does the Japanese multiplication method actually work or is it just a visual trick

Question

So theres this video going around showing a "Japanese multiplication method" where you draw lines for each digit and count intersections.

For $12 \times 34$ :
1 2
| |
3 ---|---|---
| |
4 ---|---|---
| |

Then you count the intersections in each diagonal band. For 12x34 you get 3, 10, 8 which gives 408. And $12 \times 34 = 408$ so it works!

But does this method work for ALL multiplications? What about numbers with zeros? Or larger numbers like $123 \times 456$ ?

Is this actually used in Japan or is it a TikTok myth? I want to understand WHY it works mathematically, not just how to do it.

Chen Wei · Accepted Answer

The Japanese multiplication method works because it's literally computing the product using the distributive property and place value. For 12 × 34: 12 × 34 = ( 10 + 2 ) ( 30 + 4 ) = 10 × 30 + 10 × 4 + 2 × 30 + 2 × 4 = 300 + 40 + 60 + 8 = 408 The "lines and intersections" method encodes this geometrically: - 3 lines (tens of 34) crossed with 1 line (tens of 12) gives 3 × 1 = 3 intersections in the hundreds region - The diagonal bands group intersections by place value Does it work for zeros? Yes, but zeros require drawing a "line" that looks like a dotted or dashed line (representing the zero digit), which then has zero intersections. It gets messy. Is it really Japanese? The method is known as "dot multiplication" or "Chinese multiplication" in some cultures. Its historically used in various forms across Asia but isnt "the standard method" in Japanese schools today — they use the same column multiplication as everyone else. Bottom line: Its a neat visual representation of the distributive property, not a separate mathematical discovery.

Does the Japanese multiplication method actually work or is it just a visual trick

1 Answer

Does the Japanese multiplication method actually work or is it just a visual trick

1 Answer