How it works
Free long multiplication worksheets set out the formal written method for Year 5 and Year 6, from 2-digit × 2-digit to 4-digit × 2-digit: two rows of working, a placeholder zero and a total. The answer key shows both rows.
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Long multiplication in Year 5 and Year 6
England's national curriculum has Year 5 pupils multiply numbers up to 4 digits by a one- or two-digit number. They use a formal written method, including long multiplication for two-digit numbers. Multiply by the ones digit, write a placeholder zero, multiply by the tens digit, then add. For 46 × 37 the rows are 322 and 1,380 and the total is 1,702. American standards call this the standard algorithm.
Marks for the formal method at KS2
The key stage 2 test framework gives long multiplication 2 marks in the arithmetic paper. A wrong answer can still earn a mark for correct working in the formal method but not in the grid method.
- Carry boxes sit above the top number. The curriculum's appendix notes that the position of carried digits varies, so tell pupils if your school differs.
- A digit written one column out changes the answer tenfold. These sheets print no squares, so give squared paper to pupils whose digits drift.
- Before the rows, round: 286 × 34 is near 300 × 30 = 9,000, which rules out 2,002, the total without the placeholder zero.
Questions and answers
What is the difference between short and long multiplication?
Short multiplication has a one-digit multiplier and one row, as in 2,741 × 6 = 16,446. Long multiplication has two or more digits in the multiplier, so it needs a row for each and a final addition. Short is Year 4 work, long Year 5.
Why does the second row need a zero?
The second row multiplies by tens. In 46 × 37 the 3 stands for 30, and 46 × 30 = 1,380. The placeholder moves every other digit one column left. Without it the rows are 322 and 138, and the total is 460, not 1,702.
How many problems are on one long multiplication worksheet?
Each sheet opens with 12 for 2-digit × 2-digit, 9 for 3-digit × 2-digit and 6 for 4-digit × 2-digit. That leaves room for two rows of working, a total and the carried digits. Pick from 6 to 30 under Problems.