• Key Stage 2 • Maths
Long multiplication is the formal written method for multiplying by a two-digit number. Pupils learn it in Year 5 and use it with numbers up to 4 digits in Year 6. It appears in the KS2 arithmetic paper every year. This guide explains the method step by step, with worked examples, practice questions and answers.
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The Quick Answer
- Long multiplication is a written method for multiplying by a two-digit number, such as 346 × 27.
- You multiply by the ones digit, then by the tens digit, then add the two answers.
- When multiplying by the tens digit, put a 0 in the ones column first, because you are multiplying by a multiple of 10.
- In the KS2 arithmetic paper, long multiplication questions are worth 2 marks.
When Pupils Learn Long Multiplication
| Year | What the national curriculum says |
|---|---|
| Year 4 | Multiply two-digit and three-digit numbers by a one-digit number using a formal written layout |
| Year 5 | Multiply numbers up to 4 digits by a one- or two-digit number, including long multiplication for two-digit numbers |
| Year 6 | Multiply multi-digit numbers up to 4 digits by a two-digit whole number using long multiplication |
How to Do Long Multiplication
- Write the larger number on top and the two-digit number underneath, lined up by place value.
- Multiply the top number by the ones digit. Write the answer on the first row.
- Write a 0 in the ones column of the second row. Then multiply the top number by the tens digit.
- Add the two rows together.
Worked Example: 346 × 27
| Step | Working | Result |
|---|---|---|
| 1 | Multiply by the 7 ones: 346 × 7 | 2,422 |
| 2 | Multiply by the 2 tens: 346 × 20 | 6,920 |
| 3 | Add the two rows: 2,422 + 6,920 | 9,342 |
Answer: 346 × 27 = 9,342.
Worked Example: 2,356 × 48
| Step | Working | Result |
|---|---|---|
| 1 | Multiply by the 8 ones: 2,356 × 8 | 18,848 |
| 2 | Multiply by the 4 tens: 2,356 × 40 | 94,240 |
| 3 | Add the two rows: 18,848 + 94,240 | 113,088 |
Answer: 2,356 × 48 = 113,088. Check by estimating: 2,356 is about 2,400 and 48 is about 50. 2,400 × 50 = 120,000, so the answer is sensible.
Tip: estimate first. Rounding both numbers gives a rough answer, so you can spot a mistake such as a missing zero straight away.
Long Multiplication Practice Questions
- 24 × 13
- 56 × 34
- 128 × 25
- 347 × 46
- 615 × 38
- 1,206 × 17
- 2,453 × 36
- 3,089 × 52
- A theatre has 48 rows of 26 seats. How many seats are there?
- A school orders 135 packs of pencils. Each pack has 24 pencils. How many pencils is that?
Show the answers
- 312
- 1,904
- 3,200
- 15,962
- 23,370
- 20,502
- 88,308
- 160,628
- 1,248 seats
- 3,240 pencils
Long Multiplication in the KS2 Arithmetic Paper
Long multiplication questions in the KS2 arithmetic paper are worth 2 marks. The mark schemes show that if the final answer is wrong, pupils can still get 1 mark for using the formal method of long multiplication with no more than one arithmetic error. The working must be written under the question to count. Practise with our Year 6 arithmetic questions.
Common Mistakes
- Forgetting the zero: when multiplying by the tens digit, the 0 in the ones column is essential. Without it, the second row is 10 times too small.
- Carrying errors: write carried digits small and clearly. Add them after multiplying.
- Adding the rows wrongly: line up the two rows carefully before adding.
- Times tables gaps: most mistakes come from multiplication facts, so quick recall helps. See our 7 times table and 12 times table guides.
Frequently Asked Questions
What year do children learn long multiplication?
Long multiplication for two-digit numbers is in the Year 5 national curriculum. In Year 6 pupils use it with numbers up to 4 digits.
Why do you put a zero in long multiplication?
Because the second row multiplies by the tens digit. Multiplying by 20 is the same as multiplying by 2 and then by 10, so the 0 holds the ones place.
How many marks is long multiplication in the SATs?
2 marks. Pupils can get 1 mark for a correct formal method with no more than one arithmetic error.
Is the grid method accepted in the SATs?
The marks for method in the arithmetic paper are given for the formal method of long multiplication, so pupils should practise that layout.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study, including Mathematics Appendix 1; Standards and Testing Agency, 2025 KS2 mathematics test mark schemes. Practice questions written by Monster Learning.
