Long division, step by step
Maths · Key Stage 2 · The School
One digit at a time, always the same four moves
Divide, multiply, subtract, bring down — then repeat. For 864 ÷ 24: 24 into 8 does not go, so take 86. 24 × 3 = 72, subtract to leave 14, bring down the 4 to make 144. 24 × 6 = 144, subtract to leave 0. The answer is 36. The loop never changes, however long the number.
Write a small times-table first
Before starting, jot 24, 48, 72, 96, 120 down the side of the page. Every “how many times does 24 go in?” is then a glance rather than a guess, and the guessing is where nearly all long-division errors live. Two minutes spent on this list saves more than it costs.
What to do with what is left over
869 ÷ 24 leaves 5 over. That can be written three ways and the question decides which: “36 remainder 5” for a counting problem, “36 and 5/24” as an exact fraction, or 36.2 to one decimal place by adding a point and zeros and carrying on. None is more correct than the others; they answer different questions.
Remainders in context can change the answer
If 869 people need coaches holding 24, then 36 coaches leave 5 people standing, so you need 37. If you are asking how many full coaches you can fill, the answer is 36. The arithmetic is identical and the answers differ, so read what the question is actually asking before rounding.
Estimate before you start, check when you finish
Before dividing 864 by 24, round it: 24 is nearly 25, and 25 × 30 = 750 while 25 × 40 = 1000. So the answer sits between 30 and 40. When the algorithm produces 36, that agrees. When it produces 306 — the classic slip, one step written in the wrong column — the estimate catches it in a second, before the mistake is carried into the next question. Checking at the end is the same idea run backwards: 36 × 24 should hand you 864 again. Two quick multiplications guard a whole page of division.