SarwaSamadhan

Two-digit multiplication: vertically and crosswise (Urdhva Tiryagbhyam)

ऊर्ध्व-तिर्यग्भ्याम्: दो अंकों का गुणा एक लाइन में

The general Vedic method for any multiplication: multiply vertically, then crosswise, then vertically again, carrying as you go. Works for every pair of numbers.

पहले खड़ा गुणा, फिर क्रॉस गुणा का योग, फिर खड़ा गुणा — हासिल आगे जोड़ते जाएं।

Three steps for two-digit numbers

For AB × CD (digits A, B and C, D):

  1. Right digit: B × D.
  2. Middle: A × D + B × C (crosswise).
  3. Left: A × C.
  4. Work from the right, carrying the tens digit of each step to the next.
Example 23 × 41
Right: 3 × 1 = 3. Middle: 2 × 1 + 3 × 4 = 14 → write 4, carry 1. Left: 2 × 4 = 8, + 1 = 9 → 943
Example 46 × 27
Right: 6 × 7 = 42 → 2, carry 4. Middle: 4 × 7 + 6 × 2 = 40, + 4 = 44 → 4, carry 4. Left: 4 × 2 = 8, + 4 = 12 → 1242
Example 78 × 56
Right: 48 → 8, carry 4. Middle: 7 × 6 + 8 × 5 = 82, + 4 = 86 → 6, carry 8. Left: 7 × 5 = 35, + 8 = 43 → 4368

Three-digit numbers

For ABC × DEF there are five steps: C×F; B×F + C×E; A×F + B×E + C×D; A×E + B×D; A×D.

Example 123 × 321
Digits A,B,C = 1,2,3 and D,E,F = 3,2,1. C×F = 3 | B×F + C×E = 2 + 6 = 8 | A×F + B×E + C×D = 1 + 4 + 9 = 14 | A×E + B×D = 2 + 6 = 8 | A×D = 3. From the right: 3; 8; 14 → 4 carry 1; 8 + 1 = 9; 3 → 39483

Try it yourself · अभ्यास

  1. 34 × 12 = ?
    Show answer

    Right 8, middle 3×2 + 4×1 = 10 → 0 carry 1, left 3 + 1 = 4 → 408

  2. 67 × 89 = ?
    Show answer

    Right 63 → 3 c6; middle 6×9 + 7×8 = 110 + 6 = 116 → 6 c11; left 48 + 11 = 59 → 5963