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Multiplying Right to Left

Grades 3–5 Multiplication The schoolbook method

The standard multiplication method multiplies each digit of the top number by each digit of the bottom number, starting at the ones and moving left — carrying just like addition, and writing a new row for each digit of the bottom number.

One digit first: 47 × 6

4 4 7 × 6 = 2 8 2
  1. Ones: 6 × 7 = 42. Write the 2, carry the 4 (tens).
  2. Tens: 6 × 4 = 24, plus carried 4 = 28. Write 28.
  3. Answer: 282.

Two digits: 46 × 53

Each digit of the bottom number gets its own row, and each new row starts one place to the left (shown with a placeholder zero):

4 6 × 5 3 ----- = 1 3 8 ← 46 × 3 + 2 3 0 0 ← 46 × 50 (that's why the row shifts left) ----- = 2 4 3 8
  1. Multiply by the ones digit: 46 × 3 = 138.
  2. Multiply by the tens digit: 46 × 5 = 230 — but the 5 is really 50, so write 2300 (shifted one place left).
  3. Add the rows: 138 + 2300 = 2438.
Why the rows shift left The second row isn't "46 × 5 with a mystery zero" — the 5 lives in the tens place, so you're really computing 46 × 50 = 2300. The shift is just shorthand for that.

Where the times tables come in

This method assumes you know your single-digit facts (up to 9 × 9). If the tables aren't solid yet, don't worry — the left-to-right article builds up the same answers in chunks, and practicing times tables alongside is time well spent. Try skip-counting practice: 7, 14, 21, 28… — rhythm helps facts stick.

Try it yourself:
  1. 38 × 7  (answer: 266)
  2. 54 × 23  (answer: 1,242)
  3. 125 × 84  (answer: 10,500)

The other direction: partial products biggest-first — see the left-to-right method, which is easier to carry in your head.

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