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Line Multiplication

The "Japanese" Visual Method

Multiply numbers by drawing crossing lines and counting intersection dots. Each color group of dots represents one digit in the result.

How it Works

  1. Blue Lines: Each digit of the first number becomes a group of parallel lines going diagonally.
    Example: "12" → 1 line, gap, 2 lines.
  2. Green Lines: Cross them at 90° with groups for the second number's digits.
  3. Count the Dots: Each color group sums to one digit of the final answer.

Why does it work?

It's the Distributive Property in visual form!

Crossing lines for 12 × 3 calculates:
(10 + 2) × 3 = (10 × 3) + (2 × 3)

The dot color groups separate each place value automatically.

3 Tens (30) 6 Ones (6) = 36

Try it Yourself

12 × 3 = 36
Result 36

Updates automatically — or press Enter

Dot Colors — Place Values

Ones
Tens
Hundreds
Thousands
Ten-Thousands
Hundred-Thousands

Did you know?

Despite the name, this method isn't standard in Japanese schools! It's a visual trick often shared online, similar to the "Chinese Stick Method" or "Vedic Math."

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