Multi-Digit (Long) Multiplication

Practise multiplying larger numbers — three- and four-digit numbers by one or two digits — with the standard method.

Grade 5 · 5.NBT⚡ Long multiplication
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How multi-digit multiplication works

Nothing new happens here — it is the same method as smaller problems, just with more digits and more rows. That is the reassuring part: a child who can do 2-digit by 2-digit already knows how to do this; they only need to stay organised.

  1. Multiply the top number by the ones digit of the bottom number.
  2. For each further digit (tens, hundreds…), start a new row with one more placeholder zero than the last.
  3. Multiply the top number by that digit and write the partial product.
  4. When every row is done, add them all up.

Worked examples

3-digit × 1-digit234 × 6 — 6×4 = 24 (write 4, carry 2); 6×3 = 18 + 2 = 20 (write 0, carry 2); 6×2 = 12 + 2 = 14. Answer: 1,404.
3-digit × 2-digit312 × 24 — 312×4 = 1,248; then 312×20 = 6,240. Add: 1,248 + 6,240 = 7,488.
AD AREA (parent reading zone only — never shown during practice)

Tips & common mistakes

Neatness wins here — most errors are misaligned columns, not wrong facts. Graph paper or carefully lined-up digits make a real difference, and adding a placeholder zero for each new row keeps everything in its place. Always estimate first to sanity-check the size of the answer.

  • Columns drifting out of line as the rows grow — the biggest source of errors.
  • Forgetting to add an extra placeholder zero for the hundreds row.
  • A single carrying slip early on throwing the whole total off — estimating catches these.

Frequently asked questions

How is this different from 2-digit multiplication?

Only in length. The method is identical — there are simply more digits and more partial-product rows to add.

When is multi-digit multiplication taught?

It is a core grade 5 skill, building directly on grade 4’s 2-digit work.

Should kids do this by hand or use a calculator?

By hand first — it cements place-value understanding. The calculator comes later, once the method is reliable.

How do we check such big answers?

Round each number and estimate: 312×24 ≈ 300×24 = 7,200, close to 7,488, so it looks right.

My child gets the facts right but the answer wrong — why?

Almost always alignment: a row shifted into the wrong column. Lined-up digits and the placeholder zeros fix it.

Keep practising

← All multiplication2-digit × 2-digitBy 10, 100, 10005th grade math

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