Small Friends — Make 5
When you can't add directly: activate heaven bead (+5) and remove the complement.
Example
3 + 4 = ? — 3 earth beads up. Need to add 4 but only 1 space left.
Use +4 formula: −1 earth bead, +heaven (+5)
Result: 2 earth + 1 heaven = 7 ✓
Use +4 formula: −1 earth bead, +heaven (+5)
Result: 2 earth + 1 heaven = 7 ✓
Addition
Subtraction
Big Friends — Make 10
When the rod is full: subtract the complement from current rod, carry 1 to the next rod.
Example
6 + 9 = ? — Rod shows 6. Need to add 9 but max is 9.
Use +9 formula: −1 from ones rod, +1 to tens rod (=+10)
Result: ones=5, tens=1 → 15 ✓
Use +9 formula: −1 from ones rod, +1 to tens rod (=+10)
Result: ones=5, tens=1 → 15 ✓
Addition
Subtraction
Double Combination
Combines Small and Big Friends in one move. Adjust heaven bead AND carry to next rod.
Example
5 + 6 = ? — Rod shows 5 (heaven bead active). Need to add 6.
Use +6 formula: +1 earth, −heaven (−5), +1 to tens (+10)
Result: ones=1, tens=1 → 11 ✓
Use +6 formula: +1 earth, −heaven (−5), +1 to tens (+10)
Result: ones=1, tens=1 → 11 ✓
Addition
Subtraction
Multiplication Shortcuts
Mental tricks to multiply quickly. Practice until they're automatic.
| × | Trick | Example (8×) |
|---|
Practice
Division Shortcuts
Quick division tricks for fast mental calculation.
| ÷ | Trick | Example |
|---|
Practice
📖 All Formulas
Complete reference. Use browser print (Ctrl+P) for a reference sheet.