Year 6 maths · Key Stage 2 · Number – addition, subtraction, multiplication and division

Year 6 long multiplication and long division: a guide for parents

Year 6 is where children finish learning the formal written methods for the four operations. They multiply numbers of up to four digits by a two-digit number using long multiplication, and divide numbers of up to four digits by a two-digit number using long division, deciding what to do with any remainder. They also keep building quick mental calculation, because a written method is only useful if the answer can be checked for sense.

Long multiplication and division, explained

Long multiplication is the method for something like 1,346 × 23. Instead of one multiplication, the child does two and adds them. First they multiply by the 3 ones, then by the 2 tens, which really means 20, so the second row starts with a zero written as a placeholder in the ones column. So 1,346 × 3 = 4,038 and 1,346 × 20 = 26,920, and adding the two rows gives 30,958. Each row is the short multiplication they met in Year 4, and children first used long multiplication in Year 5, so Year 6 is about using it confidently with larger numbers.

Long division is the method for dividing by a two-digit number, such as 1,230 ÷ 24. Children work from the left, asking how many 24s fit into the first digits, writing that digit above the line, subtracting, and bringing down the next digit. Most children find it much easier if they first write out a short list of multiples of the divisor (24, 48, 72, 96, 120 and so on), built up by doubling or adding. Then each step is a look-up, not a guess.

Short division is the compact version, where the subtraction is done in the head and any remainder is passed on to the next digit as a small number. The programme of study says to use it “where appropriate”. In practice many schools use it for divisors up to 12 and long division for larger two-digit divisors, but the choice belongs to the school, so ask which your child has been shown.

The statutory objectives also ask children to interpret remainders in three ways: as a whole-number remainder, as a fraction, or by rounding, depending on the question. 29 stickers shared between 4 children is 7 each with 1 left over. 29 metres of ribbon cut into 4 equal pieces is 7 1/4 metres each. 29 children needing lifts in cars that take 4 means 8 cars, because 7 cars would leave one child behind. Reading the context is part of the maths.

Mental calculation continues alongside all this, with larger numbers and mixed operations: 4,500 ÷ 90, 25 × 48 worked out as 100 × 12, or 3,000 − 1,874 by counting up. Fluent times tables underpin everything here. Children are taught to estimate first, rounding 1,346 × 23 to about 1,300 × 20 = 26,000, so that an answer ten times too big or too small shows up straight away. This checking habit matters as much as the written method itself.

Words your child will hear

Dividend: The number being divided. In 1,230 ÷ 24 it is 1,230.
Divisor: The number you divide by. In 1,230 ÷ 24 it is 24.
Quotient: The answer to a division, not including any remainder.
Remainder: What is left over when the divisor does not go into the number exactly.
Placeholder: A zero written to keep digits in the correct column, as in the second row of a long multiplication.
Partial product: One of the rows in a long multiplication, such as the answer to multiplying by the ones.
Inverse: The opposite operation, used to check: multiply the quotient by the divisor and add the remainder.

What the National Curriculum says

In Year 6, pupils should be taught to:

Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
Perform mental calculations, including with mixed operations and large numbers

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

A shop has 1,230 pencils to pack into boxes of 24. How many boxes are needed to hold every pencil?

Estimate first. 1,230 is close to 1,200, and 1,200 ÷ 24 = 50, so the answer should be around 50.
Write the multiples of 24 beside the sum so they are ready: 24, 48, 72, 96, 120, 144, 168, 192, 216.
24 does not go into 1 or into 12, so look at 123. The biggest multiple not over 123 is 120, which is 5 × 24. Write 5 above the 3, subtract 120 from 123 and leave 3.
```
            5
   24 ) 1 2 3 0
      − 1 2 0
        -----
            3
```
Bring down the 0 to make 30. 24 goes into 30 once, so write 1 above the 0. Subtract: 30 − 24 = 6. There are no more digits to bring down, so 6 is the remainder.
```
            5 1  r 6
   24 ) 1 2 3 0
      − 1 2 0
        -----
            3 0
          − 2 4
            ---
              6
```
Check with the inverse: 51 × 24 = 1,224, and 1,224 + 6 = 1,230. This matches the estimate too.
Now read the question. 51 boxes hold 1,224 pencils, so 6 pencils are still left. They need a 52nd box, so the remainder is dealt with by rounding up.

1,230 ÷ 24 = 51 remainder 6, so 52 boxes are needed.

Common mistakes and how to help

Forgetting the placeholder zero in long multiplication

When multiplying by the tens digit, the child writes the first digit of the answer in the ones column, so 346 × 20 comes out ten times too small.

What helps: Say the real value of the digit aloud: “I’m multiplying by twenty, not two.” Writing the zero first, before any other digit in that row, turns it into a habit. An estimate will also show that the answer is far too small.

Missing a zero in the answer to a division

If the divisor does not go into a digit, some children skip it, so 1,224 ÷ 12 becomes 12 instead of 102.

What helps: Remind them that every digit brought down needs an answer above it, even a 0. Multiplying back (12 × 102 = 1,224) and comparing with an estimate of about 100 catches this quickly.

Giving every remainder as “r” whatever the question asks

Practice sums nearly always end in “remainder 6”, so children stop reading the context and do not notice when a lift, a minibus or a box means rounding up.

What helps: Ask “What would really happen?” before they write the answer. Make up the same division in three settings (sharing sweets, cutting ribbon, booking cars) and compare the answers.

A remainder that is as big as, or bigger than, the divisor

The child picks a multiple that is too small, so the subtraction leaves, say, 28 when dividing by 24. They then carry on regardless.

What helps: Teach the check: whatever is left after each subtraction must be smaller than the divisor. If it is not, the digit above the line can go up by one. The list of multiples makes this easy to see.

How to help at home

Make a multiples list together. Pick a two-digit number such as 18 and build its first nine multiples by doubling and adding. Keep the list on paper. It makes long division far more manageable, and building it is good times-table practice in itself.
Estimate before every calculation. Before your child writes a long sum, ask “About how big should the answer be?” Rounding 37 × 42 to 40 × 40 takes seconds and gives them a way to spot a missing zero or a skipped column.
Turn remainders into stories. Make up real situations with the same numbers: 100 ÷ 8 as people in cars, as metres of rope and as sweets shared out. Your child decides each time whether to round up, round down, keep a fraction or state the remainder.
Quick mental challenges. In the car or on a walk, try 60 × 70, 4,800 ÷ 60 or 25 × 36. Use the tables they know and think about moving digits and splitting numbers up. Keep it short and brisk, and talk through how they found each answer.
Keep columns tidy. Squared paper, one digit per square, makes long multiplication and division much easier to line up. Many errors in Year 6 come from untidy columns, not from the maths itself.

Updated 20 October 2026.