Division for 11+ and KS2: Methods, worksheets and worked examples
Division is the operation children find hardest to get fluent with, and it's the one 11+ papers lean on heavily. Most multi-step word problems, ratio questions and fraction questions hide a division inside them.
This guide covers the three methods children need by Year 6: Mental division, short division (the bus stop method) and long division. Each one comes with a worked example you can sit down and do together, plus a quick guide to choosing the right method for a given question.
What division looks like at KS2
By the end of Year 6, children are expected to divide up to four-digit numbers by one or two-digit numbers using formal written methods, interpret remainders sensibly in context, and use division alongside the other three operations in multi-step problems. The national curriculum sets this out in the KS2 programme of study for mathematics.
The build-up across Years 3 to 6 is gradual. Year 3 introduces division facts for the 3, 4 and 8 times tables. Year 4 extends this to all times tables up to 12 x 12 and introduces remainders. Year 5 brings in short division for up to four-digit numbers. Year 6 adds long division for two-digit divisors and asks children to interpret remainders as fractions, decimals or rounded values depending on context.
Times tables are the rate-limiting step for division. If your child isn't fluent up to 12 x 12, fix that first. No amount of long division practice will compensate for slow recall of basic facts.
Mental division: When and how to use it
Mental division works when the numbers are small, the divisor is a known times table, or the calculation can be simplified by partitioning. It's the fastest method when it applies, and 11+ papers reward children who recognise when they can skip the written method entirely.
The most useful mental technique is partitioning. To divide 84 by 4, break 84 into 80 + 4. Divide each part: 80 / 4 = 20 and 4 / 4 = 1. Add the results: 20 + 1 = 21. The whole calculation takes a few seconds once it clicks.
For dividing by 10, 100 or 1,000, the rule is simply to move each digit one, two or three places to the right. 4,500 divided by 100 becomes 45. The decimal point stays where it is, the digits move.
Short division (the bus stop method)
Short division is the formal written method for dividing by a single-digit number. It works for any size of dividend and is the workhorse method at KS2.
The method in four steps. Step 1: Write the dividend (the number being divided) inside the bus stop and the divisor outside. Step 2: Working left to right, ask how many times the divisor goes into each digit. Step 3: Write the answer on top, and carry any remainder into the next digit. Step 4: Continue until you've reached the last digit, then write any final remainder.
Worked example: Short division
Divide 4,572 by 6 using short division.
Step 1: Set it out with 4,572 inside the bus stop and 6 outside.
Step 2: How many 6s in 4? Zero, remainder 4. Carry the 4 to the next column. The digits we're now working with are 45.
Step 3: How many 6s in 45? Seven, because 7 x 6 = 42. Remainder 3. Write 7 on top. Carry the 3.
Step 4: How many 6s in 37 (the 3 carried plus the 7 from the dividend)? Six, because 6 x 6 = 36. Remainder 1. Write 6 on top. Carry the 1.
Step 5: How many 6s in 12 (the 1 carried plus the 2 from the dividend)? Two exactly, no remainder. Write 2 on top.
Final answer: 4,572 / 6 = 762.
Check: 762 x 6 = 4,572. Correct.
If the question asks for an exact decimal answer instead of a remainder, continue the method past the decimal point by adding zeros to the dividend. So 4,573 / 6 would give 762 remainder 1, or 762.166... as a decimal.
Long division: For dividing by two-digit numbers
Long division is needed when the divisor has two or more digits and you can't easily hold the multiples in your head. It's the same logic as short division but with the working written out underneath rather than carried in your head.
The four-step cycle. Step 1: Divide (how many times does the divisor go into the part of the dividend you're looking at?). Step 2: Multiply (the divisor by the digit you just wrote on top). Step 3: Subtract (the result from the part of the dividend you're working with). Step 4: Bring down (the next digit of the dividend). Repeat until you've worked through every digit.
Many children find long division harder than the other methods because there's more bookkeeping. Listing the multiples of the divisor at the side before starting saves a lot of mental effort.
Worked example: Long division
Divide 1,344 by 16 using long division.
