Long Multiplication: Step by Step
Long multiplication multiplies the top number by each digit of the bottom number and adds the rows. Appendix 1 of the National Curriculum sets out 124 × 26 with the tens row first (124 × 20 = 2480) and the ones row second (124 × 6 = 744).
The worked example below follows that layout.
When is it taught?
- Year 4: multiply two-digit and three-digit numbers by a one-digit number using 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.
Worked example: 124 × 26
124×26
124×2624807443224
Left: the problem. Right: the worked answer, as in our answer keys.
Step by step
- 1Multiply by the tens digit: 124 × 20 = 2480. The 0 keeps each digit in its place.
- 2Multiply by the ones digit: 124 × 6 = 744.
- 3Add the partial products: 3224.
- 4Estimate to check: 100 × 30 = 3000, close to 3224.
Common mistakes
- Multiplying by the tens digit as if it were ones (124 × 2 instead of 124 × 20).
- Misaligning the rows before adding them.
- Estimating first: 100 × 30 = 3000 shows 3224 is about the right size.
Multiplication worksheets
- 3-digit × 1-digit short multiplicationYear 4 · National Curriculum Year 4
- Long multiplication: 2-digit × 2-digitYear 5 · National Curriculum Year 5
- Long multiplication: 4-digit × 2-digitYear 6 · National Curriculum Year 6