Multiplying Large Numbers

Nothing new happens with bigger numbers. Split by place value and multiply the pieces.

Three digits by two

243 × 15 splits 243 into 200, 40, and 3, and 15 into 10 and 5. That gives six pieces.

Estimate first

243 × 15 is roughly 240 × 15, about 3,600. That catches a misplaced digit.

The method has not changed

Multiplying 342 × 27 uses exactly the same partial products as 34 × 27 did in Grade 4 — there are simply more of them. Split both numbers by place value, multiply every part of one by every part of the other, and add all the pieces.

Organisation is the real skill

With three digits by two there are six partial products. Missing one gives a plausible-looking wrong answer. Use a grid with a box for each piece, or the standard algorithm with careful column alignment. Either works; disorganised working does not.

The placeholder zeros in the algorithm

In the standard method the second row starts with a zero because you are multiplying by 20, not 2. That zero is not decoration — it puts the row in the right columns. Understanding it means you will never omit it or add one too many.

Estimate to the leading digits

342 × 27 is roughly 350 × 30 = 10,500. The exact answer, 9,234, is in the right region. A lost partial product typically shifts the answer by hundreds or thousands, which this estimate catches immediately.