Vertical & Crosswise
The "Master Formula" for any multiplication.
Core Concepts
Urdhva-Tiryagbhyam (Vertical & Crosswise) is the most powerful Sutra in Vedic Math. Unlike other tricks that only work for specific numbers, this method works for ANY multiplication problem.
The 3-Step Pattern (2-Digit x 2-Digit)
Imagine two numbers written one below the other.
1. Vertical (Right): Multiply the unit digits.
2. Crosswise (Middle): Cross-multiply and add the results.
3. Vertical (Left): Multiply the tens digits.
Solved Examples
Example 1: 12 × 13
Question: Solve 12 × 13.
• Step 1 (Right Vertical): 2 × 3 = 6.
• Step 2 (Crosswise): (1 × 3) + (2 × 1) = 3 + 2 = 5.
• Step 3 (Left Vertical): 1 × 1 = 1.
• Answer: 156.
Example 2: 21 × 23
Question: Solve 21 × 23.
• Step 1 (Right): 1 × 3 = 3.
• Step 2 (Cross): (2 × 3) + (1 × 2) = 6 + 2 = 8.
• Step 3 (Left): 2 × 2 = 4.
• Answer: 483.
Example 3: With Carry (14 × 14)
Question: Solve 14 × 14.
• Step 1 (Right): 4 × 4 = 16. Write 6, carry 1.
• Step 2 (Cross): (1 × 4) + (4 × 1) = 4 + 4 = 8. Add carry: 8 + 1 = 9.
• Step 3 (Left): 1 × 1 = 1.
• Answer: 196.
Example 4: 23 × 12
Question: Solve 23 × 12.
• Step 1 (Right): 3 × 2 = 6.
• Step 2 (Cross): (2 × 2) + (3 × 1) = 4 + 3 = 7.
• Step 3 (Left): 2 × 1 = 2.
• Answer: 276.
