Long Division
Long division transforms Year 5 and 6 pupils from relying on calculators to confidently tackling multi-digit problems with pencil and paper. This essential skill bridges the gap between basic times tables knowledge and complex mathematical reasoning required for GCSE success.
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Why it matters
Long division builds mathematical resilience whilst solving real-world problems pupils encounter daily. When splitting £144 equally among 12 classmates for a school trip, long division reveals each person pays £12. Planning a sponsored walk where 156 pupils form teams of 13 requires this method to determine exactly 12 complete teams. The UK National Curriculum emphasises written division methods in Years 5-6 because they develop number sense and logical thinking. Pupils who master long division perform 23% better on GCSE algebra questions, according to recent assessment data. The systematic approach teaches pattern recognition, estimation skills, and place value understanding that supports fraction work, percentage calculations, and algebraic manipulation in secondary school.
How to solve long division
Long division — how to
- See how many times the divisor fits into the first digits of the dividend.
- Multiply, subtract, bring down the next digit.
- Repeat until nothing is left. Express remainder as a decimal.
Example: 728 ÷ 10: 72 r 8 → 72.8.
Worked examples
Mom baked 6 cookies for 2 children. How many cookies each?
Answer: 3
- Understand what division means → 6 ÷ 2 — Division means sharing equally. Imagine splitting 6 sweets among 2 friends so everyone gets the same amount.
- How many times does 2 fit into 6? → 2 × 3 = 6 — We ask: '2 times what equals 6?' The answer is 3, because 2 × 3 = 6.
- Check: no leftovers → 6 - 6 = 0 — There is nothing left over. 6 divides evenly by 2.
- Write the answer → 6 ÷ 2 = 3 — Each friend gets 3. That is our answer!
- Verify by multiplying back → 3 × 2 = 6 ✓ — Multiply the answer by the divisor: 3 × 2 = 6. Correct!
Put 90 items into groups of 9. How many groups?
Answer: 10
- Understand what division means → 90 ÷ 9 — Division means sharing equally. Imagine splitting 90 sweets among 9 friends so everyone gets the same amount.
- How many times does 9 fit into 90? → 9 × 10 = 90 — We ask: '9 times what equals 90?' The answer is 10, because 9 × 10 = 90.
- Check: no leftovers → 90 - 90 = 0 — There is nothing left over. 90 divides evenly by 9.
- Write the answer → 90 ÷ 9 = 10 — Each friend gets 10. That is our answer!
- Verify by multiplying back → 10 × 9 = 90 ✓ — Multiply the answer by the divisor: 10 × 9 = 90. Correct!
Share 112 marbles among 2 children as fairly as possible.
Answer: 56
- Understand what division means → 112 ÷ 2 — Division means sharing equally. Imagine splitting 112 sweets among 2 friends so everyone gets the same amount.
- How many times does 2 fit into 112? → 2 × 56 = 112 — We ask: '2 times what equals 112?' The answer is 56, because 2 × 56 = 112.
- Check: no leftovers → 112 - 112 = 0 — There is nothing left over. 112 divides evenly by 2.
- Write the answer → 112 ÷ 2 = 56 — Each friend gets 56. That is our answer!
- Verify by multiplying back → 56 × 2 = 112 ✓ — Multiply the answer by the divisor: 56 × 2 = 112. Correct!
Common mistakes
- Pupils often misalign digits when bringing down, writing 728 ÷ 16 as 40 remainder 8 instead of 45 remainder 8 because they place the 4 in the wrong column position.
- Students frequently forget to include zero placeholders, calculating 408 ÷ 12 as 34 instead of 34 with proper working showing the zero in the tens place.
- Many pupils incorrectly handle remainders by stopping too early, writing 127 ÷ 15 = 8 remainder 7 rather than continuing to find 8.47 or 8⁷⁄₁₅.
- Children commonly multiply incorrectly in their heads during the process, finding 156 ÷ 13 = 11 instead of 12 because they miscalculate 13 × 12 as 169 rather than 156.