Vedic Maths — Veda Topper

Vertically and Crosswise — Multiply Anything in One Line

The sutra Urdhva-Tiryagbhyam ("vertically and crosswise") is the one general method that multiplies any two numbers, no bases needed. For two digits it is three little steps: vertical, cross, vertical.

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14 × 121412||168= 168
Vertically and crosswise for 14 × 12: vertical ends (1 and 8) and the crosswise sum (6) give 168.

The rule (2-digit × 2-digit)

  1. Right = units × units (vertical).
  2. Middle = cross-multiply and add.
  3. Left = tens × tens (vertical).
  4. Carry any tens leftward.
Example 1 — 14 × 12
Left: 1×1 = 1 Middle: 1×2 + 4×1 = 6 Right: 4×2 = 8 Join: 1 | 6 | 8
14 × 12 = 168
Example 2 (carry) — 32 × 34
Left: 3×3 = 9 Middle: 3×4 + 2×3 = 18 → 8, carry 1 Right: 2×4 = 8 9+1 | 8 | 8
32 × 34 = 1088
Example 3 — 45 × 47
Left: 4×4 = 16 Middle: 4×7 + 5×4 = 48 Right: 5×7 = 35 16 | 48 | 35 → carry: 35→5(c3), 48+3=51→1(c5), 16+5=21
45 × 47 = 2115

Why it works

(10a+b)(10c+d) = 100(ac) + 10(ad+bc) + bd. Those three groups are exactly the vertical-left, crosswise-middle and vertical-right steps.

Practice (answers below):
1) 23 × 21   2) 56 × 54   3) 62 × 43   4) 71 × 68   5) 84 × 26

Answers: 1) 483 2) 3024 3) 2666 4) 4828 5) 2184

More Vedic Maths tricks

← Vedic Maths home Multiply by 11 in one lineSquare numbers ending in 5Base multiplication (Nikhilam)Squares near a base (Yavadunam)Instant division by 9Subtraction: all from 9All 16 Sutras & 13 sub-sutras

Frequently asked questions

What is Urdhva-Tiryagbhyam in Vedic Maths?
It means "vertically and crosswise" — a general multiplication method that works for any two numbers by multiplying vertically at the ends and crosswise in the middle, all in one line.
Is vertically and crosswise better than long multiplication?
For mental and one-line calculation, yes — it removes the separate rows and carries of long multiplication and works for any digits, not just numbers near a base.
What age is this method for?
It is usually introduced from around Grade 6 (age 11) once children are fluent with tables up to 9.
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