Urdhva Tiryagbhyam Sutra

Welcome, math explorers! Today, we're learning one of the most powerful and fun multiplication tricks in Vedic Maths: the Urdhva Tiryagbhyam Sutra. It sounds complicated, but it just means "Vertically and Crosswise."

The "Vertically and Crosswise" Pattern 🕸️

Imagine the numbers stacked. We multiply in three steps: vertically on the right, crosswise in the middle, and vertically on the left.

Example: 23 × 45

1. Step 1 (Right |): Multiply rightmost digits: $3 \times 5 = 15$. Write 5, carry 1.
2. Step 2 (Crosswise X): Multiply diagonally and add, including carry: $(2 \times 5) + (3 \times 4) + 1 = 10 + 12 + 1 = 23$. Write 3, carry 2.
3. Step 3 (Left |): Multiply leftmost digits and add carry: $(2 \times 4) + 2 = 8 + 2 = 10$. Write 10.

The answer is 1035.