Long multiplication and short division
Maths · Key Stage 2 · The School
Estimate before you calculate
For 324 × 27, round first: 300 × 30 = 9,000. Now you know the answer must be near 9,000. If your long multiplication produces 87,480 or 874, you know instantly that something slipped — probably a misplaced zero. Estimating first is not extra work; it is the only cheap way to catch place-value errors.
Long multiplication, row by row
Multiply by the ones, then by the tens, then add. 324 × 7 = 2,268. 324 × 20 = 6,480 (multiply by 2, then add the zero because it is TWENTY, not two). Add: 2,268 + 6,480 = 8,748. Close to our 9,000 estimate — good. The zero on the second row is the step people forget, and the estimate is what catches it.
Short division and what the remainder means
847 ÷ 6: six into 8 goes once, remainder 2 — carry the 2 to make 24; six into 24 goes 4; six into 7 goes 1 remainder 1. Answer 141 r 1. Then ask what the remainder means in the question: 141 full boxes with 1 left over, or 141.17 kg, or "you need 142 buses". The maths gives 141 r 1; the CONTEXT decides what to do with it.
Estimate: 300 × 30 = 9,000, so the answer is near nine thousand. Now the calculation. 324 × 7 = 2,268. 324 × 20 = 6,480 — that is 324 × 2 = 648, then a zero because it is twenty, not two. Add: 2,268 + 6,480 = 8,748. Is 8,748 near 9,000? Yes. If you had written 87,480 (a place-value slip) or 874 (a lost row), the estimate would have caught it before you moved on.
When the remainder is the answer
The algorithm gives 141 remainder 1 and the question decides what that means. If 847 sweets are shared between 6 children, each gets 141 and one is left over. If 847 people need minibuses holding 6, then 141 buses leave one person behind, so you need 142 — the remainder forces you UP. And if the question asks how many full boxes of 6 you can fill from 847 items, the answer is 141 and the leftover is simply not a box. Same division, three different final answers, and the only thing that chose between them was the sentence around it. Marks in this topic are lost far more often at that step than inside the algorithm.