Before starting, list multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160. Having these in front of you removes most of the mental arithmetic.
Step 1: 16 doesn't go into 1 or 13. 16 goes into 134 eight times (because 8 x 16 = 128, and 9 x 16 = 144 is too big). Write 8 above the 4 of 134.
Step 2: Multiply. 8 x 16 = 128. Write 128 underneath 134.
Step 3: Subtract. 134 - 128 = 6.
Step 4: Bring down the next digit (4) to make 64.
Step 5: How many 16s in 64? Exactly 4 (because 4 x 16 = 64). Write 4 on top.
Step 6: Subtract. 64 - 64 = 0. No remainder.
Final answer: 1,344 / 16 = 84.
Check: 84 x 16. (80 x 16) + (4 x 16) = 1,280 + 64 = 1,344. Correct.
The most common slip in long division is forgetting to bring down the next digit. If your child ends up with an answer that's roughly a tenth of what it should be, that's usually what's happened.
How to interpret remainders
11+ and KS2 papers often ask children to give the remainder in a particular form, or to interpret what it means in context. There are four possibilities and each one comes up.
As a whole number remainder: 17 / 5 = 3 remainder 2. This is the default if the question doesn't specify.
As a fraction: 17 / 5 = 3 and 2/5. The remainder becomes the numerator, the divisor becomes the denominator.
As a decimal: 17 / 5 = 3.4. Continue the division past the decimal point.
In context: A class of 47 children is split into teams of 6. How many teams can be made? 47 / 6 = 7 remainder 5. Seven full teams. The 5 left over can't form a complete team, so the answer is 7.
Read the question carefully before deciding what to do with a remainder. If a question asks how many minibuses are needed for 50 children when each minibus holds 12, the answer is 5 (you have to round up), not 4 (you can't leave children behind).
Which method to use, when
| Situation | Best method | Why |
|---|---|---|
| Dividing by 2, 5, 10 or a single-digit number with a small dividend | Mental | Times tables knowledge alone gives the answer in seconds |
| Dividing by 10, 100 or 1,000 | Mental (place value shift) | Move digits to the right, no calculation needed |
| Dividing a multi-digit number by a single-digit divisor | Short division | Quickest formal method when the divisor is small |
| Dividing by a two-digit number | Long division | Short division gets unreliable past single digits; long division keeps the working visible |
| Word problem with an unclear divisor | Read first, then choose | Don't pick a method until you've worked out what the question is asking |
Common mistakes to look out for
The most frequent error in short division is forgetting to carry the remainder to the next column, or carrying it as a digit rather than tucking it next to the next digit of the dividend. Writing the carried number small and to the left of the next digit (not above) helps.
In long division, the bookkeeping fails when children stop writing each step underneath the last. Lined paper or grid paper helps with alignment.
In mental division, the trap is partitioning incorrectly. 84 / 4 partitions cleanly because both 80 and 4 divide by 4. 86 / 4 doesn't partition that way (because 6 doesn't divide by 4). For 86 / 4, you'd partition into 80 + 6, get 80 / 4 = 20 and 6 / 4 = 1 remainder 2, giving 21 remainder 2. Children who don't see the issue often try to force the partition and get a wrong answer with no remainder.
How to practise division at home
Building division fluency in Years 5 and 6
What to focus on in the months before an 11+ paper.
- Times tables up to 12 x 12 with sub-three-second recall (the bottleneck for everything else)
- Ten short division questions a week, mixing two-digit, three-digit and four-digit dividends
- Five long division questions a week once short division is solid, starting with two-digit divisors that divide cleanly
- Two or three mixed word problems a week that include a division step but don't say so explicitly
- Always write a check at the end (multiply the answer by the divisor, see if you get back to the dividend)
- Practise interpreting remainders four ways: As a whole number, fraction, decimal, and in context
- Mark together but don't correct as your child works, let them finish first
Free KS2 division worksheets are widely available from the DfE, Primary Maths Challenge, NRICH and exam-board sample papers. You don't need paid resources at this stage. Pick one source and stick to it rather than scattering across many.
