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.