | Casting out nines (prova del nove) | Multiply back |
| Informal method | Chunking | Less common | Less common |
| First formal year | Year 5–6 | Classe III–IV | Klasse 3–4 |
The "nines check" surprise: Italian and Spanish pupils verify a division with la prova del nove (casting out nines) — a clever digit-sum trick. It is not taught in the UK, where children instead check by multiplying the quotient back by the divisor and adding the remainder. Same goal, different habit.
What to do with the remainder
By the end of Year 6 the National Curriculum asks children to interpret remainders in three different ways, depending on the question. The same division, 432 ÷ 15, can end in three different-looking answers.
As a whole-number remainder: 432 ÷ 15 = 28 r 12. Best when you are counting whole things (e.g. "how many full boxes of 15?").
As a fraction: 28 ⅇ⁄₁₅ — the remainder over the divisor (12/15, which simplifies to 4/5).
As a decimal, or rounded: 28.8 — carry on dividing past the decimal point, or round to the nearest whole number when the context needs a tidy answer.
The exam favourite: "245 children go on a trip, each coach holds 15. How many coaches?" Here 245 ÷ 15 = 16 r 5, but you must round up to 17 — because the 5 leftover children still need a coach. The maths gives the remainder; the context decides what to do with it.
The most common mistakes
Division is the operation where one slip wrecks everything after it, because each step feeds the next. These are the four that trip children up most.
Forgetting the carry (bus stop)
In short division the child writes the digit on top but forgets to carry the remainder to the next column, so "43" becomes "3" and the answer collapses.
A quotient digit too big
Guessing 3 instead of 2 in long division: the product is larger than the digits above, and the subtraction "can't be done". The clue to go back a step.
Forgetting to bring down
After subtracting, the next digit of the dividend is not brought down, so the quotient ends up with a missing digit (and is ten times too small).
Dropping the place value
Not lining the quotient digits up over the right columns, or skipping a needed zero (e.g. in 8 ÷ 4 inside a bigger number), which shifts every later digit.
How Matematt helps the child master division
Matematt guides division one cell at a time, so a wrong step is caught before it spreads. The app adapts to the child's curriculum — UK, US, Italian or Spanish — so the layout, the times-table range and the optional checks all match what they see at school.
The right layout for the child
Pick the curriculum and the on-screen division uses the matching shape and vocabulary — bus stop for UK learners, the bar layout for Italian and Spanish ones.
One cell at a time
The app asks only for the digit needed right now and flags it instantly if it is wrong, so an early slip never snowballs through the whole calculation.
Divide · Multiply · Subtract · Bring down
Each step is named as the child does it, so the repeating cycle of long division becomes a habit rather than a mystery.
Checks that fit the country
Where it belongs in the curriculum, Matematt even teaches the optional casting-out-nines check step by step — without ever forcing it on UK learners.
Division practice problems
Work up through the methods: short division first, then a remainder, then long division, then a chunking warm-up. Saying each step out loud helps it stick.
Bus stop, exact
96 ÷ 4
9÷4 = 2 r 1, carry to 16÷4 = 4. Answer 24.Bus stop, remainder
74 ÷ 5
Answer 14 remainder 4. Practises carrying and a leftover.Long division
864 ÷ 24
Two-digit divisor: estimate, multiply, subtract, bring down. Answer 36.Chunking warm-up
175 ÷ 8
Subtract lots of 8 (80, 80, then 8s). Answer 21 remainder 7.Frequently asked questions about division
What is the bus stop method?
It is the UK name for short division. The dividend sits inside a "bus stop" shape, the divisor is outside on the left, and the answer goes on top. You divide each digit from left to right, carrying any remainder as a small digit to the next column.
What's the difference between short and long division?
Short division (bus stop) is for one-digit divisors and carries remainders mentally; long division is for two-digit divisors and writes every multiplication and subtraction out. In England short division is mastered in Year 5, long division in Year 6.
How is UK division different from the Italian or European method?
The maths is the same; only the layout changes. UK and US put the divisor on the left and the quotient on top. Italy, Spain, France and Portugal put the divisor on the right behind a bar, with the quotient below it. Germany and Austria write it as an equation, dividend : divisor = quotient. Italian and Spanish pupils also use the casting-out-nines check, which UK schools don't teach.
What is the chunking method?
An informal method using repeated subtraction: take away easy multiples (chunks) of the divisor and add up how many lots you removed. For 132 ÷ 8 you subtract 80 (10 lots), 40 (5 lots) and 8 (1 lot), leaving 4 — so 16 remainder 4.
When is division taught in UK primary school?
Sharing and grouping in Years 1–2, written strategies and chunking in Years 3–4, the formal bus stop method for one-digit divisors in Year 5, and formal long division for two-digit divisors in Year 6 — including interpreting remainders as whole numbers, fractions, or by rounding.